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Geant4/particles/management/src/G4NucleiProperties.cc

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Differences between /particles/management/src/G4NucleiProperties.cc (Version 11.3.0) and /particles/management/src/G4NucleiProperties.cc (Version 1.1)


                                                   >>   1 // This code implementation is the intellectual property of
                                                   >>   2 // the GEANT4 collaboration.
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 19 // * technical work of the GEANT4 collaboratio << 
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 25 //                                                  7 //
 26 // G4NucleiProperties class implementation     <<   8 // $Id: G4NucleiProperties.cc,v 1.5.6.1.2.1 1999/12/08 17:34:09 gunter Exp $
                                                   >>   9 // GEANT4 tag $Name: geant4-01-01 $
 27 //                                                 10 //
 28 // Author: V.Lara, October 1998                <<  11 // 
 29 // History:                                    <<  12 // ------------------------------------------------------------
 30 // - 17.11.1998, H.Kurashige - Migrated into p <<  13 //  GEANT 4 class header file 
 31 // - 31.03.2009, T.Koi - Migrated to AME03     <<  14 //
 32 // ------------------------------------------- <<  15 //  For information related to this code contact:
 33                                                <<  16 //  CERN, IT Division, ASD group
 34 #include "G4NucleiProperties.hh"               <<  17 // ------------------------------------------------------------
 35                                                <<  18 //
 36 #include "G4NucleiPropertiesTableAME12.hh"     <<  19 // Hadronic Process: Nuclear De-excitations
 37 #include "G4NucleiPropertiesTheoreticalTable.h <<  20 // by V. Lara (Oct 1998)
 38 #include "G4ParticleTable.hh"                  <<  21 // Migrate into particles category by H.Kurashige (17 Nov. 98)
 39 #include "G4PhysicalConstants.hh"              <<  22 // Added Shell-Pairing corrections to the Cameron mass 
 40 #include "G4SystemOfUnits.hh"                  <<  23 // excess formula by V.Lara (9 May 99)
 41                                                << 
 42 G4ThreadLocal G4double G4NucleiProperties::mas << 
 43 G4ThreadLocal G4double G4NucleiProperties::mas << 
 44 G4ThreadLocal G4double G4NucleiProperties::mas << 
 45 G4ThreadLocal G4double G4NucleiProperties::mas << 
 46 G4ThreadLocal G4double G4NucleiProperties::mas << 
 47 G4ThreadLocal G4double G4NucleiProperties::mas << 
 48                                                << 
 49 G4double G4NucleiProperties::GetNuclearMass(co << 
 50 {                                              << 
 51   G4double mass = 0.0;                         << 
 52                                                << 
 53   if (std::fabs(A - G4int(A)) > 1.e-10) {      << 
 54     mass = NuclearMass(A, Z);                  << 
 55   }                                            << 
 56   else {                                       << 
 57     // use mass table                          << 
 58     auto iZ = G4int(Z);                        << 
 59     auto iA = G4int(A);                        << 
 60     mass = GetNuclearMass(iA, iZ);             << 
 61   }                                            << 
 62   return mass;                                 << 
 63 }                                              << 
 64                                                << 
 65 G4double G4NucleiProperties::GetNuclearMass(co << 
 66 {                                              << 
 67   if (mass_proton <= 0.0) {                    << 
 68     const G4ParticleDefinition* nucleus = null << 
 69     nucleus = G4ParticleTable::GetParticleTabl << 
 70     if (nucleus != nullptr) mass_neutron = nuc << 
 71                                                << 
 72     nucleus = G4ParticleTable::GetParticleTabl << 
 73     if (nucleus != nullptr) mass_deuteron = nu << 
 74                                                << 
 75     nucleus = G4ParticleTable::GetParticleTabl << 
 76     if (nucleus != nullptr) mass_triton = nucl << 
 77                                                << 
 78     nucleus = G4ParticleTable::GetParticleTabl << 
 79     if (nucleus != nullptr) mass_alpha = nucle << 
 80                                                << 
 81     nucleus = G4ParticleTable::GetParticleTabl << 
 82     if (nucleus != nullptr) mass_He3 = nucleus << 
 83                                                << 
 84     nucleus = G4ParticleTable::GetParticleTabl << 
