G4QProtonNuclearCrossSection.cc

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00025 //
00026 //
00027 // The lust update: M.V. Kossov, CERN/ITEP(Moscow) 17-June-02
00028 // GEANT4 tag $Name: not supported by cvs2svn $
00029 //
00030 //
00031 // G4 Physics class: G4QProtonNuclearCrossSection for gamma+A cross sections
00032 // Created: M.V. Kossov, CERN/ITEP(Moscow), 20-Dec-03
00033 // The last update: M.V. Kossov, CERN/ITEP (Moscow) 15-Feb-04
00034 // --------------------------------------------------------------------------------
00035 // ****************************************************************************************
00036 // This Header is a part of the CHIPS physics package (author: M. Kosov)
00037 // ****************************************************************************************
00038 // Short description: CHIPS cross-sections for proton-nuclear interactions
00039 // -----------------------------------------------------------------------
00040 //
00041 //#define debug
00042 //#define pdebug
00043 //#define debug3
00044 //#define debugn
00045 //#define debugs
00046 
00047 #include "G4QProtonNuclearCrossSection.hh"
00048 #include "G4SystemOfUnits.hh"
00049 
00050 // Initialization of the
00051 G4double* G4QProtonNuclearCrossSection::lastLEN=0; // Pointer to the lastArray of LowEn CS
00052 G4double* G4QProtonNuclearCrossSection::lastHEN=0; // Pointer to the lastArray of HighEn CS
00053 G4int     G4QProtonNuclearCrossSection::lastN=0;   // The last N of calculated nucleus
00054 G4int     G4QProtonNuclearCrossSection::lastZ=0;   // The last Z of calculated nucleus
00055 G4double  G4QProtonNuclearCrossSection::lastP=0.;  // Last used in cross section Momentum
00056 G4double  G4QProtonNuclearCrossSection::lastTH=0.; // Last threshold momentum
00057 G4double  G4QProtonNuclearCrossSection::lastCS=0.; // Last value of the Cross Section
00058 G4int     G4QProtonNuclearCrossSection::lastI=0;   // The last position in the DAMDB
00059 std::vector<G4double*>* G4QProtonNuclearCrossSection::LEN = new std::vector<G4double*>;
00060 std::vector<G4double*>* G4QProtonNuclearCrossSection::HEN = new std::vector<G4double*>;
00061 
00062 // Returns Pointer to the G4VQCrossSection class
00063 G4VQCrossSection* G4QProtonNuclearCrossSection::GetPointer()
00064 {
00065   static G4QProtonNuclearCrossSection theCrossSection; //**Static body of Cross Section**
00066   return &theCrossSection;
00067 }
00068 
00069 G4QProtonNuclearCrossSection::~G4QProtonNuclearCrossSection()
00070 {
00071   G4int lens=LEN->size();
00072   for(G4int i=0; i<lens; ++i) delete[] (*LEN)[i];
00073   delete LEN;
00074   G4int hens=HEN->size();
00075   for(G4int i=0; i<hens; ++i) delete[] (*HEN)[i];
00076   delete HEN;
00077 }
00078 
00079 // The main member function giving the collision cross section (P is in IU, CS is in mb)
00080 // Make pMom in independent units ! (Now it is MeV)
00081 G4double G4QProtonNuclearCrossSection::GetCrossSection(G4bool fCS, G4double pMom,
00082                                                        G4int tgZ, G4int tgN, G4int PDG)
00083 {
00084   //A.R.23-Oct-2012 Shadowed variable  static G4double tolerance=0.001;     // Tolerance (0.1%) to consider as "the same mom"
00085   static G4int j;                      // A#0f Z/N-records already tested in AMDB
00086   static std::vector <G4int>    colN;  // Vector of N for calculated nuclei (isotops)
00087   static std::vector <G4int>    colZ;  // Vector of Z for calculated nuclei (isotops)
00088   static std::vector <G4double> colP;  // Vector of last momenta for the reaction
00089   static std::vector <G4double> colTH; // Vector of energy thresholds for the reaction
00090   static std::vector <G4double> colCS; // Vector of last cross sections for the reaction
00091   // ***---*** End of the mandatory Static Definitions of the Associative Memory ***---***
00092 #ifdef pebug
00093   G4cout<<"G4QPrCS::GetCS:>>> f="<<fCS<<", p="<<pMom<<", Z="<<tgZ<<"("<<lastZ<<") ,N="<<tgN
