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G4QNuMuNuclearCrossSection.cc
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27 // $Id$
28 //
29 //
30 // G4 Physics class: G4QNuMuNuclearCrossSection for (nu,mu-)A cross sections
31 // Created: M.V. Kossov, CERN/ITEP(Moscow), 10-OCT-01
32 // The last update: M.V. Kossov, CERN/ITEP (Moscow) 17-Oct-03
33 //
34 // ****************************************************************************************
35 // ********** This CLASS is temporary moved from the photolepton_hadron directory *********
36 // ******* DO NOT MAKE ANY CHANGE! With time it'll move back to photolepton...(M.K.) ******
37 // ****************************************************************************************
38 // ---------------------------------------------------------------------------------------
39 // Short description: neutrino_mu -> mu nuclear XS
40 // ---------------------------------------------------------------------------------------
41 
42 //#define debug
43 //#define edebug
44 //#define pdebug
45 //#define ppdebug
46 //#define tdebug
47 //#define sdebug
48 
49 #include "G4QNuMuNuclearCrossSection.hh"
50 #include "G4SystemOfUnits.hh"
51 
52 // Initialization of the
53 G4bool G4QNuMuNuclearCrossSection::onlyCS=true;// Flag to calculate only CS (not QE)
54 G4double G4QNuMuNuclearCrossSection::lastSig=0.;// Last calculated total cross section
55 G4double G4QNuMuNuclearCrossSection::lastQEL=0.;// Last calculated quasi-el. cross section
56 G4int G4QNuMuNuclearCrossSection::lastL=0; // Last used in cross section TheLastBin
57 G4double G4QNuMuNuclearCrossSection::lastE=0.; // Last used in cross section TheEnergy
58 G4double* G4QNuMuNuclearCrossSection::lastEN=0; // Pointer to the Energy Scale of TX & QE
59 G4double* G4QNuMuNuclearCrossSection::lastTX=0; // Pointer to the LastArray of TX function
60 G4double* G4QNuMuNuclearCrossSection::lastQE=0; // Pointer to the LastArray of QE function
61 G4int G4QNuMuNuclearCrossSection::lastPDG=0; // The last PDG code of the projectile
62 G4int G4QNuMuNuclearCrossSection::lastN=0; // The last N of calculated nucleus
63 G4int G4QNuMuNuclearCrossSection::lastZ=0; // The last Z of calculated nucleus
64 G4double G4QNuMuNuclearCrossSection::lastP=0.; // Last used in cross section Momentum
65 G4double G4QNuMuNuclearCrossSection::lastTH=0.; // Last threshold momentum
66 G4double G4QNuMuNuclearCrossSection::lastCS=0.; // Last value of the Cross Section
67 G4int G4QNuMuNuclearCrossSection::lastI=0; // The last position in the DAMDB
68 std::vector<G4double*>* G4QNuMuNuclearCrossSection::TX = new std::vector<G4double*>;
69 std::vector<G4double*>* G4QNuMuNuclearCrossSection::QE = new std::vector<G4double*>;
70 
71 // Returns Pointer to the G4VQCrossSection class
72 G4VQCrossSection* G4QNuMuNuclearCrossSection::GetPointer()
73 {
74  static G4QNuMuNuclearCrossSection theCrossSection; //**Static body of the Cross Section**
75  return &theCrossSection;
76 }
77 
78 G4QNuMuNuclearCrossSection::~G4QNuMuNuclearCrossSection()
79 {
80  G4int lens=TX->size();
81  for(G4int i=0; i<lens; ++i) delete[] (*TX)[i];
82  delete TX;
83  G4int hens=QE->size();
84  for(G4int i=0; i<hens; ++i) delete[] (*QE)[i];
85  delete QE;
86 }
87 
88 // The main member function giving the collision cross section (P is in IU, CS is in mb)
89 // Make pMom in independent units ! (Now it is MeV)
90 G4double G4QNuMuNuclearCrossSection::GetCrossSection(G4bool fCS, G4double pMom,
91  G4int tgZ, G4int tgN, G4int pPDG)
92 {
93  static G4int j; // A#0f records found in DB for this projectile