 85     if (nucleus != nullptr) mass_proton = nucl << 
 86   }                                            << 
 87                                                << 
 88   if (A < 1 || Z < 0 || Z > A) {               << 
 89 #ifdef G4VERBOSE                               << 
 90     if (G4ParticleTable::GetParticleTable()->G << 
 91       G4cout << "G4NucleiProperties::GetNuclea << 
 92              << G4endl;                        << 
 93     }                                          << 
 94 #endif                                         << 
 95     return 0.0;                                << 
 96   }                                            << 
 97                                                << 
 98   G4double mass = -1.;                         << 
 99   if ((Z <= 2)) {                              << 
100     // light nuclei                            << 
101     if ((Z == 1) && (A == 1)) {                << 
102       mass = mass_proton;                      << 
103     }                                          << 
104     else if ((Z == 0) && (A == 1)) {           << 
105       mass = mass_neutron;                     << 
106     }                                          << 
107     else if ((Z == 1) && (A == 2)) {           << 
108       mass = mass_deuteron;                    << 
109     }                                          << 
110     else if ((Z == 1) && (A == 3)) {           << 
111       mass = mass_triton;                      << 
112     }                                          << 
113     else if ((Z == 2) && (A == 4)) {           << 
114       mass = mass_alpha;                       << 
115     }                                          << 
116     else if ((Z == 2) && (A == 3)) {           << 
117       mass = mass_He3;                         << 
118     }                                          << 
119   }                                            << 
120                                                << 
121   if (mass < 0.) {                             << 
122     if (G4NucleiPropertiesTableAME12::IsInTabl << 
123       // AME table                             << 
124       mass = G4NucleiPropertiesTableAME12::Get << 
125     }                                          << 
126     else if (G4NucleiPropertiesTheoreticalTabl << 
127       // Theoretical table                     << 
128       mass = G4NucleiPropertiesTheoreticalTabl << 
129     }                                          << 
130     else if (Z == A) {                         << 
131       mass = A * mass_proton;                  << 
132     }                                          << 
133     else if (0 == Z) {                         << 
134       mass = A * mass_neutron;                 << 
135     }                                          << 
136     else {                                     << 
137       mass = NuclearMass(G4double(A), G4double << 
138     }                                          << 
139   }                                            << 
140                                                << 
141   if (mass < 0.) mass = 0.0;                   << 
142   return mass;                                 << 
143 }                                              << 
144                                                << 
145 G4bool G4NucleiProperties::IsInStableTable(con << 
146 {                                              << 
147   auto iA = G4int(A);                          << 
148   auto iZ = G4int(Z);                          << 
149   return IsInStableTable(iA, iZ);              << 
150 }                                              << 
151                                                << 
152 G4bool G4NucleiProperties::IsInStableTable(con << 
153 {                                              << 
154   if (A < 1 || Z < 0 || Z > A) {               << 
155 #ifdef G4VERBOSE                               << 
156     if (G4ParticleTable::GetParticleTable()->G << 
157       G4cout << "G4NucleiProperties::IsInStabl << 
158              << " and Z = " << Z << G4endl;    << 
159     }                                          << 
160 #endif                                         << 
161     return false;                              << 
162   }                                            << 
163                                                << 
164   return G4NucleiPropertiesTableAME12::IsInTab << 
165 }                                              << 
166                                                    24 
167 G4double G4NucleiProperties::GetMassExcess(con << 
168 {                                              << 
169   auto iA = G4int(A);                          << 