00094         <<"("<<lastN<<"),PDG=2212, thresh="<<lastTH<<",Sz="<<colN.size()<<G4endl;
00095 #endif
00096   if(PDG!=2212) G4cout<<"-Warning-G4QProtonCS::GetCS:***Not a proton***,PDG="<<PDG<<G4endl;
00097   G4bool in=false;                     // By default the isotope must be found in the AMDB
00098   if(tgN!=lastN || tgZ!=lastZ)         // The nucleus was not the last used isotope
00099   {
00100     in      = false;                   // By default the isotope haven't been found in AMDB
00101     lastP   = 0.;                      // New momentum history (nothing to compare with)
00102     lastN   = tgN;                     // The last N of the calculated nucleus
00103     lastZ   = tgZ;                     // The last Z of the calculated nucleus
00104     lastI   = colN.size();             // Size of the Associative Memory DB in the heap
00105     j  = 0;                            // A#0f records found in DB for this projectile
00106 #ifdef debug
00107     G4cout<<"G4QPrCS::GetCS: the amount of records in the AMDB lastI="<<lastI<<G4endl;
00108 #endif
00109     if(lastI) for(G4int i=0; i<lastI; i++) // AMDB exists, try to find the (Z,N) isotope
00110     {
00111       if(colN[i]==tgN && colZ[i]==tgZ) // Try the record "i" in the AMDB
00112       {
00113         lastI=i;                       // Remember the index for future fast/last use
00114         lastTH =colTH[i];              // The last THreshold (A-dependent)
00115 #ifdef debug
00116         G4cout<<"G4QPrCS::GetCS:*Found* P="<<pMom<<",Threshold="<<lastTH<<",j="<<j<<G4endl;
00117 #endif
00118         if(pMom<=lastTH)
00119         {
00120 #ifdef debug
00121           G4cout<<"G4QPCS::GetCS:Found,P="<<pMom<<" < Threshold="<<lastTH<<",CS=0"<<G4endl;
00122 #endif
00123           return 0.;                   // Energy is below the Threshold value
00124         }
00125         lastP  =colP [i];              // Last Momentum  (A-dependent)
00126         lastCS =colCS[i];              // Last CrossSect (A-dependent)
00127         if(std::fabs(lastP-pMom)<tolerance*pMom)
00128         //if(lastP==pMom)              // VI do not use tolerance
00129         {
00130 #ifdef pdebug
00131           G4cout<<"..G4QPrCS::GetCS:.DoNothing.P="<<pMom<<",CS="<<lastCS*millibarn<<G4endl;
00132 #endif
00133           //CalculateCrossSection(fCS,-1,j,2212,lastZ,lastN,pMom); // Update param's only
00134           return lastCS*millibarn;     // Use theLastCS
00135         }
00136         in = true;                     // This is the case when the isotop is found in DB
00137         // Momentum pMom is in IU ! @@ Units
00138 #ifdef debug
00139         G4cout<<"G4QPrCS::G:UpdatDB P="<<pMom<<",f="<<fCS<<",lI="<<lastI<<",j="<<j<<G4endl;
00140 #endif
00141         lastCS=CalculateCrossSection(fCS,-1,j,2212,lastZ,lastN,pMom); // read & update
00142 #ifdef debug
00143         G4cout<<"G4QPrCS::GetCrosSec: *****> New (inDB) Calculated CS="<<lastCS<<G4endl;
00144 #endif
00145         if(lastCS<=0. && pMom>lastTH)  // Correct the threshold (@@ No intermediate Zeros)
00146         {
00147 #ifdef debug
00148           G4cout<<"G4QPrCS::GetCS: New P="<<pMom<<"(CS=0) > Threshold="<<lastTH<<G4endl;
00149 #endif
00150           lastCS=0.;
00151           lastTH=pMom;
00152         }
00153         break;                         // Go out of the LOOP
00154       }
00155 #ifdef debug
00156       G4cout<<"-->G4QPrCrossSec::GetCrosSec: pPDG=2212, j="<<j<<", N="<<colN[i]
00157             <<",Z["<<i<<"]="<<colZ[i]<<G4endl;
00158 #endif
00159       j++;                             // Increment a#0f records found in DB
00160     }
00161 #ifdef debug
00162     G4cout<<"-?-G4QPrCS::GetCS:RC Z="<<tgZ<<",N="<<tgN<<",in="<<in<<",j="<<j<<" ?"<<G4endl;
00163 #endif
00164     if(!in)                            // This isotope has not been calculated previously
00165     {
00166 #ifdef debug
00167       G4cout<<"^^^G4QPrCS::GetCS:CalcNew P="<<pMom<<", f="<<fCS<<", lastI="<<lastI<<G4endl;
00168 #endif
00170       lastCS=CalculateCrossSection(fCS,0,j,2212,lastZ,lastN,pMom); //calculate & create
