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Geant4/examples/extended/electromagnetic/TestEm7/src/G4ScreenedNuclearRecoil.cc

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Differences between /examples/extended/electromagnetic/TestEm7/src/G4ScreenedNuclearRecoil.cc (Version 11.3.0) and /examples/extended/electromagnetic/TestEm7/src/G4ScreenedNuclearRecoil.cc (Version 10.0.p3)


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 25 //                                                 25 //
 26 /// \file electromagnetic/TestEm7/src/G4Screen     26 /// \file electromagnetic/TestEm7/src/G4ScreenedNuclearRecoil.cc
 27 /// \brief Implementation of the G4ScreenedNuc     27 /// \brief Implementation of the G4ScreenedNuclearRecoil class
 28 //                                                 28 //
                                                   >>  29 // $Id: G4ScreenedNuclearRecoil.cc 66854 2013-01-14 16:56:24Z vnivanch $
 29 //                                                 30 //
 30 //                                                 31 //
 31 // Class Description                               32 // Class Description
 32 // Process for screened electromagnetic nuclea <<  33 // Process for screened electromagnetic nuclear elastic scattering; 
 33 // Physics comes from:                             34 // Physics comes from:
 34 // Marcus H. Mendenhall and Robert A. Weller,  <<  35 // Marcus H. Mendenhall and Robert A. Weller, 
 35 // "Algorithms  for  the rapid  computation  o <<  36 // "Algorithms  for  the rapid  computation  of  classical  cross  
 36 // sections  for  screened  Coulomb  collision     37 // sections  for  screened  Coulomb  collisions  "
 37 // Nuclear  Instruments  and  Methods  in  Phy <<  38 // Nuclear  Instruments  and  Methods  in  Physics  Research  B58  (1991)  11-17  
 38 // The only input required is a screening func     39 // The only input required is a screening function phi(r/a) which is the ratio
 39 // of the actual interatomic potential for two <<  40 // of the actual interatomic potential for two atoms with atomic numbers Z1 and Z2,
 40 // numbers Z1 and Z2,                          <<  41 // to the unscreened potential Z1*Z2*e^2/r where e^2 is elm_coupling in Geant4 units
 41 // to the unscreened potential Z1*Z2*e^2/r whe << 
 42 // Geant4 units                                << 
 43 //                                                 42 //
 44 // First version, April 2004, Marcus H. Menden     43 // First version, April 2004, Marcus H. Mendenhall, Vanderbilt University
 45 //                                                 44 //
 46 // 5 May, 2004, Marcus Mendenhall                  45 // 5 May, 2004, Marcus Mendenhall
 47 // Added an option for enhancing hard collisio <<  46 // Added an option for enhancing hard collisions statistically, to allow 
 48 // backscattering calculations to be carried o     47 // backscattering calculations to be carried out with much improved event rates,
 49 // without distorting the multiple-scattering      48 // without distorting the multiple-scattering broadening too much.
 50 // the method SetCrossSectionHardening(G4doubl <<  49 // the method SetCrossSectionHardening(G4double fraction, G4double HardeningFactor)
 51 //                                     Hardeni << 
 52 // sets what fraction of the events will be ra     50 // sets what fraction of the events will be randomly hardened,
 53 // and the factor by which the impact area is      51 // and the factor by which the impact area is reduced for such selected events.
 54 //                                                 52 //
 55 // 21 November, 2004, Marcus Mendenhall            53 // 21 November, 2004, Marcus Mendenhall
 56 // added static_nucleus to IsApplicable            54 // added static_nucleus to IsApplicable
 57 //                                             <<  55 // 
 58 // 7 December, 2004, Marcus Mendenhall             56 // 7 December, 2004, Marcus Mendenhall
 59 // changed mean free path of stopping particle     57 // changed mean free path of stopping particle from 0.0 to 1.0*nanometer
 60 // to avoid new verbose warning about 0 MFP in     58 // to avoid new verbose warning about 0 MFP in 4.6.2p02
 61 //                                             <<  59 // 
 62 // 17 December, 2004, Marcus Mendenhall            60 // 17 December, 2004, Marcus Mendenhall
 63 // added code to permit screening out overly c <<  61 // added code to permit screening out overly close collisions which are 
 64 // expected to be hadronic, not Coulombic          62 // expected to be hadronic, not Coulombic
 65 //                                                 63 //
 66 // 19 December, 2004, Marcus Mendenhall            64 // 19 December, 2004, Marcus Mendenhall
 67 // massive rewrite to add modular physics stag     65 // massive rewrite to add modular physics stages and plug-in cross section table
 68 // computation.  This allows one to select (e. <<  66 // computation.  This allows one to select (e.g.) between the normal external python
 69 // python process and an embedded python inter <<  67 // process and an embedded python interpreter (which is much faster) for generating
 70 // for generating the tables.                  <<  68 // the tables.
 71 // It also allows one to switch between sub-sa <<  69 // It also allows one to switch between sub-sampled scattering (event biasing) and
 72 // and normal scattering, and between non-rela <<  70 // normal scattering, and between non-relativistic kinematics and relativistic
 73 // relativistic kinematic approximations, with <<  71 // kinematic approximations, without having a class for every combination. Further, one can
 74 // combination. Further, one can add extra sta <<  72 // add extra stages to the scattering, which can implement various book-keeping processes.
 75 // implement various book-keeping processes.   <<  73 // 
 76 //                                             << 
 77 // January 2007, Marcus Mendenhall                 74 // January 2007, Marcus Mendenhall
 78 // Reorganized heavily for inclusion in Geant4 <<  75 // Reorganized heavily for inclusion in Geant4 Core.  All modules merged into 
 79 // one source and header, all historic code re     76 // one source and header, all historic code removed.
 80 //                                             <<  77 // 
 81 // Class Description - End                         78 // Class Description - End
 82                                                    79 
 83 //....oooOO0OOooo........oooOO0OOooo........oo << 
 84                                                    80 
 85 #include "G4ScreenedNuclearRecoil.hh"          <<  81 #include <stdio.h>
 86                                                    82 
 87 #include "globals.hh"                              83 #include "globals.hh"
 88                                                    84 
 89 #include <stdio.h>                             <<  85 #include "G4ScreenedNuclearRecoil.hh"
 90                                                    86 
 91 const char* G4ScreenedCoulombCrossSectionInfo: <<  87 const char* G4ScreenedCoulombCrossSectionInfo::CVSFileVers() { return 
 92 {                                              <<  88         "G4ScreenedNuclearRecoil.cc,v 1.57 2008/05/07 11:51:26 marcus Exp GEANT4 tag ";
 93   return "G4ScreenedNuclearRecoil.cc,v 1.57 20 << 
 94 }                                                  89 }
 95                                                    90 
 96 #include "c2_factory.hh"                       <<  91 #include "G4ParticleTypes.hh"
 97                                                <<  92 #include "G4ParticleTable.hh"
                                                   >>  93 #include "G4VParticleChange.hh"
                                                   >>  94 #include "G4ParticleChangeForLoss.hh"
 98 #include "G4DataVector.hh"                         95 #include "G4DataVector.hh"
 99 #include "G4DynamicParticle.hh"                <<  96 #include "G4Track.hh"
                                                   >>  97 #include "G4Step.hh"
                                                   >>  98 
                                                   >>  99 #include "G4Material.hh"
100 #include "G4Element.hh"                           100 #include "G4Element.hh"
101 #include "G4ElementVector.hh"                  << 
102 #include "G4EmProcessSubType.hh"               << 
103 #include "G4IonTable.hh"                       << 
104 #include "G4Isotope.hh"                           101 #include "G4Isotope.hh"
105 #include "G4IsotopeVector.hh"                  << 
106 #include "G4LindhardPartition.hh"              << 
107 #include "G4Material.hh"                       << 
108 #include "G4MaterialCutsCouple.hh"                102 #include "G4MaterialCutsCouple.hh"
109 #include "G4ParticleChangeForLoss.hh"          << 103 #include "G4ElementVector.hh"
                                                   >> 104 #include "G4IsotopeVector.hh"
                                                   >> 105 
                                                   >> 106 #include "G4EmProcessSubType.hh"
                                                   >> 107 
110 #include "G4ParticleDefinition.hh"                108 #include "G4ParticleDefinition.hh"
111 #include "G4ParticleTable.hh"                  << 109 #include "G4DynamicParticle.hh"
112 #include "G4ParticleTypes.hh"                  << 
113 #include "G4ProcessManager.hh"                    110 #include "G4ProcessManager.hh"
114 #include "G4StableIsotopes.hh"                    111 #include "G4StableIsotopes.hh"
115 #include "G4Step.hh"                           << 112 #include "G4LindhardPartition.hh"
116 #include "G4Track.hh"                          << 113 
117 #include "G4VParticleChange.hh"                << 114 #include "G4PhysicalConstants.hh"
                                                   >> 115 #include "G4SystemOfUnits.hh"
118 #include "Randomize.hh"                           116 #include "Randomize.hh"
119                                                   117 
120 #include <iomanip>                             << 
121 #include <iostream>                               118 #include <iostream>
122 static c2_factory<G4double> c2;  // this makes << 119 #include <iomanip>
                                                   >> 120 
                                                   >> 121 #include "c2_factory.hh"
                                                   >> 122 static c2_factory<G4double> c2; // this makes a lot of notation shorter
123 typedef c2_ptr<G4double> c2p;                     123 typedef c2_ptr<G4double> c2p;
124                                                   124 
125 G4ScreenedCoulombCrossSection::~G4ScreenedCoul    125 G4ScreenedCoulombCrossSection::~G4ScreenedCoulombCrossSection()
126 {                                                 126 {
127   screeningData.clear();                       << 127         screeningData.clear();
128   MFPTables.clear();                           << 128         MFPTables.clear();        
129 }                                                 129 }
130                                                   130 
131 const G4double G4ScreenedCoulombCrossSection:: << 131 const G4double G4ScreenedCoulombCrossSection::massmap[nMassMapElements+1]={
132   0,          1.007940,   4.002602,   6.941000 << 132         0, 1.007940, 4.002602, 6.941000, 9.012182, 10.811000, 12.010700, 
133   15.999400,  18.998403,  20.179700,  22.98977 << 133         14.006700, 15.999400, 18.998403, 20.179700, 22.989770, 24.305000, 26.981538, 28.085500, 
134   32.065000,  35.453000,  39.948000,  39.09830 << 134         30.973761, 32.065000, 35.453000, 39.948000, 39.098300, 40.078000, 44.955910, 47.867000, 
135   51.996100,  54.938049,  55.845000,  58.93320 << 135         50.941500, 51.996100, 54.938049, 55.845000, 58.933200, 58.693400, 63.546000, 65.409000, 
136   72.640000,  74.921600,  78.960000,  79.90400 << 136         69.723000, 72.640000, 74.921600, 78.960000, 79.904000, 83.798000, 85.467800, 87.620000, 
137   91.224000,  92.906380,  95.940000,  98.00000 << 137         88.905850, 91.224000, 92.906380, 95.940000, 98.000000, 101.070000, 102.905500, 106.420000, 
138   112.411000, 114.818000, 118.710000, 121.7600 << 138         107.868200, 112.411000, 114.818000, 118.710000, 121.760000, 127.600000, 126.904470, 131.293000, 
139   137.327000, 138.905500, 140.116000, 140.9076 << 139         132.905450, 137.327000, 138.905500, 140.116000, 140.907650, 144.240000, 145.000000, 150.360000, 
140   157.250000, 158.925340, 162.500000, 164.9303 << 140         151.964000, 157.250000, 158.925340, 162.500000, 164.930320, 167.259000, 168.934210, 173.040000, 
141   178.490000, 180.947900, 183.840000, 186.2070 << 141         174.967000, 178.490000, 180.947900, 183.840000, 186.207000, 190.230000, 192.217000, 195.078000, 
142   200.590000, 204.383300, 207.200000, 208.9803 << 142         196.966550, 200.590000, 204.383300, 207.200000, 208.980380, 209.000000, 210.000000, 222.000000, 
143   226.000000, 227.000000, 232.038100, 231.0358 << 143         223.000000, 226.000000, 227.000000, 232.038100, 231.035880, 238.028910, 237.000000, 244.000000, 
144   247.000000, 247.000000, 251.000000, 252.0000 << 144         243.000000, 247.000000, 247.000000, 251.000000, 252.000000, 257.000000, 258.000000, 259.000000, 
145   261.000000, 262.000000, 266.000000, 264.0000 << 145         262.000000, 261.000000, 262.000000, 266.000000, 264.000000, 277.000000, 268.000000, 281.000000, 
146   285.000000, 282.500000, 289.000000, 287.5000 << 146         272.000000, 285.000000, 282.500000, 289.000000, 287.500000, 292.000000};
147                                                << 147 
148 G4ParticleDefinition*                          << 148 G4ParticleDefinition* G4ScreenedCoulombCrossSection::SelectRandomUnweightedTarget(const G4MaterialCutsCouple* couple)
149 G4ScreenedCoulombCrossSection::SelectRandomUnw << 149 {
150 {                                              << 150         // Select randomly an element within the material, according to number density only        
151   // Select randomly an element within the mat << 151         const G4Material* material = couple->GetMaterial();
152   // density only                              << 152         G4int nMatElements = material->GetNumberOfElements();
153   const G4Material* material = couple->GetMate << 153         const G4ElementVector* elementVector = material->GetElementVector();
154   G4int nMatElements = material->GetNumberOfEl << 154         const G4Element *element=0;
155   const G4ElementVector* elementVector = mater << 155         G4ParticleDefinition*target=0;
156   const G4Element* element = 0;                << 156         
157   G4ParticleDefinition* target = 0;            << 157         // Special case: the material consists of one element
158                                                << 158         if (nMatElements == 1)
159   // Special case: the material consists of on << 159     {
160   if (nMatElements == 1) {                     << 160                 element= (*elementVector)[0];
161     element = (*elementVector)[0];             << 161     }
162   }                                            << 162         else
163   else {                                       << 163     {
164     // Composite material                      << 164                 // Composite material
165     G4double random = G4UniformRand() * materi << 165                 G4double random = G4UniformRand() * material->GetTotNbOfAtomsPerVolume();
166     G4double nsum = 0.0;                       << 166                 G4double nsum=0.0;
167     const G4double* atomDensities = material-> << 167                 const G4double *atomDensities=material->GetVecNbOfAtomsPerVolume();
168                                                << 168                 
169     for (G4int k = 0; k < nMatElements; k++) { << 169                 for (G4int k=0 ; k < nMatElements ; k++ )
170       nsum += atomDensities[k];                << 170         {
171       element = (*elementVector)[k];           << 171                         nsum+=atomDensities[k];
172       if (nsum >= random) break;               << 172                         element= (*elementVector)[k];