170   auto iZ = G4int(Z);                          << 
171   return GetMassExcess(iA, iZ);                << 
172 }                                              << 
173                                                    25 
174 G4double G4NucleiProperties::GetMassExcess(con <<  26 #include "G4NucleiProperties.hh"
175 {                                              << 
176   if (A < 1 || Z < 0 || Z > A) {               << 
177 #ifdef G4VERBOSE                               << 
178     if (G4ParticleTable::GetParticleTable()->G << 
179       G4cout << "G4NucleiProperties::GetMassEx << 
180              << G4endl;                        << 
181     }                                          << 
182 #endif                                         << 
183     return 0.0;                                << 
184   }                                            << 
185                                                << 
186   if (G4NucleiPropertiesTableAME12::IsInTable( << 
187     // AME table                               << 
188     return G4NucleiPropertiesTableAME12::GetMa << 
189   }                                            << 
190   if (G4NucleiPropertiesTheoreticalTable::IsIn << 
191     return G4NucleiPropertiesTheoreticalTable: << 
192   }                                            << 
193   return MassExcess(A, Z);                     << 
194 }                                              << 
195                                                    27 
196 G4double G4NucleiProperties::GetAtomicMass(con << 
197 {                                              << 
198   if (A < 1 || Z < 0 || Z > A) {               << 
199 #ifdef G4VERBOSE                               << 
200     if (G4ParticleTable::GetParticleTable()->G << 
201       G4cout << "G4NucleiProperties::GetAtomic << 
202              << G4endl;                        << 
203     }                                          << 
204 #endif                                         << 
205     return 0.0;                                << 
206   }                                            << 
207   if (std::fabs(A - G4int(A)) > 1.e-10) {      << 
208     return AtomicMass(A, Z);                   << 
209   }                                            << 
210                                                << 
211   auto iA = G4int(A);                          << 
212   auto iZ = G4int(Z);                          << 
213   if (G4NucleiPropertiesTableAME12::IsInTable( << 
214     return G4NucleiPropertiesTableAME12::GetAt << 
215   }                                            << 
216   if (G4NucleiPropertiesTheoreticalTable::IsIn << 
217     return G4NucleiPropertiesTheoreticalTable: << 
218   }                                            << 
219   return AtomicMass(A, Z);                     << 
220 }                                              << 
221                                                    28 
222 G4double G4NucleiProperties::GetBindingEnergy( << 
223 {                                              << 
224   auto iA = G4int(A);                          << 
225   auto iZ = G4int(Z);                          << 
226   return GetBindingEnergy(iA, iZ);             << 
227 }                                              << 
228                                                    29 
229 G4double G4NucleiProperties::GetBindingEnergy( <<  30 G4double  G4NucleiProperties::AtomicMass(G4double A, G4double Z)
230 {                                                  31 {
231   if (A < 1 || Z < 0 || Z > A) {               <<  32   const G4double hydrogen_mass_excess = G4NucleiPropertiesTable::GetMassExcess(1,1);
232 #ifdef G4VERBOSE                               <<  33   const G4double neutron_mass_excess =  G4NucleiPropertiesTable::GetMassExcess(0,1);
233     if (G4ParticleTable::GetParticleTable()->G << 
234       G4cout << "G4NucleiProperties::GetMassEx << 
235              << G4endl;                        << 
236     }                                          << 
237 #endif                                         << 
238     return 0.0;                                << 
239   }                                            << 
240                                                << 
241   if (G4NucleiPropertiesTableAME12::IsInTable( << 
242     return G4NucleiPropertiesTableAME12::GetBi << 
243   }                                            << 
244   if (G4NucleiPropertiesTheoreticalTable::IsIn << 
245     return G4NucleiPropertiesTheoreticalTable: << 
246   }                                            << 
247   return BindingEnergy(A, Z);                  << 
248 }                                              << 