00171       //if(lastCS>0.)                   // It means that the AMBD was initialized
00172       //{
00173 
00174         lastTH = ThresholdEnergy(tgZ, tgN); // The Threshold Energy which is now the last
00175 #ifdef debug
00176         G4cout<<"G4QPrCrossSection::GetCrossSect: NewThresh="<<lastTH<<",P="<<pMom<<G4endl;
00177 #endif
00178         colN.push_back(tgN);
00179         colZ.push_back(tgZ);
00180         colP.push_back(pMom);
00181         colTH.push_back(lastTH);
00182         colCS.push_back(lastCS);
00183 #ifdef debug
00184         G4cout<<"G4QPrCS::GetCrosSec:recCS="<<lastCS<<",lZ="<<lastN<<",lN="<<lastZ<<G4endl;
00185 #endif
00186         //} // M.K. Presence of H1 with high threshold breaks the syncronization
00187 #ifdef pdebug
00188       G4cout<<"G4QPrCS::GetCS:1st,P="<<pMom<<"(MeV),CS="<<lastCS*millibarn<<"(mb)"<<G4endl;
00189 #endif
00190       return lastCS*millibarn;
00191     } // End of creation of the new set of parameters
00192     else
00193     {
00194 #ifdef debug
00195       G4cout<<"G4QPrCS::GetCS: Update lastI="<<lastI<<",j="<<j<<G4endl;
00196 #endif
00197       colP[lastI]=pMom;
00198       colCS[lastI]=lastCS;
00199     }
00200   } // End of parameters udate
00201   else if(pMom<=lastTH)
00202   {
00203 #ifdef debug
00204     G4cout<<"G4QPrCS::GetCS: Current P="<<pMom<<" < Threshold="<<lastTH<<", CS=0"<<G4endl;
00205 #endif
00206     return 0.;                         // Momentum is below the Threshold Value -> CS=0
00207   }
00208   else if(std::fabs(lastP-pMom)<tolerance*pMom)
00209   //else if(lastP==pMom)               // VI do not use tolerance
00210   {
00211 #ifdef pdebug
00212     G4cout<<"..G4QPCS::GetCS:OldNZ&P="<<lastP<<"="<<pMom<<",CS="<<lastCS*millibarn<<G4endl;
00213 #endif
00214     return lastCS*millibarn;           // Use theLastCS
00215   }
00216   else                                 // It is the last used -> use the current tables
00217   {
00218 #ifdef debug
00219     G4cout<<"-!-G4QPCS::GetCS:UseCur P="<<pMom<<",f="<<fCS<<",I="<<lastI<<",j="<<j<<G4endl;
00220 #endif
00221     lastCS=CalculateCrossSection(fCS,1,j,2212,lastZ,lastN,pMom); // Only read and UpdateDB
00222     lastP=pMom;
00223   }
00224 #ifdef debug
00225   G4cout<<"==>G4QPrCS::GetCroSec: P="<<pMom<<"(MeV),CS="<<lastCS*millibarn<<"(mb)"<<G4endl;
00226 #endif
00227   return lastCS*millibarn;
00228 }
00229 
00230 // The main member function giving the gamma-A cross section (E in GeV, CS in mb)
00231 G4double G4QProtonNuclearCrossSection::CalculateCrossSection(G4bool, G4int F, G4int I,
00232                                         G4int, G4int targZ, G4int targN, G4double Momentum)
00233 {
00234   static const G4double THmin=27.;     // default minimum Momentum (MeV/c) Threshold
00235   static const G4double THmiG=THmin*.001; // minimum Momentum (GeV/c) Threshold
00236   static const G4double dP=10.;        // step for the LEN (Low ENergy) table MeV/c
00237   static const G4double dPG=dP*.001;   // step for the LEN (Low ENergy) table GeV/c
00238   static const G4int    nL=105;        // A#of LEN points in E (step 10 MeV/c)
00239   static const G4double Pmin=THmin+(nL-1)*dP; // minP for the HighE part with safety
00240   static const G4double Pmax=227000.;  // maxP for the HEN (High ENergy) part 227 GeV
00241   static const G4int    nH=224;        // A#of HEN points in lnE
00242   static const G4double milP=std::log(Pmin);// Low logarithm energy for the HEN part
00243   static const G4double malP=std::log(Pmax);// High logarithm energy (each 2.75 percent)
00244   static const G4double dlP=(malP-milP)/(nH-1); // Step in log energy in the HEN part
00245   static const G4double milPG=std::log(.001*Pmin);// Low logarithmEnergy for HEN part GeV/c
00246 #ifdef debug
00247   G4cout<<"G4QProtNCS::CalCS:N="<<targN<<",Z="<<targZ<<",P="<<Momentum<<">"<<THmin<<G4endl;
00248 #endif
00249   G4double sigma=0.;
00250   if(F&&I) sigma=0.;                   // @@ *!* Fake line *!* to use F & I !!!Temporary!!!