173     }                                          << 173                         if (nsum >= random) break;
174   }                                            << 174         }
175                                                << 
176   G4int N = 0;                                 << 
177   G4int Z = element->GetZasInt();              << 
178                                                << 
179   G4int nIsotopes = element->GetNumberOfIsotop << 
180   if (0 < nIsotopes) {                         << 
181     if (Z <= 92) {                             << 
182       // we have no detailed material isotopic << 
183       // so use G4StableIsotopes table up to Z << 
184       static G4StableIsotopes theIso;          << 
185       // get a stable isotope table for defaul << 
186       nIsotopes = theIso.GetNumberOfIsotopes(Z << 
187       G4double random = 100.0 * G4UniformRand( << 
188       // values are expressed as percent, sum  << 
189       G4int tablestart = theIso.GetFirstIsotop << 
190       G4double asum = 0.0;                     << 
191       for (G4int i = 0; i < nIsotopes; i++) {  << 
192         asum += theIso.GetAbundance(i + tables << 
193         N = theIso.GetIsotopeNucleonCount(i +  << 
194         if (asum >= random) break;             << 
195       }                                        << 
196     }                                          << 
197     else {                                     << 
198       // too heavy for stable isotope table, j << 
199       N = (G4int)std::floor(element->GetN() +  << 
200     }                                          << 
201   }                                            << 
202   else {                                       << 
203     G4int i;                                   << 
204     const G4IsotopeVector* isoV = element->Get << 
205     G4double random = G4UniformRand();         << 
206     G4double* abundance = element->GetRelative << 
207     G4double asum = 0.0;                       << 
208     for (i = 0; i < nIsotopes; i++) {          << 
209       asum += abundance[i];                    << 
210       N = (*isoV)[i]->GetN();                  << 
211       if (asum >= random) break;               << 
212     }                                             175     }
213   }                                            << 
214                                                   176 
215   // get the official definition of this nucle << 177         G4int N=0;
216   // value of A note that GetIon is very slow, << 178         G4int Z=(G4int)std::floor(element->GetZ()+0.5);
217   // we have already found ourselves.          << 179         
218   ParticleCache::iterator p = targetMap.find(Z << 180         G4int nIsotopes=element->GetNumberOfIsotopes();
219   if (p != targetMap.end()) {                  << 181         if(!nIsotopes) {
220     target = (*p).second;                      << 182                 if(Z<=92) {
221   }                                            << 183                         // we have no detailed material isotopic info available, 
222   else {                                       << 184                         // so use G4StableIsotopes table up to Z=92
223     target = G4IonTable::GetIonTable()->GetIon << 185                         static G4StableIsotopes theIso; // get a stable isotope table for default results
224     targetMap[Z * 1000 + N] = target;          << 186                         nIsotopes=theIso.GetNumberOfIsotopes(Z);
225   }                                            << 187                         G4double random = 100.0*G4UniformRand(); // values are expressed as percent, sum is 100
226   return target;                               << 188                         G4int tablestart=theIso.GetFirstIsotope(Z);
                                                   >> 189                         G4double asum=0.0;
                                                   >> 190                         for(G4int i=0; i<nIsotopes; i++) {
                                                   >> 191                                 asum+=theIso.GetAbundance(i+tablestart);
                                                   >> 192                                 N=theIso.GetIsotopeNucleonCount(i+tablestart);
                                                   >> 193                                 if(asum >= random) break;
                                                   >> 194                         }
                                                   >> 195                 } else {
                                                   >> 196                         // too heavy for stable isotope table, just use mean mass
                                                   >> 197                         N=(G4int)std::floor(element->GetN()+0.5);
                                                   >> 198                 }
                                                   >> 199         } else {
                                                   >> 200                 G4int i;
                                                   >> 201                 const G4IsotopeVector *isoV=element->GetIsotopeVector();
                                                   >> 202                 G4double random = G4UniformRand();
                                                   >> 203                 G4double *abundance=element->GetRelativeAbundanceVector();
                                                   >> 204                 G4double asum=0.0;
                                                   >> 205                 for(i=0; i<nIsotopes; i++) {
                                                   >> 206                         asum+=abundance[i];
                                                   >> 207                         N=(*isoV)[i]->GetN();
                                                   >> 208                         if(asum >= random) break;
                                                   >> 209                 }
                                                   >> 210         }
                                                   >> 211         
                                                   >> 212         // get the official definition of this nucleus, to get the correct value of A
                                                   >> 213         // note that GetIon is very slow, so we will cache ones we have already found ourselves.
                                                   >> 214         ParticleCache::iterator p=targetMap.find(Z*1000+N);
                                                   >> 215         if (p != targetMap.end()) {
                                                   >> 216                 target=(*p).second;
                                                   >> 217         } else{
                                                   >> 218                 target=G4ParticleTable::GetParticleTable()->GetIon(Z, N, 0.0);        
                                                   >> 219                 targetMap[Z*1000+N]=target;
                                                   >> 220         }
                                                   >> 221         return target;
227 }                                                 222 }
228                                                   223 
229 void G4ScreenedCoulombCrossSection::BuildMFPTa    224 void G4ScreenedCoulombCrossSection::BuildMFPTables()
230 {                                                 225 {
231   const G4int nmfpvals = 200;                  << 226         const G4int nmfpvals=200;
232                                                   227 
233   std::vector<G4double> evals(nmfpvals), mfpva << 228         std::vector<G4double> evals(nmfpvals), mfpvals(nmfpvals);
234                                                   229 
235   // sum up inverse MFPs per element for each  << 230         // sum up inverse MFPs per element for each material        
236   const G4MaterialTable* materialTable = G4Mat << 231         const G4MaterialTable* materialTable = G4Material::GetMaterialTable();
237   if (materialTable == 0) {                    << 232         if (materialTable == 0) { return; }
238     return;                                    << 233         //G4Exception("G4ScreenedCoulombCrossSection::BuildMFPTables - no MaterialTable found)");
239   }                                            << 234         
240   // G4Exception("G4ScreenedCoulombCrossSectio << 235         G4int nMaterials = G4Material::GetNumberOfMaterials();
241   //- no MaterialTable found)");               << 236 
242                                                << 237         for (G4int matidx=0; matidx < nMaterials; matidx++) {
243   G4int nMaterials = G4Material::GetNumberOfMa << 238 
244                                                << 239                 const G4Material* material= (*materialTable)[matidx];
245   for (G4int matidx = 0; matidx < nMaterials;  << 240                 const G4ElementVector &elementVector = *(material->GetElementVector());
246     const G4Material* material = (*materialTab << 241                 const G4int nMatElements = material->GetNumberOfElements();
247     const G4ElementVector& elementVector = *(m << 242 
248     const G4int nMatElements = material->GetNu << 243                 const G4Element *element=0;
249                                                << 244                 const G4double *atomDensities=material->GetVecNbOfAtomsPerVolume();
250     const G4Element* element = 0;              << 245                 
251     const G4double* atomDensities = material-> << 246                 G4double emin=0, emax=0; // find innermost range of cross section functions
252                                                << 247                 for (G4int kel=0 ; kel < nMatElements ; kel++ )
253     G4double emin = 0, emax = 0;               << 248         {
254     // find innermost range of cross section f << 249                         element=elementVector[kel];
255     for (G4int kel = 0; kel < nMatElements; ke << 250                         G4int Z=(G4int)std::floor(element->GetZ()+0.5);
256       element = elementVector[kel];            << 251                         const G4_c2_function &ifunc=sigmaMap[Z];
257       G4int Z = (G4int)std::floor(element->Get << 252                         if(!kel || ifunc.xmin() > emin) emin=ifunc.xmin();
258       const G4_c2_function& ifunc = sigmaMap[Z << 253                         if(!kel || ifunc.xmax() < emax) emax=ifunc.xmax();                        
259       if (!kel || ifunc.xmin() > emin) emin =  << 254         }
260       if (!kel || ifunc.xmax() < emax) emax =  << 255                 
261     }                                          << 256                 G4double logint=std::log(emax/emin) / (nmfpvals-1) ; // logarithmic increment for tables
262                                                << 257                 
263     G4double logint = std::log(emax / emin) /  << 258                 // compute energy scale for interpolator.  Force exact values at both ends to avoid range errors
264     // logarithmic increment for tables        << 259                 for (G4int i=1; i<nmfpvals-1; i++) evals[i]=emin*std::exp(logint*i);
265                                                << 260                 evals.front()=emin;
266     // compute energy scale for interpolator.  << 261                 evals.back()=emax;
267     // both ends to avoid range errors         << 262                 
268     for (G4int i = 1; i < nmfpvals - 1; i++)   << 263                 // zero out the inverse mfp sums to start
269       evals[i] = emin * std::exp(logint * i);  << 264                 for (G4int eidx=0; eidx < nmfpvals; eidx++) mfpvals[eidx] = 0.0; 
270     evals.front() = emin;                      << 265                 
271     evals.back() = emax;                       << 266                 // sum inverse mfp for each element in this material and for each energy
272                                                << 267                 for (G4int kel=0 ; kel < nMatElements ; kel++ )
273     // zero out the inverse mfp sums to start  << 268         {
274     for (G4int eidx = 0; eidx < nmfpvals; eidx << 269                         element=elementVector[kel];
275       mfpvals[eidx] = 0.0;                     << 270                         G4int Z=(G4int)std::floor(element->GetZ()+0.5);
276                                                << 271                         const G4_c2_function &sigma=sigmaMap[Z];
277     // sum inverse mfp for each element in thi << 272                         G4double ndens = atomDensities[kel]; // compute atom fraction for this element in this material
278     // energy                                  << 273                                                 
279     for (G4int kel = 0; kel < nMatElements; ke << 274                         for (G4int eidx=0; eidx < nmfpvals; eidx++) {
280       element = elementVector[kel];            << 275                                         mfpvals[eidx] += ndens*sigma(evals[eidx]);
281       G4int Z = (G4int)std::floor(element->Get << 276                         }
282       const G4_c2_function& sigma = sigmaMap[Z << 277         }
283       G4double ndens = atomDensities[kel];     << 278                 
284       // compute atom fraction for this elemen << 279                 // convert inverse mfp to regular mfp
285                                                << 280                 for (G4int eidx=0; eidx < nmfpvals; eidx++) {
286       for (G4int eidx = 0; eidx < nmfpvals; ei << 281                         mfpvals[eidx] = 1.0/mfpvals[eidx];
287         mfpvals[eidx] += ndens * sigma(evals[e << 282                 }
288       }                                        << 283                 // and make a new interpolating function out of the sum
289     }                                          << 284                 MFPTables[matidx] = c2.log_log_interpolating_function().load(evals, mfpvals,true,0,true,0);
290                                                << 
291     // convert inverse mfp to regular mfp      << 
292     for (G4int eidx = 0; eidx < nmfpvals; eidx << 
293       mfpvals[eidx] = 1.0 / mfpvals[eidx];     << 
294     }                                             285     }
295     // and make a new interpolating function o << 
296     MFPTables[matidx] = c2.log_log_interpolati << 
297   }                                            << 
298 }                                                 286 }
299                                                   287 
300 G4ScreenedNuclearRecoil::G4ScreenedNuclearReco << 288 G4ScreenedNuclearRecoil::
301                                                << 289 G4ScreenedNuclearRecoil(const G4String& processName, 
302                                                << 290       const G4String &ScreeningKey,
303                                                << 291       G4bool GenerateRecoils, 
304   : G4VDiscreteProcess(processName, fElectroma << 292       G4double RecoilCutoff, G4double PhysicsCutoff) : 
305     screeningKey(ScreeningKey),                << 293   G4VDiscreteProcess(processName, fElectromagnetic),
306     generateRecoils(GenerateRecoils),          << 294         screeningKey(ScreeningKey),
307     avoidReactions(1),                         << 295         generateRecoils(GenerateRecoils), avoidReactions(1), 
308     recoilCutoff(RecoilCutoff),                << 296         recoilCutoff(RecoilCutoff), physicsCutoff(PhysicsCutoff),
309     physicsCutoff(PhysicsCutoff),              << 297         hardeningFraction(0.0), hardeningFactor(1.0),
310     hardeningFraction(0.0),                    << 298         externalCrossSectionConstructor(0),
311     hardeningFactor(1.0),                      << 299         NIELPartitionFunction(new G4LindhardRobinsonPartition)
312     externalCrossSectionConstructor(0),        << 300 {
313     NIELPartitionFunction(new G4LindhardRobins << 301                 // for now, point to class instance of this. Doing it by creating a new one fails
314 {                                              << 302                 // to correctly update NIEL
315   // for now, point to class instance of this. << 303                 // not even this is needed... done in G4VProcess().