249                                                    34 
250 G4double G4NucleiProperties::MassExcess(G4doub << 
251 {                                              << 
252   return GetAtomicMass(A, Z) - A * amu_c2;     << 
253 }                                              << 
254                                                << 
255 G4double G4NucleiProperties::AtomicMass(G4doub << 
256 {                                              << 
257   G4double hydrogen_mass_excess;               << 
258   G4double neutron_mass_excess;                << 
259   hydrogen_mass_excess = G4NucleiPropertiesTab << 
260   neutron_mass_excess = G4NucleiPropertiesTabl << 
261   G4double mass =                                  35   G4double mass =
262     (A - Z) * neutron_mass_excess + Z * hydrog <<  36       (A-Z)*neutron_mass_excess + Z*hydrogen_mass_excess - BindingEnergy(A,Z) + A*amu_c2;
263   return mass;                                 << 
264 }                                              << 
265                                                << 
266 G4double G4NucleiProperties::NuclearMass(G4dou << 
267 {                                              << 
268   if (A < 1 || Z < 0 || Z > A) {               << 
269 #ifdef G4VERBOSE                               << 
270     if (G4ParticleTable::GetParticleTable()->G << 
271       G4cout << "G4NucleiProperties::NuclearMa << 
272              << G4endl;                        << 
273     }                                          << 
274 #endif                                         << 
275     return 0.0;                                << 
276   }                                            << 
277                                                << 
278   G4double mass = AtomicMass(A, Z);            << 
279                                                << 
280   // atomic mass is converted to nuclear mass  << 
281   // formula in  AME03 and 12                  << 
282   //                                           << 
283   mass -= Z * electron_mass_c2;                << 
284   mass += (14.4381 * std::pow(Z, 2.39) + 1.554 << 
285                                                    37 
286   return mass;                                     38   return mass;
287 }                                                  39 }
288                                                    40 
289 G4double G4NucleiProperties::BindingEnergy(G4d <<  41 G4double  G4NucleiProperties::BindingEnergy(G4double A, G4double Z)
290 {                                              <<  42 { 
291   //                                               43   //
292   // Weitzsaecker's Mass formula                   44   // Weitzsaecker's Mass formula
293   //                                               45   //
294   G4int Npairing = G4int(A - Z) % 2;  // pairi <<  46   G4int Npairing = G4int(A-Z)%2;                  // pairing
295   G4int Zpairing = G4int(Z) % 2;               <<  47   G4int Zpairing = G4int(Z)%2;
296   G4double binding = -15.67 * A  // nuclear vo <<  48   G4double binding =
297                      + 17.23 * std::pow(A, 2.  <<  49       - 15.67*A                           // nuclear volume
298                      + 93.15 * ((A / 2. - Z) * <<  50       + 17.23*pow(A,2./3.)                // surface energy
299                      + 0.6984523 * Z * Z * std <<  51       + 93.15*((A/2.-Z)*(A/2.-Z))/A       // asymmetry
300   if (Npairing == Zpairing) {                  <<  52       + 0.6984523*Z*Z*pow(A,-1./3.);      // coulomb
301     binding += (Npairing + Zpairing - 1) * 12. <<  53   if( Npairing == Zpairing ) binding += (Npairing+Zpairing-1) * 12.0 / sqrt(A);  // pairing
302   }                                            << 
303                                                    54 
304   return -binding * MeV;                       <<  55   return -binding*MeV;
305 }                                                  56 }
                                                   >>  57 
                                                   >>  58 
                                                   >>  59 G4double G4NucleiProperties::GetNuclearMass(const G4double A, const G4double Z)
                                                   >>  60 {
                                                   >>  61   if (A < 1 || Z < 0 || Z > A) {
                                                   >>  62     G4cout << "G4NucleiProperties::GetNuclearMass: Wrong values for A = " << A 
                                                   >>  63          << " and Z = " << Z << G4endl;
                                                   >>  64     return 0.0;
                                                   >>  65   } else {