00251   //G4double A=targN+targZ;              // A of the target
00252 #ifdef debug
00253   G4cout<<"G4QProtNucCS::CalCS: A="<<A<<",F="<<F<<",I="<<I<<",nL="<<nL<<",nH="<<nH<<G4endl;
00254 #endif
00255   if(F<=0)                             // This isotope was not the last used isotop
00256   {
00257     if(F<0)                            // This isotope was found in DAMDB =-----=> RETRIEVE
00258     {
00259       G4int sync=LEN->size();
00260       if(sync<=I) G4cout<<"*!*G4QProtonNuclCS::CalcCrossSect:Sync="<<sync<<"<="<<I<<G4endl;
00261       lastLEN=(*LEN)[I];               // Pointer to prepared LowEnergy cross sections
00262       lastHEN=(*HEN)[I];               // Pointer to prepared High Energy cross sections
00263     }
00264     else                               // This isotope wasn't calculated before => CREATE
00265     {
00266       lastLEN = new G4double[nL];      // Allocate memory for the new LEN cross sections
00267       lastHEN = new G4double[nH];      // Allocate memory for the new HEN cross sections
00268       // --- Instead of making a separate function ---
00269       G4double P=THmiG;                // Table threshold in GeV/c
00270       for(G4int n=0; n<nL; n++)
00271       {
00272         lastLEN[n] = CrossSectionLin(targZ, targN, P);
00273         P+=dPG;
00274       }
00275       G4double lP=milPG;
00276       for(G4int n=0; n<nH; n++)
00277       {
00278         lastHEN[n] = CrossSectionLog(targZ, targN, lP);
00279         lP+=dlP;
00280       }
00281 #ifdef debug
00282       G4cout<<"-*->G4QPr0tNucCS::CalcCS:Tab for Z="<<targZ<<",N="<<targN<<",I="<<I<<G4endl;
00283 #endif
00284       // --- End of possible separate function
00285       // *** The synchronization check ***
00286       G4int sync=LEN->size();
00287       if(sync!=I)
00288       {
00289         G4cout<<"***G4QProtonNuclCS::CalcCrossSect: Sinc="<<sync<<"#"<<I<<", Z=" <<targZ
00290               <<", N="<<targN<<", F="<<F<<G4endl;
00291         //G4Exception("G4ProtonNuclearCS::CalculateCS:","39",FatalException,"overflow DB");
00292       }
00293       LEN->push_back(lastLEN);          // remember the Low Energy Table
00294       HEN->push_back(lastHEN);          // remember the High Energy Table
00295     } // End of creation of the new set of parameters
00296   } // End of parameters udate
00297   // =------------------= NOW the Magic Formula =-----------------------=
00298 #ifdef debug
00299   G4cout<<"G4QPrNCS::CalcCS:lTH="<<lastTH<<",Pmi="<<Pmin<<",dP="<<dP<<",dlP="<<dlP<<G4endl;
00300 #endif
00301   if (Momentum<lastTH) return 0.;      // It must be already checked in the interface class
00302   else if (Momentum<Pmin)              // High Energy region
00303   {
00304 #ifdef debug
00305     G4cout<<"G4QPrNCS::CalcCS:bLEN nL="<<nL<<",TH="<<THmin<<",dP="<<dP<<G4endl;
00306 #endif
00307     sigma=EquLinearFit(Momentum,nL,THmin,dP,lastLEN);
00308 #ifdef debugn
00309     if(sigma<0.)