316   // one fails                                 << 304                 // pParticleChange=&aParticleChange; 
317   // to correctly update NIEL                  << 305                 processMaxEnergy=50000.0*MeV;
318   // not even this is needed... done in G4VPro << 306                 highEnergyLimit=100.0*MeV;
319   // pParticleChange=&aParticleChange;         << 307                 lowEnergyLimit=physicsCutoff;
320   processMaxEnergy = 50000.0 * MeV;            << 308                 registerDepositedEnergy=1; // by default, don't hide NIEL
321   highEnergyLimit = 100.0 * MeV;               << 309                 MFPScale=1.0;
322   lowEnergyLimit = physicsCutoff;              << 310                 // SetVerboseLevel(2);
323   registerDepositedEnergy = 1;  // by default, << 311                 AddStage(new G4ScreenedCoulombClassicalKinematics);
324   MFPScale = 1.0;                              << 312                 AddStage(new G4SingleScatter); 
325   // SetVerboseLevel(2);                       << 313                 SetProcessSubType(fCoulombScattering);
326   AddStage(new G4ScreenedCoulombClassicalKinem << 
327   AddStage(new G4SingleScatter);               << 
328   SetProcessSubType(fCoulombScattering);       << 
329 }                                                 314 }
330                                                   315 
331 void G4ScreenedNuclearRecoil::ResetTables()       316 void G4ScreenedNuclearRecoil::ResetTables()
332 {                                                 317 {
333   std::map<G4int, G4ScreenedCoulombCrossSectio << 318         
334   for (; xt != crossSectionHandlers.end(); xt+ << 319         std::map<G4int, G4ScreenedCoulombCrossSection*>::iterator xt=crossSectionHandlers.begin();
335     delete (*xt).second;                       << 320         for(;xt != crossSectionHandlers.end(); xt++) {
336   }                                            << 321                 delete (*xt).second;
337   crossSectionHandlers.clear();                << 322         }
                                                   >> 323         crossSectionHandlers.clear();
338 }                                                 324 }
339                                                   325 
340 void G4ScreenedNuclearRecoil::ClearStages()       326 void G4ScreenedNuclearRecoil::ClearStages()
341 {                                                 327 {
342   // I don't think I like deleting the process << 328         // I don't think I like deleting the processes here... they are better abandoned
343   // abandoned                                 << 329         // if the creator doesn't get rid of them
344   // if the creator doesn't get rid of them    << 330         // std::vector<G4ScreenedCollisionStage *>::iterator stage=collisionStages.begin();
345   // std::vector<G4ScreenedCollisionStage *>:: << 331         //for(; stage != collisionStages.end(); stage++) delete (*stage);
346   // collisionStages.begin();                  << 
347   // for(; stage != collisionStages.end(); sta << 
348                                                   332 
349   collisionStages.clear();                     << 333         collisionStages.clear();
350 }                                                 334 }
351                                                   335 
352 void G4ScreenedNuclearRecoil::SetNIELPartition << 336 void G4ScreenedNuclearRecoil::SetNIELPartitionFunction(const G4VNIELPartition *part)
353 {                                                 337 {
354   if (NIELPartitionFunction) delete NIELPartit << 338         if(NIELPartitionFunction) delete NIELPartitionFunction;
355   NIELPartitionFunction = part;                << 339         NIELPartitionFunction=part;
356 }                                                 340 }
357                                                   341 
358 void G4ScreenedNuclearRecoil::DepositEnergy(G4 << 342 void G4ScreenedNuclearRecoil::DepositEnergy(G4int z1, G4double a1, const G4Material *material, G4double energy)
359                                             G4 << 
360 {                                                 343 {
361   if (!NIELPartitionFunction) {                << 344         if(!NIELPartitionFunction) {
362     IonizingLoss += energy;                    << 345                 IonizingLoss+=energy;
363   }                                            << 346         } else {
364   else {                                       << 347                 G4double part=NIELPartitionFunction->PartitionNIEL(z1, a1, material, energy);
365     G4double part = NIELPartitionFunction->Par << 348                 IonizingLoss+=energy*(1-part);
366     IonizingLoss += energy * (1 - part);       << 349                 NIEL += energy*part;
367     NIEL += energy * part;                     << 350         }
368   }                                            << 
369 }                                                 351 }
370                                                   352 
371 G4ScreenedNuclearRecoil::~G4ScreenedNuclearRec    353 G4ScreenedNuclearRecoil::~G4ScreenedNuclearRecoil()
372 {                                                 354 {
373   ResetTables();                               << 355         ResetTables();
374 }                                                 356 }
375                                                   357 
376 // returns true if it appears the nuclei colli << 358 // returns true if it appears the nuclei collided, and we are interested in checking
377 // in checking                                 << 359 G4bool G4ScreenedNuclearRecoil::CheckNuclearCollision(
378 G4bool G4ScreenedNuclearRecoil::CheckNuclearCo << 360                         G4double A, G4double a1, G4double apsis) {
379 {                                              << 361         return avoidReactions && (apsis < (1.1*(std::pow(A,1.0/3.0)+std::pow(a1,1.0/3.0)) + 1.4)*fermi);
380   return avoidReactions                        << 362         // nuclei are within 1.4 fm (reduced pion Compton wavelength) of each other at apsis, 
381          && (apsis < (1.1 * (std::pow(A, 1.0 / << 363         // this is hadronic, skip it
382   // nuclei are within 1.4 fm (reduced pion Co << 
383   // other at apsis,                           << 
384   // this is hadronic, skip it                 << 
385 }                                                 364 }
386                                                   365 
387 G4ScreenedCoulombCrossSection* G4ScreenedNucle << 366 G4ScreenedCoulombCrossSection *G4ScreenedNuclearRecoil::GetNewCrossSectionHandler(void) {
388 {                                              << 367         G4ScreenedCoulombCrossSection *xc;
389   G4ScreenedCoulombCrossSection* xc;           << 368         if(!externalCrossSectionConstructor) xc=new G4NativeScreenedCoulombCrossSection;
390   if (!externalCrossSectionConstructor)        << 369         else xc=externalCrossSectionConstructor->create();
391     xc = new G4NativeScreenedCoulombCrossSecti << 370         xc->SetVerbosity(verboseLevel);
392   else                                         << 371         return xc;
393     xc = externalCrossSectionConstructor->crea << 
394   xc->SetVerbosity(verboseLevel);              << 
395   return xc;                                   << 
396 }                                                 372 }
397                                                   373 
398 G4double G4ScreenedNuclearRecoil::GetMeanFreeP << 374 G4double G4ScreenedNuclearRecoil::GetMeanFreePath(const G4Track& track,
                                                   >> 375                                                   G4double, 
399                                                   376                                                   G4ForceCondition* cond)
400 {                                                 377 {
401   const G4DynamicParticle* incoming = track.Ge << 378         const G4DynamicParticle* incoming = track.GetDynamicParticle();
402   G4double energy = incoming->GetKineticEnergy << 379         G4double energy = incoming->GetKineticEnergy();
403   G4double a1 = incoming->GetDefinition()->Get << 380         G4double a1=incoming->GetDefinition()->GetPDGMass()/amu_c2;
404                                                << 381         
405   G4double meanFreePath;                       << 382         G4double meanFreePath;
406   *cond = NotForced;                           << 383         *cond=NotForced;
407                                                << 384         
408   if (energy < lowEnergyLimit || energy < reco << 385         if (energy < lowEnergyLimit || energy < recoilCutoff*a1) {
409     *cond = Forced;                            << 386                 *cond=Forced;
410     return 1.0 * nm;                           << 387                 return 1.0*nm; /* catch and stop slow particles to collect their NIEL! */
411     /* catch and stop slow particles to collec << 388         } else if (energy > processMaxEnergy*a1) {
412   }                                            << 389                 return DBL_MAX; // infinite mean free path
413   else if (energy > processMaxEnergy * a1) {   << 390         } else if (energy > highEnergyLimit*a1) energy=highEnergyLimit*a1; /* constant MFP at high energy */
414     return DBL_MAX;  // infinite mean free pat << 391 
415   }                                            << 392         G4double fz1=incoming->GetDefinition()->GetPDGCharge();
416   else if (energy > highEnergyLimit * a1)      << 393         G4int z1=(G4int)(fz1/eplus + 0.5);
417     energy = highEnergyLimit * a1;             << 394 
418   /* constant MFP at high energy */            << 395         std::map<G4int, G4ScreenedCoulombCrossSection*>::iterator xh=
419                                                << 396                 crossSectionHandlers.find(z1);
420   G4double fz1 = incoming->GetDefinition()->Ge << 397         G4ScreenedCoulombCrossSection *xs;
421   G4int z1 = (G4int)(fz1 / eplus + 0.5);       << 398         
422                                                << 399         if (xh==crossSectionHandlers.end()) {
423   std::map<G4int, G4ScreenedCoulombCrossSectio << 400                 xs =crossSectionHandlers[z1]=GetNewCrossSectionHandler();
424   G4ScreenedCoulombCrossSection* xs;           << 401                 xs->LoadData(screeningKey, z1, a1, physicsCutoff);
425                                                << 402                 xs->BuildMFPTables();
426   if (xh == crossSectionHandlers.end()) {      << 403         } else xs=(*xh).second;
427     xs = crossSectionHandlers[z1] = GetNewCros << 404         
428     xs->LoadData(screeningKey, z1, a1, physics << 405         const G4MaterialCutsCouple* materialCouple = track.GetMaterialCutsCouple();
429     xs->BuildMFPTables();                      << 406         size_t materialIndex = materialCouple->GetMaterial()->GetIndex();
430   }                                            << 407 
431   else                                         << 408         const G4_c2_function &mfp=*(*xs)[materialIndex];
432     xs = (*xh).second;                         << 409         
433                                                << 410         // make absolutely certain we don't get an out-of-range energy
434   const G4MaterialCutsCouple* materialCouple = << 411         meanFreePath = mfp(std::min(std::max(energy, mfp.xmin()), mfp.xmax()));
435   size_t materialIndex = materialCouple->GetMa << 412         
436                                                << 413         // G4cout << "MFP: " << meanFreePath << " index " << materialIndex << " energy " << energy << " MFPScale " << MFPScale << G4endl;
437   const G4_c2_function& mfp = *(*xs)[materialI << 414         
438                                                << 415         return meanFreePath*MFPScale;
439   // make absolutely certain we don't get an o << 
440   meanFreePath = mfp(std::min(std::max(energy, << 
441                                                << 
442   // G4cout << "MFP: " << meanFreePath << " in << 
443   //<< " energy " << energy << " MFPScale " << << 
444                                                << 
445   return meanFreePath * MFPScale;              << 
446 }                                                 416 }
447                                                   417 
448 G4VParticleChange* G4ScreenedNuclearRecoil::Po    418 G4VParticleChange* G4ScreenedNuclearRecoil::PostStepDoIt(const G4Track& aTrack, const G4Step& aStep)
449 {                                                 419 {
450   validCollision = 1;                          << 420         validCollision=1;
451   pParticleChange->Initialize(aTrack);         << 421         pParticleChange->Initialize(aTrack);
452   NIEL = 0.0;  // default is no NIEL deposited << 422         NIEL=0.0; // default is no NIEL deposited
453   IonizingLoss = 0.0;                          << 423         IonizingLoss=0.0;
454                                                << 424         
455   // do universal setup                        << 425         // do universal setup
456                                                << 426         
457   const G4DynamicParticle* incidentParticle =  << 427         const G4DynamicParticle* incidentParticle = aTrack.GetDynamicParticle();
458   G4ParticleDefinition* baseParticle = aTrack. << 428         G4ParticleDefinition *baseParticle=aTrack.GetDefinition();
459                                                << 429         
460   G4double fz1 = baseParticle->GetPDGCharge()  << 430         G4double fz1=baseParticle->GetPDGCharge()/eplus;
461   G4int z1 = (G4int)(fz1 + 0.5);               << 431         G4int z1=(G4int)(fz1+0.5);
462   G4double a1 = baseParticle->GetPDGMass() / a << 432         G4double a1=baseParticle->GetPDGMass()/amu_c2;
463   G4double incidentEnergy = incidentParticle-> << 433         G4double incidentEnergy = incidentParticle->GetKineticEnergy();
464                                                << 434                 
465   // Select randomly one element and (possibly << 435         // Select randomly one element and (possibly) isotope in the current material.