                                                   >>  66     G4ParticleDefinition * nucleus = 0;
                                                   >>  67     if ( (Z<=2) ) {
                                                   >>  68       if ( (Z==1)&&(A==1) ) {
                                                   >>  69         nucleus = G4ParticleTable::GetParticleTable()->FindParticle("proton"); // proton 
                                                   >>  70       } else if ( (Z==0)&&(A==1) ) {
                                                   >>  71           nucleus = G4ParticleTable::GetParticleTable()->FindParticle("neutron"); // neutron 
                                                   >>  72         } else if ( (Z==1)&&(A==2) ) {
                                                   >>  73           nucleus = G4ParticleTable::GetParticleTable()->FindParticle("deuteron"); // deuteron 
                                                   >>  74         } else if ( (Z==1)&&(A==3) ) {
                                                   >>  75           nucleus = G4ParticleTable::GetParticleTable()->FindParticle("triton"); // triton 
                                                   >>  76         } else if ( (Z==2)&&(A==4) ) {
                                                   >>  77           nucleus = G4ParticleTable::GetParticleTable()->FindParticle("alpha"); // alpha 
                                                   >>  78         } else if ( (Z==2)&&(A==3) ) {
                                                   >>  79           nucleus = G4ParticleTable::GetParticleTable()->FindParticle("He3"); // He3 
                                                   >>  80       }
                                                   >>  81       }
                                                   >>  82     if (nucleus!=0) {
                                                   >>  83       return nucleus->GetPDGMass();
                                                   >>  84       }else {
                                                   >>  85       return GetAtomicMass(A,Z) - Z*electron_mass_c2 + 1.433e-5*MeV*pow(Z,2.39);
                                                   >>  86     }
                                                   >>  87   }
                                                   >>  88 }
                                                   >>  89 
                                                   >>  90 
                                                   >>  91 // G4double G4NucleiProperties::CameronMassExcess(const G4int A, const G4int Z)
                                                   >>  92 // {
                                                   >>  93 //  const G4double alpha = -17.0354*MeV;
                                                   >>  94 //  const G4double beta = -31.4506*MeV;
                                                   >>  95 //  const G4double phi = 44.2355*MeV;
                                                   >>  96 //  const G4double gamma = 25.8357*MeV;
                                                   >>  97 //   
                                                   >>  98 //  const G4double A13 = pow(G4double(A),1.0/3.0);
                                                   >>  99 //  const G4double A23 = A13*A13;
                                                   >> 100 //  const G4double A43 = A23*A23;
                                                   >> 101 //  const G4double Z43 = pow(G4double(Z),4.0/3.0);
                                                   >> 102 //  G4double D = (G4double(A) - 2.0*G4double(Z))/G4double(A);
                                                   >> 103 //  D *= D; // D = pow((A-2Z)/A,2)
                                                   >> 104 //   
                                                   >> 105 //   
                                                   >> 106 //  // Surface term
                                                   >> 107 //  G4double SurfaceEnergy = (gamma - phi*D)*(1.0 - 0.62025/A23)*(1.0 - 0.62025/A23)*A23;
                                                   >> 108 // 
                                                   >> 109 //  // Coulomb term
                                                   >> 110 //  G4double CoulombEnergy = 0.779*MeV*(G4double(Z*(Z-1))/A13)*(1.0-1.5849/A23+1.2273/A+1.5772/A43);
                                                   >> 111 // 
                                                   >> 112 //  // Exchange term
                                                   >> 113 //  G4double ExchangeEnergy = -0.4323*MeV*(Z43/A13)*(1.0-0.57811/A13-0.14518/A23+0.49597/A);