00310       G4cout<<"G4QPrNuCS::CalcCS: E="<<Momentum<<",T="<<THmin<<",dP="<<dP<<G4endl;
00311 #endif
00312   }
00313   else if (Momentum<Pmax)              // High Energy region
00314   {
00315     G4double lP=std::log(Momentum);
00316 #ifdef debug
00317     G4cout<<"G4QProtNucCS::CalcCS: before HEN nH="<<nH<<",iE="<<milP<<",dlP="<<dlP<<G4endl;
00318 #endif
00319     sigma=EquLinearFit(lP,nH,milP,dlP,lastHEN);
00320   }
00321   else                                 // UHE region (calculation, not frequent)
00322   {
00323     G4double P=0.001*Momentum;         // Approximation formula is for P in GeV/c
00324     sigma=CrossSectionFormula(targZ, targN, P, std::log(P));
00325   }
00326 #ifdef debug
00327   G4cout<<"G4QProtonNuclearCrossSection::CalcCS: CS="<<sigma<<G4endl;
00328 #endif
00329   if(sigma<0.) return 0.;
00330   return sigma;
00331 }
00332 
00333 // Electromagnetic momentum-threshold (in MeV/c) 
00334 G4double G4QProtonNuclearCrossSection::ThresholdMomentum(G4int tZ, G4int tN)
00335 {
00336   static const G4double third=1./3.;
00337   static const G4double pM = G4QPDGCode(2212).GetMass(); // Projectile mass in MeV
00338   static const G4double tpM= pM+pM;       // Doubled projectile mass (MeV)
00339   G4double tA=tZ+tN;
00340   if(tZ<.99 || tN<0.) return 0.;
00341   else if(tZ==1 && tN==0) return 800.;    // A threshold on the free proton
00342   //G4double dE=1.263*tZ/(1.+std::pow(tA,third));
00343   G4double dE=tZ/(1.+std::pow(tA,third)); // Safety for diffused edge of the nucleus (QE)
00344   G4double tM=931.5*tA;
00345   G4double T=dE+dE*(dE/2+pM)/tM;
00346   return std::sqrt(T*(tpM+T));
00347 }
00348 
00349 // Calculation formula for proton-nuclear inelastic cross-section (mb) (P in GeV/c)
00350 G4double G4QProtonNuclearCrossSection::CrossSectionLin(G4int tZ, G4int tN, G4double P)
00351 {
00352   G4double sigma=0.;
00353   if(P<ThresholdMomentum(tZ,tN)*.001) return sigma;
00354   G4double lP=std::log(P);
00355   if(tZ==1&&!tN){if(P>.35) sigma=CrossSectionFormula(tZ,tN,P,lP);}// s(pp)=0 below 350Mev/c
00356   else if(tZ<97 && tN<152)                // General solution
00357   {
00358     G4double pex=0.;
00359     G4double pos=0.;
00360     G4double wid=1.;
00361     if(tZ==13 && tN==14)                  // Excited metastable states
00362     {
00363       pex=230.;
00364       pos=.13;
00365       wid=8.e-5;
00366     }
00367     else if(tZ<7)
00368     {
00369       if(tZ==6 && tN==6)
00370       {
00371         pex=320.;
00372         pos=.14;
00373         wid=7.e-6;
00374       }
00375       else if(tZ==5 && tN==6)
00376       {
00377         pex=270.;
00378         pos=.17;
00379         wid=.002;
00380       }
00381       else if(tZ==4 && tN==5)
00382       {
00383         pex=600.;
00384         pos=.132;
00385         wid=.005;
00386       }
00387       else if(tZ==3 && tN==4)
00388       {
00389         pex=280.;
00390         pos=.19;
00391         wid=.0025;
00392       }
00393       else if(tZ==3 && tN==3)
00394       {
00395         pex=370.;
00396         pos=.171;
00397         wid=.006;
00398       }
00399       else if(tZ==2 && tN==1)
00400       {
00401         pex=30.;
00402         pos=.22;
00403         wid=.0005;
00404       }
00405     }
00406     sigma=CrossSectionFormula(tZ,tN,P,lP);
00407     if(pex>0.)