466   // current material.                         << 436         const G4MaterialCutsCouple* couple = aTrack.GetMaterialCutsCouple();
467   const G4MaterialCutsCouple* couple = aTrack. << 437         
468                                                << 438         const G4Material* mat = couple->GetMaterial();
469   const G4Material* mat = couple->GetMaterial( << 439 
470                                                << 440         G4double P=0.0; // the impact parameter of this collision
471   G4double P = 0.0;  // the impact parameter o << 441 
472                                                << 442         if(incidentEnergy < GetRecoilCutoff()*a1) { // check energy sanity on entry
473   if (incidentEnergy < GetRecoilCutoff() * a1) << 443                 DepositEnergy(z1, baseParticle->GetPDGMass()/amu_c2, mat, incidentEnergy);
474     // check energy sanity on entry            << 444                 GetParticleChange().ProposeEnergy(0.0);
475     DepositEnergy(z1, baseParticle->GetPDGMass << 445                 // stop the particle and bail out
476     GetParticleChange().ProposeEnergy(0.0);    << 446                 validCollision=0;
477     // stop the particle and bail out          << 447         } else {
478     validCollision = 0;                        << 448                 
479   }                                            << 449                 G4double numberDensity=mat->GetTotNbOfAtomsPerVolume();
480   else {                                       << 450                 G4double lattice=0.5/std::pow(numberDensity,1.0/3.0); // typical lattice half-spacing
481     G4double numberDensity = mat->GetTotNbOfAt << 451                 G4double length=GetCurrentInteractionLength();
482     G4double lattice = 0.5 / std::pow(numberDe << 452                 G4double sigopi=1.0/(CLHEP::pi*numberDensity*length);  // this is sigma0/pi
483     // typical lattice half-spacing            << 453                 
484     G4double length = GetCurrentInteractionLen << 454                 // compute the impact parameter very early, so if is rejected as too far away, little effort is wasted
485     G4double sigopi = 1.0 / (pi * numberDensit << 455                 // this is the TRIM method for determining an impact parameter based on the flight path
486     // this is sigma0/pi                       << 456                 // this gives a cumulative distribution of N(P)= 1-exp(-pi P^2 n l)
487                                                << 457                 // which says the probability of NOT hitting a disk of area sigma= pi P^2 =exp(-sigma N l) 
488     // compute the impact parameter very early << 458                 // which may be reasonable
489     // as too far away, little effort is waste << 459                 if(sigopi < lattice*lattice) { 
490     // this is the TRIM method for determining << 460                         // normal long-flight approximation
491     // based on the flight path                << 461                         P = std::sqrt(-std::log(G4UniformRand()) *sigopi);
492     // this gives a cumulative distribution of << 462                 } else {
493     // N(P)= 1-exp(-pi P^2 n l)                << 463                         // short-flight limit
494     // which says the probability of NOT hitti << 464                         P = std::sqrt(G4UniformRand())*lattice;
495     // sigma= pi P^2 =exp(-sigma N l)          << 465                 }
496     // which may be reasonable                 << 466                         
497     if (sigopi < lattice * lattice) {          << 467                 G4double fraction=GetHardeningFraction();
498       // normal long-flight approximation      << 468                 if(fraction && G4UniformRand() < fraction) { 
499       P = std::sqrt(-std::log(G4UniformRand()) << 469                         // pick out some events, and increase the central cross section
500     }                                          << 470                         // by reducing the impact parameter
501     else {                                     << 471                         P /= std::sqrt(GetHardeningFactor());
502       // short-flight limit                    << 472                 }
503       P = std::sqrt(G4UniformRand()) * lattice << 473                 
504     }                                          << 474                 
505                                                << 475                 // check if we are far enough away that the energy transfer must be below cutoff, 
506     G4double fraction = GetHardeningFraction() << 476                 // and leave everything alone if so, saving a lot of time.
507     if (fraction && G4UniformRand() < fraction << 477                 if(P*P > sigopi) {
508       // pick out some events, and increase th << 478                         if(GetVerboseLevel() > 1) 
509       // section by reducing the impact parame << 479                                 printf("ScreenedNuclear impact reject: length=%.3f P=%.4f limit=%.4f\n",
510       P /= std::sqrt(GetHardeningFactor());    << 480                                            length/angstrom, P/angstrom,std::sqrt(sigopi)/angstrom);
511     }                                          << 481                         // no collision, don't follow up with anything
512                                                << 482                         validCollision=0;
513     // check if we are far enough away that th << 483                 }
514     // must be below cutoff,                   << 484         }
515     // and leave everything alone if so, savin << 485         
516     if (P * P > sigopi) {                      << 486         // find out what we hit, and record it in our kinematics block.
517       if (GetVerboseLevel() > 1)               << 487         kinematics.targetMaterial=mat;
518         printf("ScreenedNuclear impact reject: << 488         kinematics.a1=a1;
519                P / angstrom, std::sqrt(sigopi) << 489         
520       // no collision, don't follow up with an << 490         if(validCollision) {
521       validCollision = 0;                      << 491                 G4ScreenedCoulombCrossSection        *xsect=GetCrossSectionHandlers()[z1];
522     }                                          << 492                 G4ParticleDefinition *recoilIon=
523   }                                            << 493                         xsect->SelectRandomUnweightedTarget(couple);
524                                                << 494                 kinematics.crossSection=xsect;
525   // find out what we hit, and record it in ou << 495                 kinematics.recoilIon=recoilIon;
526   kinematics.targetMaterial = mat;             << 496                 kinematics.impactParameter=P;
527   kinematics.a1 = a1;                          << 497                 kinematics.a2=recoilIon->GetPDGMass()/amu_c2;
528                                                << 498         } else {
529   if (validCollision) {                        << 499                 kinematics.recoilIon=0;
530     G4ScreenedCoulombCrossSection* xsect = Get << 500                 kinematics.impactParameter=0;
531     G4ParticleDefinition* recoilIon = xsect->S << 501                 kinematics.a2=0;
532     kinematics.crossSection = xsect;           << 502         }
533     kinematics.recoilIon = recoilIon;          << 503         
534     kinematics.impactParameter = P;            << 504         std::vector<G4ScreenedCollisionStage *>::iterator stage=collisionStages.begin();
535     kinematics.a2 = recoilIon->GetPDGMass() /  << 505         
536   }                                            << 506         for(; stage != collisionStages.end(); stage++) 
537   else {                                       << 507                 (*stage)->DoCollisionStep(this,aTrack, aStep);
538     kinematics.recoilIon = 0;                  << 508         
539     kinematics.impactParameter = 0;            << 509         if(registerDepositedEnergy) {
540     kinematics.a2 = 0;                         << 510                 pParticleChange->ProposeLocalEnergyDeposit(IonizingLoss+NIEL);
541   }                                            << 511                 pParticleChange->ProposeNonIonizingEnergyDeposit(NIEL);
542                                                << 512                 //MHM G4cout << "depositing energy, total = " << IonizingLoss+NIEL << " NIEL = " << NIEL << G4endl;
543   std::vector<G4ScreenedCollisionStage*>::iter << 513         }
544                                                << 
545   for (; stage != collisionStages.end(); stage << 
546     (*stage)->DoCollisionStep(this, aTrack, aS << 
547                                                << 
548   if (registerDepositedEnergy) {               << 
549     pParticleChange->ProposeLocalEnergyDeposit << 
550     pParticleChange->ProposeNonIonizingEnergyD << 
551     // MHM G4cout << "depositing energy, total << 
552     //<< IonizingLoss+NIEL << " NIEL = " << NI << 
553   }                                            << 
554                                                << 
555   return G4VDiscreteProcess::PostStepDoIt(aTra << 
556 }                                              << 
557                                                << 
558 G4ScreenedCoulombClassicalKinematics::G4Screen << 
559   :  // instantiate all the needed functions s << 
560      // done at run time                       << 
561      // we will be solving x^2 - x phi(x*au)/e << 
562      // or, for easier scaling, x'^2 - x' au p << 
563      // note that only the last of these gets  << 
564     phifunc(c2.const_plugin_function()),       << 
565     xovereps(c2.linear(0., 0., 0.)),           << 
566     // will fill this in with the right slope  << 
567     diff(c2.quadratic(0., 0., 0., 1.) - xovere << 
568 {}                                             << 
569                                                << 
570 G4bool G4ScreenedCoulombClassicalKinematics::D << 
571                                                << 
572                                                << 
573 {                                              << 
574   G4double au = screen->au;                    << 
575   G4CoulombKinematicsInfo& kin = master->GetKi << 
576   G4double A = kin.a2;                         << 
577   G4double a1 = kin.a1;                        << 
578                                                << 
579   G4double xx0;  // first estimate of closest  << 
580   if (eps < 5.0) {                             << 
581     G4double y = std::log(eps);                << 
582     G4double mlrho4 = ((((3.517e-4 * y + 1.401 << 
583     G4double rho4 = std::exp(-mlrho4);  // W&M << 
584     G4double bb2 = 0.5 * beta * beta;          << 
585     xx0 = std::sqrt(bb2 + std::sqrt(bb2 * bb2  << 
586   }                                            << 
587   else {                                       << 
588     G4double ee = 1.0 / (2.0 * eps);           << 
589     xx0 = ee + std::sqrt(ee * ee + beta * beta << 
590     if (master->CheckNuclearCollision(A, a1, x << 
591     // nuclei too close                        << 
592   }                                            << 
593                                                << 
594   // we will be solving x^2 - x phi(x*au)/eps  << 
595   // or, for easier scaling, x'^2 - x' au phi( << 
596   xovereps.reset(0., 0.0, au / eps);  // slope << 
597   phifunc.set_function(&(screen->EMphiData.get << 
598   // install interpolating table               << 
599   G4double xx1, phip, phip2;                   << 
600   G4int root_error;                            << 
601   xx1 = diff->find_root(phifunc.xmin(), std::m << 
602                         std::min(xx0 * au, phi << 
603                         &phip, &phip2)         << 
604         / au;                                  << 
605                                                << 
606   if (root_error) {                            << 
607     G4cout << "Screened Coulomb Root Finder Er << 
608     G4cout << "au " << au << " A " << A << " a << 
609            << " beta " << beta << G4endl;      << 
610     G4cout << " xmin " << phifunc.xmin() << "  << 
611     G4cout << " f(xmin) " << phifunc(phifunc.x << 
612            << phifunc(std::min(10 * xx0 * au,  << 
613     G4cout << " xstart " << std::min(xx0 * au, << 
614            << beta * beta * au * au;           << 
615     G4cout << G4endl;                          << 
616     throw c2_exception("Failed root find");    << 
617   }                                            << 
618                                                << 
619   // phiprime is scaled by one factor of au be << 
620   // at (xx0*au),                              << 
621   G4double phiprime = phip * au;               << 
622                                                << 
623   // lambda0 is from W&M 19                    << 
624   G4double lambda0 =                           << 
625     1.0 / std::sqrt(0.5 + beta * beta / (2.0 * << 
626                                                << 
627   // compute the 6-term Lobatto integral alpha << 
628   // different coefficients)                   << 
629   // this is probably completely un-needed but << 
630   // quality results,                          << 
631   G4double alpha = (1.0 + lambda0) / 30.0;     << 
632   G4double xvals[] = {0.98302349, 0.84652241,  << 
633   G4double weights[] = {0.03472124, 0.14769029 << 
634   for (G4int k = 0; k < 4; k++) {              << 
635     G4double x, ff;                            << 
636     x = xx1 / xvals[k];                        << 
637     ff = 1.0 / std::sqrt(1.0 - phifunc(x * au) << 
638     alpha += weights[k] * ff;                  << 
639   }                                            << 
640                                                << 
641   phifunc.unset_function();                    << 
642   // throws an exception if used without setti << 
643                                                   514 
644   G4double thetac1 = pi * beta * alpha / xx1;  << 515         return G4VDiscreteProcess::PostStepDoIt( aTrack, aStep );
645   // complement of CM scattering angle         << 
646   G4double sintheta = std::sin(thetac1);  // n << 
647   G4double costheta = -std::cos(thetac1);  //  << 
648   // G4double psi=std::atan2(sintheta, costhet << 
649   // lab scattering angle (M&T 3rd eq. 8.69)   << 
650                                                << 
651   // numerics note:  because we checked above  << 
652   // of beta which give real recoils,          << 
653   // we don't have to look too closely for the << 
654   // (which would cause sin(theta)             << 
655   // and 1-cos(theta) to both vanish and make  << 
656   G4double zeta = std::atan2(sintheta, 1 - cos << 
657   // lab recoil angle (M&T 3rd eq. 8.73)       << 
658   G4double coszeta = std::cos(zeta);           << 
659   G4double sinzeta = std::sin(zeta);           << 
660                                                << 
661   kin.sinTheta = sintheta;                     << 
662   kin.cosTheta = costheta;                     << 