                                                   >> 114 //  
                                                   >> 115 //  // Volume term
                                                   >> 116 //  G4double VolumeEnergy = G4double(A)*(alpha-beta*D);
                                                   >> 117 // 
                                                   >> 118 //  // Shell+Pairing corrections for protons
                                                   >> 119 //  G4double SPcorrectionZ;
                                                   >> 120 //  if (Z <= TableSize) SPcorrectionZ = SPZTable[Z-1]*MeV;
                                                   >> 121 //  else SPcorrectionZ = 0.0;
                                                   >> 122 //  
                                                   >> 123 //  // Shell+Pairing corrections for protons
                                                   >> 124 //  G4int N = A - Z;
                                                   >> 125 //  G4double SPcorrectionN;
                                                   >> 126 //  if (N <= TableSize) SPcorrectionN = SPNTable[N-1]*MeV;
                                                   >> 127 //  else SPcorrectionN = 0.0;
                                                   >> 128 // 
                                                   >> 129 // 
                                                   >> 130 //  // Mass Excess
                                                   >> 131 //  // First two terms give the mass excess of the neutrons and protons in the nucleus
                                                   >> 132 //  // (see Cameron, Canadian Journal of Physics, 35, 1957 page 1022) 
                                                   >> 133 //  G4double MassExcess = 8.367*MeV*A - 0.783*MeV*Z + 
                                                   >> 134 //                 SurfaceEnergy + CoulombEnergy + ExchangeEnergy + VolumeEnergy +
                                                   >> 135 //                 SPcorrectionZ + SPcorrectionN;
                                                   >> 136 //       
                                                   >> 137 //  return MassExcess;
                                                   >> 138 // }
                                                   >> 139 
                                                   >> 140 
                                                   >> 141 // S(Z)+P(Z) from Tab. 1 from A.G.W. Cameron, Canad. J. Phys., 35(1957)1021
                                                   >> 142 //                   or Delta M(Z) from Tab. 97 of book [1]
                                                   >> 143 // const G4double G4NucleiProperties::SPZTable[TableSize] = {
                                                   >> 144 //   20.80, 15.80, 21.00, 16.80, 19.80, 16.50, 18.80, 16.50, 18.50, 17.20, //   1 - 10
                                                   >> 145 //   18.26, 15.05, 16.01, 12.04, 13.27, 11.09, 12.17, 10.26, 11.04,  8.41, //  11 - 20 
                                                   >> 146 //    9.79,  7.36,  8.15,  5.63,  5.88,  3.17,  3.32,   .82,  1.83,   .97, //  21 - 30
                                                   >> 147 //    2.33,  1.27,  2.92,  1.61,  2.91,  1.35,  2.40,   .89,  1.74,   .36, //  31
                                                   >> 148 //    0.95, -0.65, -0.04, -1.73, -0.96, -2.87, -2.05, -4.05, -3.40, -5.72, //  41
                                                   >> 149 //   -3.75, -4.13, -2.42, -2.85, -1.01, -1.33,  0.54, -0.02,  1.74,  0.75, //  51
                                                   >> 150 //    2.24,  1.00,  1.98,  0.79,  1.54,  0.39,  1.08,  0.00,  0.78, -0.35, //  61
                                                   >> 151 //    0.58, -0.55,  0.59, -0.61,  0.59, -0.35,  0.32, -0.96, -0.52, -2.08, //  71
                                                   >> 152 //   -2.46, -3.64, -1.55, -0.96,  0.97,  0.88,  2.37,  1.75,  2.72,  1.90, //  81
                                                   >> 153 //    2.55,  1.46,  1.93,  0.86,  1.17,  0.08,  0.39, -0.76, -0.39, -1.51, //  91 - 100
                                                   >> 154 //   -1.17, -2.36, -1.95, -3.06, -2.62, -3.55, -2.95, -3.75, -3.07, -3.79, // 101 - 110
                                                   >> 155 //   -3.06, -3.77, -3.05, -3.78, -3.12, -3.90, -3.35, -4.24, -3.86, -4.92, // 111 - 120
                                                   >> 156 //   -5.06, -6.77, -7.41, -9.18,-10.16,-11.12, -9.76, -9.23, -7.96, -7.65, // 121 - 130