00408     {
00409       G4double dp=P-pos;
00410       sigma+=pex*std::exp(-dp*dp/wid);
00411     }
00412   }
00413   else
00414   {
00415     G4cerr<<"-Warning-G4QProtonNuclearCroSect::CSLin:*Bad A* Z="<<tZ<<", N="<<tN<<G4endl;
00416     sigma=0.;
00417   }
00418   if(sigma<0.) return 0.;
00419   return sigma;  
00420 }
00421 
00422 // Calculation formula for proton-nuclear inelastic cross-section (mb) log(P in GeV/c)
00423 G4double G4QProtonNuclearCrossSection::CrossSectionLog(G4int tZ, G4int tN, G4double lP)
00424 {
00425   G4double P=std::exp(lP);
00426   return CrossSectionFormula(tZ, tN, P, lP);
00427 }
00428 // Calculation formula for proton-nuclear inelastic cross-section (mb) log(P in GeV/c)
00429 G4double G4QProtonNuclearCrossSection::CrossSectionFormula(G4int tZ, G4int tN,
00430                                                            G4double P, G4double lP)
00431 {
00432   G4double sigma=0.;
00433   if(tZ==1 && !tN)                        // pp interaction (from G4QuasiElasticRatios)
00434   {
00435     G4double El(0.),To(0.);               // Uzhi
00436     if(P<0.1)                             // Copied from G4QuasiElasticRatios Uzhi / start
00437     {
00438       G4double p2=P*P;
00439       El=1./(0.00012+p2*0.2);
00440       To=El;
00441     }
00442     else if(P>1000.)
00443     {
00444       G4double lp=std::log(P)-3.5;
00445       G4double lp2=lp*lp;
00446       El=0.0557*lp2+6.72;
00447       To=0.3*lp2+38.2;
00448     }
00449     else
00450     {
00451       G4double p2=P*P;
00452       G4double LE=1./(0.00012+p2*0.2);
00453       G4double lp=std::log(P)-3.5;
00454       G4double lp2=lp*lp;
00455       G4double rp2=1./p2;
00456       El=LE+(0.0557*lp2+6.72+32.6/P)/(1.+rp2/P);
00457       To=LE+(0.3   *lp2+38.2+52.7*rp2)/(1.+2.72*rp2*rp2);
00458     }                                   // Copied from G4QuasiElasticRatios Uzhi / end
00459 
00460 /*                                                                         // Uzhi
00461     G4double p2=P*P;
00462     G4double lp=lP-3.5;
00463     G4double lp2=lp*lp;
00464     G4double rp2=1./p2;
00465     G4double El=(.0557*lp2+6.72+30./P)/(1.+.49*rp2/P);
00466     G4double To=(.3*lp2+38.2)/(1.+.54*rp2*rp2);
00467 */                                                                        // Uzhi
00468     sigma=To-El;
00469   }
00470   else if(tZ<97 && tN<152)                // General solution
00471   {
00472     //G4double lP=std::log(P);            // Already calculated
00473     G4double d=lP-4.2;
00474     G4double p2=P*P;
00475     G4double p4=p2*p2;
00476     G4double a=tN+tZ;                       // A of the target
00477     G4double al=std::log(a);
00478     G4double sa=std::sqrt(a);
00479     G4double a2=a*a;
00480     G4double a2s=a2*sa;
00481     G4double a4=a2*a2;
00482     G4double a8=a4*a4;
00483     G4double a12=a8*a4;
00484     G4double a16=a8*a8;
00485     G4double c=(170.+3600./a2s)/(1.+65./a2s);
00486     G4double dl=al-3.;
00487     G4double dl2=dl*dl;
00488     G4double r=.21+.62*dl2/(1.+.5*dl2);
00489     G4double g_value=40.*std::exp(al*0.712)/(1.+12.2/a)/(1.+34./a2);
00490     G4double e=318.+a4/(1.+.0015*a4/std::exp(al*0.09))/(1.+4.e-28*a12)+
00491                8.e-18/(1./a16+1.3e-20)/(1.+1.e-21*a12);
00492     G4double s_value=3.57+.009*a2/(1.+.0001*a2*a);
00493     G4double h=(.01/a4+2.5e-6/a)*(1.+6.e-6*a2*a)/(1.+6.e7/a12/a2);
00494     sigma=(c+d*d)/(1.+r/p4)+(g_value+e*std::exp(-s_value*P))/(1.+h/p4/p4);
00495 #ifdef pdebug
00496     G4cout<<"G4QProtNucCS::CSForm: A="<<a<<",P="<<P<<",CS="<<sigma<<",c="<<c<<",g="<<g_value
00497           <<",d="<<d<<",r="<<r<<",e="<<e<<",h="<<h<<G4endl;
00498 #endif
00499   }
00500   else
00501   {
00502     G4cerr<<"-Warning-G4QProtonNuclearCroSect::CSForm:*Bad A* Z="<<tZ<<", N="<<tN<<G4endl;
00503     sigma=0.;
00504   }
00505   if(sigma<0.) return 0.;
00506   return sigma;  
00507 }

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