663   kin.sinZeta = sinzeta;                       << 
664   kin.cosZeta = coszeta;                       << 
665   return 1;  // all OK, collision is valid     << 
666 }                                                 516 }
667                                                   517 
668 void G4ScreenedCoulombClassicalKinematics::DoC << 518 G4ScreenedCoulombClassicalKinematics::G4ScreenedCoulombClassicalKinematics() :
669                                                << 519 // instantiate all the needed functions statically, so no allocation is done at run time
                                                   >> 520 // we will be solving x^2 - x phi(x*au)/eps - beta^2 == 0.0
                                                   >> 521 // or, for easier scaling, x'^2 - x' au phi(x')/eps - beta^2 au^2
                                                   >> 522 // note that only the last of these gets deleted, since it owns the rest
                                                   >> 523 phifunc(c2.const_plugin_function()),
                                                   >> 524 xovereps(c2.linear(0., 0., 0.)), // will fill this in with the right slope at run time
                                                   >> 525 diff(c2.quadratic(0., 0., 0., 1.)-xovereps*phifunc)
670 {                                                 526 {
671   if (!master->GetValidCollision()) return;    << 
672                                                << 
673   G4ParticleChange& aParticleChange = master-> << 
674   G4CoulombKinematicsInfo& kin = master->GetKi << 
675                                                << 
676   const G4DynamicParticle* incidentParticle =  << 
677   G4ParticleDefinition* baseParticle = aTrack. << 
678                                                << 
679   G4double incidentEnergy = incidentParticle-> << 
680                                                << 
681   // this adjustment to a1 gives the right res << 
682   // (constant gamma)                          << 
683   // relativistic collisions.  Hard collisions << 
684   // Coulombic and hadronic terms interfere an << 
685   G4double gamma = (1.0 + incidentEnergy / bas << 
686   G4double a1 = kin.a1 * gamma;  // relativist << 
687                                                << 
688   G4ParticleDefinition* recoilIon = kin.recoil << 
689   G4double A = recoilIon->GetPDGMass() / amu_c << 
690   G4int Z = (G4int)((recoilIon->GetPDGCharge() << 
691                                                << 
692   G4double Ec = incidentEnergy * (A / (A + a1) << 
693   // energy in CM frame (non-relativistic!)    << 
694   const G4ScreeningTables* screen = kin.crossS << 
695   G4double au = screen->au;  // screening leng << 
696                                                << 
697   G4double beta = kin.impactParameter / au;    << 
698   // dimensionless impact parameter            << 
699   G4double eps = Ec / (screen->z1 * Z * elm_co << 
700   // dimensionless energy                      << 
701                                                << 
702   G4bool ok = DoScreeningComputation(master, s << 
703   if (!ok) {                                   << 
704     master->SetValidCollision(0);  // flag bad << 
705     return;  // just bail out without setting  << 
706   }                                            << 
707                                                << 
708   G4double eRecoil =                           << 
709     4 * incidentEnergy * a1 * A * kin.cosZeta  << 
710   kin.eRecoil = eRecoil;                       << 
711                                                << 
712   if (incidentEnergy - eRecoil < master->GetRe << 
713     aParticleChange.ProposeEnergy(0.0);        << 
714     master->DepositEnergy(int(screen->z1), a1, << 
715   }                                            << 
716                                                << 
717   if (master->GetEnableRecoils() && eRecoil >  << 
718     kin.recoilIon = recoilIon;                 << 
719   }                                            << 
720   else {                                       << 
721     kin.recoilIon = 0;  // this flags no recoi << 
722     master->DepositEnergy(Z, A, kin.targetMate << 
723   }                                            << 
724 }                                                 527 }
725                                                   528 
726 void G4SingleScatter::DoCollisionStep(G4Screen << 529 G4bool G4ScreenedCoulombClassicalKinematics::DoScreeningComputation(G4ScreenedNuclearRecoil *master,
727                                       const G4 << 530                 const G4ScreeningTables *screen, G4double eps, G4double beta)
728 {                                              << 531 {
729   if (!master->GetValidCollision()) return;    << 532         G4double au=screen->au;
730                                                << 533         G4CoulombKinematicsInfo &kin=master->GetKinematics();
731   G4CoulombKinematicsInfo& kin = master->GetKi << 534         G4double A=kin.a2;
732   G4ParticleChange& aParticleChange = master-> << 535         G4double a1=kin.a1;
733                                                << 536         
734   const G4DynamicParticle* incidentParticle =  << 537         G4double xx0; // first estimate of closest approach
735   G4double incidentEnergy = incidentParticle-> << 538         if(eps < 5.0) {
736   G4double eRecoil = kin.eRecoil;              << 539                 G4double y=std::log(eps);
737                                                << 540                 G4double mlrho4=((((3.517e-4*y+1.401e-2)*y+2.393e-1)*y+2.734)*y+2.220);
738   G4double azimuth = G4UniformRand() * (2.0 *  << 541                 G4double rho4=std::exp(-mlrho4); // W&M eq. 18
739   G4double sa = std::sin(azimuth);             << 542                 G4double bb2=0.5*beta*beta;
740   G4double ca = std::cos(azimuth);             << 543                 xx0=std::sqrt(bb2+std::sqrt(bb2*bb2+rho4)); // W&M eq. 17
741                                                << 544         } else {
742   G4ThreeVector recoilMomentumDirection(kin.si << 545                 G4double ee=1.0/(2.0*eps);
743   G4ParticleMomentum incidentDirection = incid << 546                 xx0=ee+std::sqrt(ee*ee+beta*beta); // W&M eq. 15 (Rutherford value)                
744   recoilMomentumDirection = recoilMomentumDire << 547                 if(master->CheckNuclearCollision(A, a1, xx0*au)) return 0; // nuclei too close
745   G4ThreeVector recoilMomentum =               << 548                 
746     recoilMomentumDirection * std::sqrt(2.0 *  << 549         }
747                                                << 550         
748   if (aParticleChange.GetEnergy() != 0.0) {    << 551         // we will be solving x^2 - x phi(x*au)/eps - beta^2 == 0.0
749     // DoKinematics hasn't stopped it!         << 552         // or, for easier scaling, x'^2 - x' au phi(x')/eps - beta^2 au^2
750     G4ThreeVector beamMomentum = incidentParti << 553         xovereps.reset(0., 0.0, au/eps); // slope of x*au/eps term
751     aParticleChange.ProposeMomentumDirection(b << 554         phifunc.set_function(&(screen->EMphiData.get())); // install interpolating table
752     aParticleChange.ProposeEnergy(incidentEner << 555         G4double xx1, phip, phip2;
753   }                                            << 556         G4int root_error;        
754                                                << 557         xx1=diff->find_root(phifunc.xmin(), std::min(10*xx0*au,phifunc.xmax()), 
755   if (kin.recoilIon) {                         << 558                                            std::min(xx0*au, phifunc.xmax()), beta*beta*au*au, &root_error, &phip, &phip2)/au; 
756     G4DynamicParticle* recoil =                << 559         
757       new G4DynamicParticle(kin.recoilIon, rec << 560         if(root_error) {
                                                   >> 561                 G4cout << "Screened Coulomb Root Finder Error" << G4endl;
                                                   >> 562                 G4cout << "au " << au << " A " << A << " a1 " << a1 << " xx1 " << xx1 << " eps " << eps << " beta " << beta << G4endl;
                                                   >> 563                 G4cout << " xmin " << phifunc.xmin() << " xmax " << std::min(10*xx0*au,phifunc.xmax()) ;
                                                   >> 564                 G4cout << " f(xmin) " << phifunc(phifunc.xmin()) <<  " f(xmax) " << phifunc(std::min(10*xx0*au,phifunc.xmax())) ;
                                                   >> 565                 G4cout << " xstart " << std::min(xx0*au, phifunc.xmax()) <<  " target " <<  beta*beta*au*au ;
                                                   >> 566                 G4cout << G4endl;
                                                   >> 567                 throw c2_exception("Failed root find");
                                                   >> 568         }
                                                   >> 569         
                                                   >> 570         // phiprime is scaled by one factor of au because phi is evaluated at (xx0*au),
                                                   >> 571         G4double phiprime=phip*au;
                                                   >> 572         
                                                   >> 573         //lambda0 is from W&M 19
                                                   >> 574         G4double lambda0=1.0/std::sqrt(0.5+beta*beta/(2.0*xx1*xx1)-phiprime/(2.0*eps));
                                                   >> 575         
                                                   >> 576         //compute the 6-term Lobatto integral alpha (per W&M 21, with different coefficients)
                                                   >> 577         // this is probably completely un-needed but gives the highest quality results,
                                                   >> 578         G4double alpha=(1.0+ lambda0)/30.0;
                                                   >> 579         G4double xvals[]={0.98302349, 0.84652241, 0.53235309, 0.18347974};
                                                   >> 580         G4double weights[]={0.03472124, 0.14769029, 0.23485003, 0.18602489};
                                                   >> 581         for(G4int k=0; k<4; k++) {
                                                   >> 582                 G4double x, ff;
                                                   >> 583                 x=xx1/xvals[k];
                                                   >> 584                 ff=1.0/std::sqrt(1.0-phifunc(x*au)/(x*eps)-beta*beta/(x*x));
                                                   >> 585                 alpha+=weights[k]*ff;
                                                   >> 586         }
                                                   >> 587         
                                                   >> 588         phifunc.unset_function(); // throws an exception if used without setting again
758                                                   589 
759     aParticleChange.SetNumberOfSecondaries(1); << 590         G4double thetac1=CLHEP::pi*beta*alpha/xx1; // complement of CM scattering angle
760     aParticleChange.AddSecondary(recoil);      << 591         G4double sintheta=std::sin(thetac1); //note sin(pi-theta)=sin(theta)
761   }                                            << 592         G4double costheta=-std::cos(thetac1); // note cos(pi-theta)=-cos(theta)
                                                   >> 593                                                                                   // G4double psi=std::atan2(sintheta, costheta+a1/A); // lab scattering angle (M&T 3rd eq. 8.69)
                                                   >> 594         
                                                   >> 595         // numerics note:  because we checked above for reasonable values of beta which give real recoils,
                                                   >> 596         // we don't have to look too closely for theta -> 0 here (which would cause sin(theta)
                                                   >> 597         // and 1-cos(theta) to both vanish and make the atan2 ill behaved).
                                                   >> 598         G4double zeta=std::atan2(sintheta, 1-costheta); // lab recoil angle (M&T 3rd eq. 8.73)
                                                   >> 599         G4double coszeta=std::cos(zeta);
                                                   >> 600         G4double sinzeta=std::sin(zeta);
                                                   >> 601 
                                                   >> 602         kin.sinTheta=sintheta;
                                                   >> 603         kin.cosTheta=costheta;
                                                   >> 604         kin.sinZeta=sinzeta;
                                                   >> 605         kin.cosZeta=coszeta;
                                                   >> 606         return 1; // all OK, collision is valid
                                                   >> 607 }
                                                   >> 608 
                                                   >> 609 void G4ScreenedCoulombClassicalKinematics::DoCollisionStep(G4ScreenedNuclearRecoil *master,
                                                   >> 610                 const G4Track& aTrack, const G4Step&) {
                                                   >> 611         
                                                   >> 612         if(!master->GetValidCollision()) return;
                                                   >> 613         
                                                   >> 614         G4ParticleChange &aParticleChange=master->GetParticleChange();
                                                   >> 615         G4CoulombKinematicsInfo &kin=master->GetKinematics();
                                                   >> 616         
                                                   >> 617         const G4DynamicParticle* incidentParticle = aTrack.GetDynamicParticle();
                                                   >> 618         G4ParticleDefinition *baseParticle=aTrack.GetDefinition();
                                                   >> 619         
                                                   >> 620         G4double incidentEnergy = incidentParticle->GetKineticEnergy();
                                                   >> 621         
                                                   >> 622         // this adjustment to a1 gives the right results for soft (constant gamma)
                                                   >> 623         // relativistic collisions.  Hard collisions are wrong anyway, since the
                                                   >> 624         // Coulombic and hadronic terms interfere and cannot be added.