                                                   >> 157 //   // --------- from this point there are not tabulated values -----------------------
                                                   >> 158 //    0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00, // 131 - 140
                                                   >> 159 //    0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00, // 141 - 150
                                                   >> 160 //    0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00, // 151
                                                   >> 161 //    0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00, // 161
                                                   >> 162 //    0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00, // 171
                                                   >> 163 //    0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00, // 181
                                                   >> 164 //    0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00,  0.00  // 191 - 200
                                                   >> 165 // };
                                                   >> 166 
                                                   >> 167 // S(N)+P(N) from Tab. 1 from A.G.W. Cameron, Canad. J. Phys., 35(1957)1021
                                                   >> 168 //                   or Delta M(N) from Tab. 97 of book [1]
                                                   >> 169 // const G4double G4NucleiProperties::SPNTable[TableSize] = {
                                                   >> 170 //   -8.40,-12.90, -8.00, 11.90, -9.20,-12.50,-10.80,-13.60,-11.20,-12.20, //   1 - 10
                                                   >> 171 //  -12.81,-15.40,-13.07,-15.80,-13.81,-14.98,-12.63,-13.76,-11.37,-12.38, //  11 - 20
                                                   >> 172 //   -9.23, -9.65, -7.64, -9.17, -8.05, -9.72, -8.87,-10.76, -8.64, -8.89, //  21 - 30
                                                   >> 173 //   -6.60, -7.13, -4.77, -5.33, -3.06, -3.79, -1.72, -2.79, -0.93, -2.19, //  31
                                                   >> 174 //   -0.52, -1.90, -0.45, -2.20, -1.22, -3.07, -2.42, -4.37, -3.94, -6.08, //  41
                                                   >> 175 //   -4.49, -4.50, -3.14, -2.93, -1.04, -1.36,  0.69,  0.21,  2.11,  1.33, //  51
                                                   >> 176 //    3.29,  2.46,  4.30,  3.32,  4.79,  3.62,  4.97,  3.64,  4.63,  3.07, //  61
                                                   >> 177 //    4.06,  2.49,  3.30,  1.46,  2.06,  0.51,  0.74, -1.18, -1.26, -3.54, //  71
                                                   >> 178 //   -3.97, -5.26, -4.18, -3.71, -2.10, -1.70, -0.08, -0.18,  0.94,  0.27, //  81
                                                   >> 179 //    1.13,  0.08,  0.91, -0.31,  0.49, -0.78,  0.08, -1.15, -0.23, -1.41, //  91 - 100
                                                   >> 180 //   -0.42, -1.55, -0.55, -1.66, -0.66, -1.73, -0.75, -1.74, -0.78, -1.69, // 101 - 110
                                                   >> 181 //   -0.78, -1.60, -0.75, -1.46, -0.67, -1.26, -0.51, -1.04, -0.53, -1.84, // 111 - 120
                                                   >> 182 //   -2.42, -4.52, -4.76, -6.33, -6.76, -7.81, -5.80, -5.37, -3.63, -3.35, // 121 - 130
                                                   >> 183 //   -1.75, -1.88, -0.61, -0.90,  0.09, -0.32,  0.55, -0.13,  0.70, -0.06, // 131 - 140
                                                   >> 184 //    0.49, -0.20,  0.40, -0.22,  0.36, -0.09,  0.58,  0.12,  0.75,  0.15, // 141 - 150
                                                   >> 185 //    0.70,  0.17,  1.11,  0.89,  1.85,  1.62,  2.54,  2.29,  3.20,  2.91, // 151
                                                   >> 186 //    3.84,  3.53,  4.48,  4.15,  5.12,  4.78,  5.75,  5.39,  6.31,  5.91, // 161
                                                   >> 187 //    6.87,  6.33,  7.13,  6.61,  7.30,  6.31,  6.27,  4.83,  4.49,  2.85, // 171
                                                   >> 188 //    2.32,  0.58, -0.11, -0.98,  0.81,  1.77,  3.37,  4.13,  5.60,  6.15, // 181
                                                   >> 189 //    7.29,  7.35,  7.95,  7.67,  8.16,  7.83,  8.31,  8.01,  8.53,  8.27  // 191 - 200
                                                   >> 190 // };
                                                   >> 191 
                                                   >> 192 
306                                                   193