                                                   >> 625         G4double gamma=(1.0+incidentEnergy/baseParticle->GetPDGMass());
                                                   >> 626         G4double a1=kin.a1*gamma; // relativistic gamma correction
                                                   >> 627         
                                                   >> 628         G4ParticleDefinition *recoilIon=kin.recoilIon;
                                                   >> 629         G4double A=recoilIon->GetPDGMass()/amu_c2;
                                                   >> 630         G4int Z=(G4int)((recoilIon->GetPDGCharge()/eplus)+0.5);
                                                   >> 631         
                                                   >> 632         G4double Ec = incidentEnergy*(A/(A+a1)); // energy in CM frame (non-relativistic!)
                                                   >> 633         const G4ScreeningTables *screen=kin.crossSection->GetScreening(Z);
                                                   >> 634         G4double au=screen->au; // screening length
                                                   >> 635         
                                                   >> 636         G4double beta = kin.impactParameter/au; // dimensionless impact parameter
                                                   >> 637         G4double eps = Ec/(screen->z1*Z*elm_coupling/au); // dimensionless energy
                                                   >> 638         
                                                   >> 639         G4bool ok=DoScreeningComputation(master, screen, eps, beta);        
                                                   >> 640         if(!ok) {
                                                   >> 641                 master->SetValidCollision(0); // flag bad collision
                                                   >> 642                 return; // just bail out without setting valid flag
                                                   >> 643         }
                                                   >> 644         
                                                   >> 645         G4double eRecoil=4*incidentEnergy*a1*A*kin.cosZeta*kin.cosZeta/((a1+A)*(a1+A));
                                                   >> 646         kin.eRecoil=eRecoil;
                                                   >> 647         
                                                   >> 648         if(incidentEnergy-eRecoil < master->GetRecoilCutoff()*a1) {
                                                   >> 649                 aParticleChange.ProposeEnergy(0.0);
                                                   >> 650                 master->DepositEnergy(int(screen->z1), a1, kin.targetMaterial, incidentEnergy-eRecoil);
                                                   >> 651         } 
                                                   >> 652         
                                                   >> 653         if(master->GetEnableRecoils() && eRecoil > master->GetRecoilCutoff() * kin.a2) {
                                                   >> 654                 kin.recoilIon=recoilIon;                
                                                   >> 655         } else {
                                                   >> 656                 kin.recoilIon=0; // this flags no recoil to be generated
                                                   >> 657                 master->DepositEnergy(Z, A, kin.targetMaterial, eRecoil) ;
                                                   >> 658         }        
                                                   >> 659 }
                                                   >> 660 
                                                   >> 661 void G4SingleScatter::DoCollisionStep(G4ScreenedNuclearRecoil *master,
                                                   >> 662                                                                                 const G4Track& aTrack, const G4Step&) {
                                                   >> 663         
                                                   >> 664         if(!master->GetValidCollision()) return;
                                                   >> 665 
                                                   >> 666         G4CoulombKinematicsInfo &kin=master->GetKinematics();
                                                   >> 667         G4ParticleChange &aParticleChange=master->GetParticleChange();
                                                   >> 668 
                                                   >> 669         const G4DynamicParticle* incidentParticle = aTrack.GetDynamicParticle();
                                                   >> 670         G4double incidentEnergy = incidentParticle->GetKineticEnergy();
                                                   >> 671         G4double eRecoil=kin.eRecoil;
                                                   >> 672         
                                                   >> 673         G4double azimuth=G4UniformRand()*(2.0*CLHEP::pi);
                                                   >> 674         G4double sa=std::sin(azimuth);
                                                   >> 675         G4double ca=std::cos(azimuth);
                                                   >> 676 
                                                   >> 677         G4ThreeVector recoilMomentumDirection(kin.sinZeta*ca, kin.sinZeta*sa, kin.cosZeta);
                                                   >> 678         G4ParticleMomentum incidentDirection = incidentParticle->GetMomentumDirection();
                                                   >> 679         recoilMomentumDirection=recoilMomentumDirection.rotateUz(incidentDirection);
                                                   >> 680         G4ThreeVector recoilMomentum=recoilMomentumDirection*std::sqrt(2.0*eRecoil*kin.a2*amu_c2);
                                                   >> 681         
                                                   >> 682         if(aParticleChange.GetEnergy() != 0.0) { // DoKinematics hasn't stopped it!
                                                   >> 683                 G4ThreeVector beamMomentum=incidentParticle->GetMomentum()-recoilMomentum;
                                                   >> 684                 aParticleChange.ProposeMomentumDirection(beamMomentum.unit()) ;
                                                   >> 685                 aParticleChange.ProposeEnergy(incidentEnergy-eRecoil);
                                                   >> 686         }
                                                   >> 687         
                                                   >> 688         if(kin.recoilIon) {
                                                   >> 689                 G4DynamicParticle* recoil = new G4DynamicParticle (kin.recoilIon,
                                                   >> 690                                 recoilMomentumDirection,eRecoil) ;
                                                   >> 691                 
                                                   >> 692                 aParticleChange.SetNumberOfSecondaries(1);
                                                   >> 693                 aParticleChange.AddSecondary(recoil);   
                                                   >> 694         }
762 }                                                 695 }
763                                                   696 
764 G4bool G4ScreenedNuclearRecoil::IsApplicable(c << 697 G4bool G4ScreenedNuclearRecoil::
                                                   >> 698 IsApplicable(const G4ParticleDefinition& aParticleType)
765 {                                                 699 {
766   return aParticleType == *(G4Proton::Proton() << 700         return  aParticleType == *(G4Proton::Proton()) ||
767          || aParticleType.GetParticleType() == << 701         aParticleType.GetParticleType() == "nucleus" ||
                                                   >> 702         aParticleType.GetParticleType() == "static_nucleus";
768 }                                                 703 }
769                                                   704 
770 void G4ScreenedNuclearRecoil::BuildPhysicsTabl << 705 void 
                                                   >> 706 G4ScreenedNuclearRecoil::
                                                   >> 707 BuildPhysicsTable(const G4ParticleDefinition& aParticleType)
771 {                                                 708 {
772   G4String nam = aParticleType.GetParticleName    709   G4String nam = aParticleType.GetParticleName();
773   if (nam == "GenericIon" || nam == "proton" | << 710   if(nam == "GenericIon" || nam == "proton" 
774       || nam == "alpha" || nam == "He3")       << 711      || nam == "deuteron" || nam == "triton" || nam == "alpha" || nam == "He3") {
775   {                                            << 
776     G4cout << G4endl << GetProcessName() << ":    712     G4cout << G4endl << GetProcessName() << ":   for  " << nam
777            << "    SubType= " << GetProcessSub << 713            << "    SubType= " << GetProcessSubType() 
778            << "    maxEnergy(MeV)= " << proces << 714      << "    maxEnergy(MeV)= " << processMaxEnergy/MeV << G4endl;
779   }                                               715   }
780 }                                                 716 }
781                                                   717 
782 void G4ScreenedNuclearRecoil::DumpPhysicsTable << 718 void 
                                                   >> 719 G4ScreenedNuclearRecoil::
                                                   >> 720 DumpPhysicsTable(const G4ParticleDefinition&)
                                                   >> 721 {
                                                   >> 722 }
783                                                   723 
784 // This used to be the file mhmScreenedNuclear    724 // This used to be the file mhmScreenedNuclearRecoil_native.cc
785 // it has been included here to collect this f << 725 // it has been included here to collect this file into a smaller number of packages
786 // number of packages                          << 
787                                                   726 
788 #include "G4DataVector.hh"                        727 #include "G4DataVector.hh"
                                                   >> 728 #include "G4Material.hh"
789 #include "G4Element.hh"                           729 #include "G4Element.hh"
790 #include "G4ElementVector.hh"                  << 
791 #include "G4Isotope.hh"                           730 #include "G4Isotope.hh"
792 #include "G4Material.hh"                       << 
793 #include "G4MaterialCutsCouple.hh"                731 #include "G4MaterialCutsCouple.hh"
794                                                << 732 #include "G4ElementVector.hh"
795 #include <vector>                                 733 #include <vector>
796                                                   734 
797 G4_c2_function& ZBLScreening(G4int z1, G4int z << 735 G4_c2_function &ZBLScreening(G4int z1, G4int z2, size_t npoints, G4double rMax, G4double *auval)
798 {                                              << 
799   static const size_t ncoef = 4;               << 
800   static G4double scales[ncoef] = {-3.2, -0.94 << 
801   static G4double coefs[ncoef] = {0.1818, 0.50 << 
802                                                << 
803   G4double au = 0.8854 * angstrom * 0.529 / (s << 
804   std::vector<G4double> r(npoints), phi(npoint << 
805                                                << 
806   for (size_t i = 0; i < npoints; i++) {       << 
807     G4double rr = (float)i / (float)(npoints - << 
808     r[i] = rr * rr * rMax;                     << 
809     // use quadratic r scale to make sampling  << 
810     G4double sum = 0.0;                        << 
811     for (size_t j = 0; j < ncoef; j++)         << 
812       sum += coefs[j] * std::exp(scales[j] * r << 
813     phi[i] = sum;                              << 
814   }                                            << 
815                                                << 
816   // compute the derivative at the origin for  << 
817   G4double phiprime0 = 0.0;                    << 
818   for (size_t j = 0; j < ncoef; j++)           << 
819     phiprime0 += scales[j] * coefs[j] * std::e << 
820   phiprime0 *= (1.0 / au);  // put back in nat << 
821                                                << 
822   *auval = au;                                 << 
823   return c2.lin_log_interpolating_function().l << 
824 }                                              << 
825                                                << 
826 G4_c2_function& MoliereScreening(G4int z1, G4i << 
827 {                                              << 
828   static const size_t ncoef = 3;               << 
829   static G4double scales[ncoef] = {-6.0, -1.2, << 
830   static G4double coefs[ncoef] = {0.10, 0.55,  << 
831                                                << 
832   G4double au = 0.8853 * 0.529 * angstrom / st << 
833   std::vector<G4double> r(npoints), phi(npoint << 
834                                                << 
835   for (size_t i = 0; i < npoints; i++) {       << 
836     G4double rr = (float)i / (float)(npoints - << 
837     r[i] = rr * rr * rMax;                     << 
838     // use quadratic r scale to make sampling  << 
839     G4double sum = 0.0;                        << 
840     for (size_t j = 0; j < ncoef; j++)         << 
841       sum += coefs[j] * std::exp(scales[j] * r << 
842     phi[i] = sum;                              << 
843   }                                            << 
844                                                << 
845   // compute the derivative at the origin for  << 
846   G4double phiprime0 = 0.0;                    << 
847   for (size_t j = 0; j < ncoef; j++)           << 
848     phiprime0 += scales[j] * coefs[j] * std::e << 
849   phiprime0 *= (1.0 / au);  // put back in nat << 
850                                                << 
851   *auval = au;                                 << 
852   return c2.lin_log_interpolating_function().l << 
853 }                                              << 
854                                                << 
855 G4_c2_function& LJScreening(G4int z1, G4int z2 << 
856 {                                              << 
857   // from Loftager, Besenbacher, Jensen & Sore << 
858   // PhysRev A20, 1443++, 1979                 << 
859   G4double au = 0.8853 * 0.529 * angstrom / st << 
860   std::vector<G4double> r(npoints), phi(npoint << 
861                                                << 
862   for (size_t i = 0; i < npoints; i++) {       << 
863     G4double rr = (float)i / (float)(npoints - << 
864     r[i] = rr * rr * rMax;                     << 
865     // use quadratic r scale to make sampling  << 
866                                                << 
867     G4double y = std::sqrt(9.67 * r[i] / au);  << 
868     G4double ysq = y * y;                      << 
869     G4double phipoly = 1 + y + 0.3344 * ysq +  << 
870     phi[i] = phipoly * std::exp(-y);           << 
871     // G4cout << r[i] << " " << phi[i] << G4en << 
872   }                                            << 
873                                                << 
874   // compute the derivative at the origin for  << 
875   G4double logphiprime0 = (9.67 / 2.0) * (2 *  << 
876   // #avoid 0/0 on first element               << 
877   logphiprime0 *= (1.0 / au);  // #put back in << 
878                                                << 
879   *auval = au;                                 << 
880   return c2.lin_log_interpolating_function().l << 
881 }                                              << 
882                                                << 
883 G4_c2_function& LJZBLScreening(G4int z1, G4int << 
884 {                                              << 
885   // hybrid of LJ and ZBL, uses LJ if x < 0.25 << 
886   /// connector in between.  These numbers are << 
887   // is very near the point where the function << 
888   G4double auzbl, aulj;                        << 
889                                                << 
890   c2p zbl = ZBLScreening(z1, z2, npoints, rMax << 
891   c2p lj = LJScreening(z1, z2, npoints, rMax,  << 
892                                                << 
893   G4double au = (auzbl + aulj) * 0.5;          << 
894   lj->set_domain(lj->xmin(), 0.25 * au);       << 
895   zbl->set_domain(1.5 * au, zbl->xmax());      << 
896                                                << 
897   c2p conn = c2.connector_function(lj->xmax(), << 
898   c2_piecewise_function_p<G4double>& pw = c2.p << 
899   c2p keepit(pw);                              << 
900   pw.append_function(lj);                      << 
901   pw.append_function(conn);                    << 
902   pw.append_function(zbl);                     << 
903                                                << 
904   *auval = au;                                 << 
905   keepit.release_for_return();                 << 
906   return pw;                                   << 
907 }                                              << 
908                                                << 
909 G4NativeScreenedCoulombCrossSection::~G4Native << 
910                                                << 
911 G4NativeScreenedCoulombCrossSection::G4NativeS << 
912 {                                              << 
913   AddScreeningFunction("zbl", ZBLScreening);   << 
914   AddScreeningFunction("lj", LJScreening);     << 
915   AddScreeningFunction("mol", MoliereScreening << 
916   AddScreeningFunction("ljzbl", LJZBLScreening << 
917 }                                              << 
918                                                << 
919 std::vector<G4String> G4NativeScreenedCoulombC << 
920 {                                                 736 {
921   std::vector<G4String> keys;                  << 737         static const size_t ncoef=4;
922   // find the available screening keys         << 738         static G4double scales[ncoef]={-3.2, -0.9432, -0.4028, -0.2016};
923   std::map<std::string, ScreeningFunc>::const_ << 739         static G4double coefs[ncoef]={0.1818,0.5099,0.2802,0.0281};
924   for (; sfunciter != phiMap.end(); sfunciter+ << 740         
925     keys.push_back((*sfunciter).first);        << 741         G4double au=0.8854*angstrom*0.529/(std::pow(z1, 0.23)+std::pow(z2,0.23));
926   return keys;                                 << 742         std::vector<G4double> r(npoints), phi(npoints);
927 }                                              << 743         
928                                                << 744         for(size_t i=0; i<npoints; i++) {
929 static inline G4double cm_energy(G4double a1,  << 745                 G4double rr=(float)i/(float)(npoints-1);
930 {                                              << 746                 r[i]=rr*rr*rMax; // use quadratic r scale to make sampling fine near the center
931   // "relativistically correct energy in CM fr << 747                 G4double sum=0.0;
932   G4double m1 = a1 * amu_c2, mass2 = a2 * amu_ << 748                 for(size_t j=0; j<ncoef; j++) sum+=coefs[j]*std::exp(scales[j]*r[i]/au);
933   G4double mc2 = (m1 + mass2);                 << 749                 phi[i]=sum;
934   G4double f = 2.0 * mass2 * t0 / (mc2 * mc2); << 750         }
935   // old way: return (f < 1e-6) ?  0.5*mc2*f : << 
936   // formally equivalent to previous, but nume << 
937   // f without conditional                     << 
938   // uses identity (sqrt(1+x) - 1)(sqrt(1+x) + << 
939   return mc2 * f / (std::sqrt(1.0 + f) + 1.0); << 
940 }                                              << 
941                                                << 
942 static inline G4double thetac(G4double m1, G4d << 
943 {                                              << 
944   G4double s2th2 = eratio * ((m1 + mass2) * (m << 
945   G4double sth2 = std::sqrt(s2th2);            << 
946   return 2.0 * std::asin(sth2);                << 
947 }                                              << 
948                                                   751 
949 void G4NativeScreenedCoulombCrossSection::Load << 752         // compute the derivative at the origin for the spline
950                                                << 753         G4double phiprime0=0.0;
951 {                                              << 754         for(size_t j=0; j<ncoef; j++) phiprime0+=scales[j]*coefs[j]*std::exp(scales[j]*r[0]/au);
952   static const size_t sigLen = 200;            << 755         phiprime0*=(1.0/au); // put back in natural units;
953   // since sigma doesn't matter much, a very c << 756         
954   G4DataVector energies(sigLen);               << 757         *auval=au;
955   G4DataVector data(sigLen);                   << 758         return c2.lin_log_interpolating_function().load(r, phi, false, phiprime0,true,0);
956                                                << 759 }
957   a1 = standardmass(z1);                       << 760 
958   // use standardized values for mass for buil << 761 G4_c2_function &MoliereScreening(G4int z1, G4int z2, size_t npoints, G4double rMax, G4double *auval)
959                                                << 762 {        
960   const G4MaterialTable* materialTable = G4Mat << 763         static const size_t ncoef=3;
961   G4int nMaterials = G4Material::GetNumberOfMa << 764         static G4double scales[ncoef]={-6.0, -1.2, -0.3};
962                                                << 765         static G4double coefs[ncoef]={0.10, 0.55, 0.35};
963   for (G4int im = 0; im < nMaterials; im++) {  << 766         
964     const G4Material* material = (*materialTab << 767         G4double au=0.8853*0.529*angstrom/std::sqrt(std::pow(z1, 0.6667)+std::pow(z2,0.6667));
965     const G4ElementVector* elementVector = mat << 768         std::vector<G4double> r(npoints), phi(npoints);
966     const G4int nMatElements = material->GetNu << 769         
967                                                << 770         for(size_t i=0; i<npoints; i++) {
968     for (G4int iEl = 0; iEl < nMatElements; iE << 771                 G4double rr=(float)i/(float)(npoints-1);
969       const G4Element* element = (*elementVect << 772                 r[i]=rr*rr*rMax; // use quadratic r scale to make sampling fine near the center
970       G4int Z = element->GetZasInt();          << 773                 G4double sum=0.0;
971       G4double a2 = element->GetA() * (mole /  << 774                 for(size_t j=0; j<ncoef; j++) sum+=coefs[j]*std::exp(scales[j]*r[i]/au);
972                                                << 775                 phi[i]=sum;
973       if (sigmaMap.find(Z) != sigmaMap.end())  << 
974       // we've already got this element        << 
975                                                << 
976       // find the screening function generator << 
977       std::map<std::string, ScreeningFunc>::it << 
978       if (sfunciter == phiMap.end()) {         << 
979         G4ExceptionDescription ed;             << 
980         ed << "No such screening key <" << scr << 
981         G4Exception("G4NativeScreenedCoulombCr << 
982       }                                        << 
983       ScreeningFunc sfunc = (*sfunciter).secon << 
984                                                << 
985       G4double au;                             << 
986       G4_c2_ptr screen = sfunc(z1, Z, 200, 50. << 
987       // generate the screening data           << 
988       G4ScreeningTables st;                    << 
989                                                << 
990       st.EMphiData = screen;  // save our phi  << 
991       st.z1 = z1;                              << 
992       st.m1 = a1;                              << 
993       st.z2 = Z;                               << 
994       st.m2 = a2;                              << 
995       st.emin = recoilCutoff;                  << 
996       st.au = au;                              << 
997                                                << 
998       // now comes the hard part... build the  << 
999       // tables from the phi table             << 
1000       // based on (pi-thetac) = pi*beta*alpha << 
1001       // alpha is very nearly unity, always   << 
1002       // so just solve it wth alpha=1, which  << 
1003       // much easier                          << 
1004       // this function returns an approximati << 
1005       // (beta/x0)^2=phi(x0)/(eps*x0)-1 ~ ((p << 
1006       // Since we don't need exact sigma valu << 
1007       // (within a factor of 2 almost always) << 
1008       // this rearranges to phi(x0)/(x0*eps)  << 
1009       // 2*theta/pi - theta^2/pi^2            << 
1010                                               << 
1011       c2_linear_p<G4double>& c2eps = c2.linea << 
1012       // will store an appropriate eps inside << 
1013       G4_c2_ptr phiau = screen(c2.linear(0.0, << 
1014       G4_c2_ptr x0func(phiau / c2eps);        << 
1015       // this will be phi(x)/(x*eps) when c2e << 
1016       x0func->set_domain(1e-6 * angstrom / au << 
1017       // needed for inverse function          << 
1018       // use the c2_inverse_function interfac << 
1019       // it is more efficient for an ordered  << 
1020       // computation of values.               << 
1021       G4_c2_ptr x0_solution(c2.inverse_functi << 
1022                                               << 
1023       G4double m1c2 = a1 * amu_c2;            << 
1024       G4double escale = z1 * Z * elm_coupling << 
1025       // energy at screening distance         << 
1026       G4double emax = m1c2;                   << 
1027       // model is doubtful in very relativist << 
1028       G4double eratkin = 0.9999 * (4 * a1 * a << 
1029       // #maximum kinematic ratio possible at << 
1030       G4double cmfact0 = st.emin / cm_energy( << 
1031       G4double l1 = std::log(emax);           << 
1032       G4double l0 = std::log(st.emin * cmfact << 
1033                                               << 
1034       if (verbosity >= 1)                     << 
1035         G4cout << "Native Screening: " << scr << 
1036                << a2 << " " << recoilCutoff < << 
1037                                               << 
1038       for (size_t idx = 0; idx < sigLen; idx+ << 
1039         G4double ee = std::exp(idx * ((l1 - l << 
1040         G4double gamma = 1.0 + ee / m1c2;     << 
1041         G4double eratio = (cmfact0 * st.emin) << 
1042         // factor by which ee needs to be red << 
1043         G4double theta = thetac(gamma * a1, a << 
1044                                               << 
1045         G4double eps = cm_energy(a1, a2, ee)  << 
1046         // #make sure lab energy is converted << 
1047         // calculations                       << 
1048         c2eps.reset(0.0, 0.0, eps);           << 
1049         // set correct slope in this function << 
1050                                               << 
1051         G4double q = theta / pi;              << 
1052         // G4cout << ee << " " << m1c2 << " " << 
1053         // << eps << " " << theta << " " << q << 
1054         // old way using root finder          << 
1055         // G4double x0= x0func->find_root(1e- << 
1056         // 0.9999*screen.xmax()/au, 1.0, 2*q- << 
1057         // new way using c2_inverse_function  << 
1058         // useful information so should be a  << 
1059         // since we are scanning this in stri << 
1060         G4double x0 = 0;                      << 
1061         try {                                 << 
1062           x0 = x0_solution(2 * q - q * q);    << 
1063         }                                        776         }
1064         catch (c2_exception&) {               << 777         
1065           G4Exception("G4ScreenedNuclearRecoi << 778         // compute the derivative at the origin for the spline
1066                       "failure in inverse sol << 779         G4double phiprime0=0.0;
                                                   >> 780         for(size_t j=0; j<ncoef; j++) phiprime0+=scales[j]*coefs[j]*std::exp(scales[j]*r[0]/au);
                                                   >> 781         phiprime0*=(1.0/au); // put back in natural units;
                                                   >> 782         
                                                   >> 783         *auval=au;
                                                   >> 784         return c2.lin_log_interpolating_function().load(r, phi, false, phiprime0,true,0);
                                                   >> 785 }
                                                   >> 786 
                                                   >> 787 G4_c2_function &LJScreening(G4int z1, G4int z2, size_t npoints, G4double rMax, G4double *auval)
                                                   >> 788 {        
                                                   >> 789 //from Loftager, Besenbacher, Jensen & Sorensen
                                                   >> 790 //PhysRev A20, 1443++, 1979
                                                   >> 791         G4double au=0.8853*0.529*angstrom/std::sqrt(std::pow(z1, 0.6667)+std::pow(z2,0.6667));
                                                   >> 792         std::vector<G4double> r(npoints), phi(npoints);
                                                   >> 793         
                                                   >> 794         for(size_t i=0; i<npoints; i++) {
                                                   >> 795                 G4double rr=(float)i/(float)(npoints-1);
                                                   >> 796                 r[i]=rr*rr*rMax; // use quadratic r scale to make sampling fine near the center
                                                   >> 797 
                                                   >> 798                 G4double y=std::sqrt(9.67*r[i]/au);
                                                   >> 799                 G4double ysq=y*y;
                                                   >> 800                 G4double phipoly=1+y+0.3344*ysq+0.0485*y*ysq+0.002647*ysq*ysq;
                                                   >> 801                 phi[i]=phipoly*std::exp(-y);
                                                   >> 802                 // G4cout << r[i] << " " << phi[i] << G4endl;
                                                   >> 803         }
                                                   >> 804 
                                                   >> 805         // compute the derivative at the origin for the spline
                                                   >> 806         G4double logphiprime0=(9.67/2.0)*(2*0.3344-1.0); // #avoid 0/0 on first element
                                                   >> 807         logphiprime0 *= (1.0/au); // #put back in natural units
                                                   >> 808         
                                                   >> 809         *auval=au;
                                                   >> 810         return c2.lin_log_interpolating_function().load(r, phi, false, logphiprime0*phi[0],true,0);
                                                   >> 811 }
                                                   >> 812 
                                                   >> 813 G4_c2_function &LJZBLScreening(G4int z1, G4int z2, size_t npoints, G4double rMax, G4double *auval)
                                                   >> 814 {        
                                                   >> 815 // hybrid of LJ and ZBL, uses LJ if x < 0.25*auniv, ZBL if x > 1.5*auniv, and 
                                                   >> 816 /// connector in between.  These numbers are selected so the switchover
                                                   >> 817 // is very near the point where the functions naturally cross.
                                                   >> 818         G4double auzbl, aulj;
                                                   >> 819         
                                                   >> 820         c2p zbl=ZBLScreening(z1, z2, npoints, rMax, &auzbl);
                                                   >> 821         c2p lj=LJScreening(z1, z2, npoints, rMax, &aulj);
                                                   >> 822 
                                                   >> 823         G4double au=(auzbl+aulj)*0.5;
                                                   >> 824         lj->set_domain(lj->xmin(), 0.25*au);
                                                   >> 825         zbl->set_domain(1.5*au,zbl->xmax());
                                                   >> 826         
                                                   >> 827         c2p conn=c2.connector_function(lj->xmax(), lj, zbl->xmin(), zbl, true,0);
                                                   >> 828         c2_piecewise_function_p<G4double> &pw=c2.piecewise_function();
                                                   >> 829         c2p keepit(pw);
                                                   >> 830         pw.append_function(lj);
                                                   >> 831         pw.append_function(conn);
                                                   >> 832         pw.append_function(zbl);
                                                   >> 833         
                                                   >> 834         *auval=au;
                                                   >> 835         keepit.release_for_return();
                                                   >> 836         return pw;
                                                   >> 837 }
                                                   >> 838 
                                                   >> 839 G4NativeScreenedCoulombCrossSection::~G4NativeScreenedCoulombCrossSection() {
                                                   >> 840 }
                                                   >> 841 
                                                   >> 842 G4NativeScreenedCoulombCrossSection::G4NativeScreenedCoulombCrossSection() {
                                                   >> 843         AddScreeningFunction("zbl", ZBLScreening);
                                                   >> 844         AddScreeningFunction("lj", LJScreening);        
                                                   >> 845         AddScreeningFunction("mol", MoliereScreening);        
                                                   >> 846         AddScreeningFunction("ljzbl", LJZBLScreening);        
                                                   >> 847 }
                                                   >> 848 
                                                   >> 849 std::vector<G4String> G4NativeScreenedCoulombCrossSection::GetScreeningKeys() const {
                                                   >> 850         std::vector<G4String> keys;
                                                   >> 851         // find the available screening keys
                                                   >> 852         std::map<std::string, ScreeningFunc>::const_iterator sfunciter=phiMap.begin();
                                                   >> 853         for(; sfunciter != phiMap.end(); sfunciter++) keys.push_back((*sfunciter).first);
                                                   >> 854         return keys;
                                                   >> 855 }
                                                   >> 856 
                                                   >> 857 static inline G4double cm_energy(G4double a1, G4double a2, G4double t0) {
                                                   >> 858         // "relativistically correct energy in CM frame"
                                                   >> 859         G4double m1=a1*amu_c2, mass2=a2*amu_c2;
                                                   >> 860         G4double mc2=(m1+mass2);
                                                   >> 861         G4double f=2.0*mass2*t0/(mc2*mc2);
                                                   >> 862         // old way: return (f < 1e-6) ?  0.5*mc2*f : mc2*(std::sqrt(1.0+f)-1.0);
                                                   >> 863         // formally equivalent to previous, but numerically stable for all f without conditional
                                                   >> 864         // uses identity (sqrt(1+x) - 1)(sqrt(1+x) + 1) = x
                                                   >> 865         return mc2*f/(std::sqrt(1.0+f)+1.0); 
                                                   >> 866 }
                                                   >> 867 
                                                   >> 868 static inline G4double  thetac(G4double m1, G4double mass2, G4double eratio) {
                                                   >> 869         G4double s2th2=eratio*( (m1+mass2)*(m1+mass2)/(4.0*m1*mass2) );
                                                   >> 870         G4double sth2=std::sqrt(s2th2);
                                                   >> 871         return 2.0*std::asin(sth2);
                                                   >> 872 }
                                                   >> 873 
                                                   >> 874 void G4NativeScreenedCoulombCrossSection::LoadData(G4String screeningKey, G4int z1, G4double a1, G4double recoilCutoff)
                                                   >> 875 {                        
                                                   >> 876         static const size_t sigLen=200; // since sigma doesn't matter much, a very coarse table will do                        
                                                   >> 877         G4DataVector energies(sigLen);
                                                   >> 878         G4DataVector data(sigLen);
                                                   >> 879         
                                                   >> 880         a1=standardmass(z1); // use standardized values for mass for building tables
                                                   >> 881         
                                                   >> 882         const G4MaterialTable* materialTable = G4Material::GetMaterialTable();
                                                   >> 883         if (materialTable == 0) { return; }
                                                   >> 884         //G4Exception("mhmNativeCrossSection::LoadData - no MaterialTable found)");
                                                   >> 885         
                                                   >> 886         G4int nMaterials = G4Material::GetNumberOfMaterials();
                                                   >> 887         
                                                   >> 888         for (G4int im=0; im<nMaterials; im++)
                                                   >> 889     {
                                                   >> 890                 const G4Material* material= (*materialTable)[im];
                                                   >> 891                 const G4ElementVector* elementVector = material->GetElementVector();
                                                   >> 892                 const G4int nMatElements = material->GetNumberOfElements();
                                                   >> 893                 
                                                   >> 894                 for (G4int iEl=0; iEl<nMatElements; iEl++)
                                                   >> 895                 {
                                                   >> 896                         G4Element* element = (*elementVector)[iEl];
                                                   >> 897                         G4int Z = (G4int) element->GetZ();
                                                   >> 898                         G4double a2=element->GetA()*(mole/gram);
                                                   >> 899                         
                                                   >> 900                         if(sigmaMap.find(Z)!=sigmaMap.end()) continue; // we've already got this element
                                                   >> 901                         
                                                   >> 902                         // find the screening function generator we need
                                                   >> 903                         std::map<std::string, ScreeningFunc>::iterator sfunciter=phiMap.find(screeningKey);
                                                   >> 904                         if(sfunciter==phiMap.end()) {
                                                   >> 905                                 G4cout << "no such screening key " << screeningKey << G4endl; // FIXME later
                                                   >> 906                                 exit(1);
                                                   >> 907                         }
                                                   >> 908                         ScreeningFunc sfunc=(*sfunciter).second;
                                                   >> 909                         
                                                   >> 910                         G4double au; 
                                                   >> 911                         G4_c2_ptr screen=sfunc(z1, Z, 200, 50.0*angstrom, &au); // generate the screening data
                                                   >> 912                         G4ScreeningTables st;
                                                   >> 913         
                                                   >> 914                         st.EMphiData=screen; //save our phi table
                                                   >> 915                         st.z1=z1; st.m1=a1; st.z2=Z; st.m2=a2; st.emin=recoilCutoff;
                                                   >> 916                         st.au=au;
                                                   >> 917 
                                                   >> 918                         // now comes the hard part... build the total cross section tables from the phi table                        
                                                   >> 919                         //based on (pi-thetac) = pi*beta*alpha/x0, but noting that alpha is very nearly unity, always
                                                   >> 920                         //so just solve it wth alpha=1, which makes the solution much easier
                                                   >> 921                         //this function returns an approximation to (beta/x0)^2=phi(x0)/(eps*x0)-1 ~ ((pi-thetac)/pi)^2
                                                   >> 922                         //Since we don't need exact sigma values, this is good enough (within a factor of 2 almost always)
                                                   >> 923                         //this rearranges to phi(x0)/(x0*eps) = 2*theta/pi - theta^2/pi^2
                                                   >> 924                         
                                                   >> 925                         c2_linear_p<G4double> &c2eps=c2.linear(0.0, 0.0, 1.0); // will store an appropriate eps inside this in loop
                                                   >> 926                         G4_c2_ptr phiau=screen(c2.linear(0.0, 0.0, au));
                                                   >> 927                         G4_c2_ptr x0func(phiau/c2eps); // this will be phi(x)/(x*eps) when c2eps is correctly set
                                                   >> 928                         x0func->set_domain(1e-6*angstrom/au, 0.9999*screen->xmax()/au); // needed for inverse function
                                                   >> 929                         // use the c2_inverse_function interface for the root finder... it is more efficient for an ordered 
                                                   >> 930                         // computation of values.
                                                   >> 931                         G4_c2_ptr x0_solution(c2.inverse_function(x0func));
                                                   >> 932                         
                                                   >> 933                         G4double m1c2=a1*amu_c2;
                                                   >> 934                         G4double escale=z1*Z*elm_coupling/au; // energy at screening distance
                                                   >> 935                         G4double emax=m1c2; // model is doubtful in very relativistic range
                                                   >> 936                         G4double eratkin=0.9999*(4*a1*a2)/((a1+a2)*(a1+a2)); // #maximum kinematic ratio possible at 180 degrees
                                                   >> 937                         G4double cmfact0=st.emin/cm_energy(a1, a2, st.emin);
                                                   >> 938                         G4double l1=std::log(emax);
                                                   >> 939                         G4double l0=std::log(st.emin*cmfact0/eratkin);
                                                   >> 940 
                                                   >> 941                         if(verbosity >=1) 
                                                   >> 942                                 G4cout << "Native Screening: " << screeningKey << " " << z1 << " " << a1 << " " << 
                                                   >> 943                                         Z << " " << a2 << " " << recoilCutoff << G4endl;
                                                   >> 944                         
                                                   >> 945                         for(size_t idx=0; idx<sigLen; idx++) {
                                                   >> 946                                 G4double ee=std::exp(idx*((l1-l0)/sigLen)+l0);
                                                   >> 947                                 G4double gamma=1.0+ee/m1c2;
                                                   >> 948                                 G4double eratio=(cmfact0*st.emin)/ee; // factor by which ee needs to be reduced to get emin
                                                   >> 949                                 G4double theta=thetac(gamma*a1, a2, eratio);
                                                   >> 950                         
                                                   >> 951                                 G4double eps=cm_energy(a1, a2, ee)/escale; // #make sure lab energy is converted to CM for these calculations
                                                   >> 952                                 c2eps.reset(0.0, 0.0, eps); // set correct slope in this function
                                                   >> 953                                 
                                                   >> 954                                 G4double q=theta/pi;
                                                   >> 955                                 // G4cout << ee << " " << m1c2 << " " << gamma << " " << eps << " " << theta << " " << q << G4endl;
                                                   >> 956                                 // old way using root finder
                                                   >> 957                                 // G4double x0= x0func->find_root(1e-6*angstrom/au, 0.9999*screen.xmax()/au, 1.0, 2*q-q*q);
                                                   >> 958                                 // new way using c2_inverse_function which caches useful information so should be a bit faster
                                                   >> 959                                 // since we are scanning this in strict order.
                                                   >> 960                                 G4double x0=0;
                                                   >> 961                                 try {
                                                   >> 962                                         x0=x0_solution(2*q-q*q);
                                                   >> 963                                 } catch(c2_exception e) {
                                                   >> 964                                   //G4Exception(G4String("G4ScreenedNuclearRecoil: failure in inverse solution to generate MFP Tables: ")+e.what());
                                                   >> 965                                 }
                                                   >> 966                                 G4double betasquared=x0*x0 - x0*phiau(x0)/eps;        
                                                   >> 967                                 G4double sigma=pi*betasquared*au*au;
                                                   >> 968                                 energies[idx]=ee;
                                                   >> 969                                 data[idx]=sigma;
                                                   >> 970                         }
                                                   >> 971                         screeningData[Z]=st;
                                                   >> 972                         sigmaMap[Z] = c2.log_log_interpolating_function().load(energies, data, true,0,true,0);
                                                   >> 973                 }
1067         }                                        974         }
1068         G4double betasquared = x0 * x0 - x0 * << 
1069         G4double sigma = pi * betasquared * a << 
1070         energies[idx] = ee;                   << 
1071         data[idx] = sigma;                    << 
1072       }                                       << 
1073       screeningData[Z] = st;                  << 
1074       sigmaMap[Z] = c2.log_log_interpolating_ << 
1075     }                                         << 
1076   }                                           << 
1077 }                                                975 }
1078                                                  976