94  static std::vector <G4int> colPDG;// Vector of the projectile PDG code
95  static std::vector <G4int> colN; // Vector of N for calculated nuclei (isotops)
96  static std::vector <G4int> colZ; // Vector of Z for calculated nuclei (isotops)
97  static std::vector <G4double> colP; // Vector of last momenta for the reaction
98  static std::vector <G4double> colTH; // Vector of energy thresholds for the reaction
99  static std::vector <G4double> colCS; // Vector of last cross sections for the reaction
100  // ***---*** End of the mandatory Static Definitions of the Associative Memory ***---***
101  G4double pEn=pMom;
102 #ifdef debug
103  G4cout<<"G4QNMNCS::GetCS:>> f="<<fCS<<", p="<<pMom<<", Z="<<tgZ<<"("<<lastZ<<") ,N="<<tgN
104  <<"("<<lastN<<"),PDG="<<pPDG<<"("<<lastPDG<<"), T="<<pEn<<"("<<lastTH<<")"<<",Sz="
105  <<colN.size()<<G4endl;
106  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
107 #endif
108  if(pPDG!=14)
109  {
110 #ifdef pdebug
111  G4cout<<"G4QNMNCS::GetCS: *** Found pPDG="<<pPDG<<" =--=> CS=0"<<G4endl;
112  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
113 #endif
114  return 0.; // projectile PDG=0 is a mistake (?!) @@
115  }
116  G4bool in=false; // By default the isotope must be found in the AMDB
117  if(tgN!=lastN || tgZ!=lastZ || pPDG!=lastPDG)// The nucleus was not the last used isotope
118  {
119  in = false; // By default the isotope haven't be found in AMDB
120  lastP = 0.; // New momentum history (nothing to compare with)
121  lastPDG = pPDG; // The last PDG of the projectile
122  lastN = tgN; // The last N of the calculated nucleus
123  lastZ = tgZ; // The last Z of the calculated nucleus
124  lastI = colN.size(); // Size of the Associative Memory DB in the heap
125  j = 0; // A#0f records found in DB for this projectile
126  if(lastI) for(G4int i=0; i<lastI; i++) if(colPDG[i]==pPDG) // The partType is found
127  { // The nucleus with projPDG is found in AMDB
128  if(colN[i]==tgN && colZ[i]==tgZ)
129  {
130  lastI=i;
131  lastTH =colTH[i]; // Last THreshold (A-dependent)
132 #ifdef pdebug
133  G4cout<<"G4QNMNCS::GetCS:*Found*P="<<pMom<<",Threshold="<<lastTH<<",j="<<j<<G4endl;
134  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
135 #endif
136  if(pEn<=lastTH)
137  {
138 #ifdef pdebug
139  G4cout<<"G4QNMNCS::GetCS:Found T="<<pEn<<" < Threshold="<<lastTH<<",X=0"<<G4endl;
140  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
141 #endif
142  return 0.; // Energy is below the Threshold value
143  }
144  lastP =colP [i]; // Last Momentum (A-dependent)
145  lastCS =colCS[i]; // Last CrossSect (A-dependent)
146  if(std::fabs(lastP/pMom-1.)<tolerance)
147  {
148 #ifdef pdebug
149  G4cout<<"G4QNMNCS::GetCS:P="<<pMom<<",CS="<<lastCS*millibarn<<G4endl;
150  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
151 #endif
152  return lastCS*millibarn; // Use theLastCS
153  }
154  in = true; // This is the case when the isotop is found in DB
155  // Momentum pMom is in IU ! @@ Units
156 #ifdef pdebug
157  G4cout<<"G4QNMNCS::G:UpdaDB P="<<pMom<<",f="<<fCS<<",lI="<<lastI<<",j="<<j<<G4endl;
158 #endif
159  lastCS=CalculateCrossSection(fCS,-1,j,lastPDG,lastZ,lastN,pMom); // read & update
160 #ifdef pdebug
161  G4cout<<"G4QNMNCS::GetCrosSec: *****> New (inDB) Calculated CS="<<lastCS<<G4endl;
162  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
163 #endif
164  if(lastCS<=0. && pEn>lastTH) // Correct the threshold
165  {
166 #ifdef pdebug
167  G4cout<<"G4QNMNCS::GetCS: New T="<<pEn<<"(CS=0) > Threshold="<<lastTH<<G4endl;
168 #endif
169  lastTH=pEn;
170  }
171  break; // Go out of the LOOP
172  }
173 #ifdef pdebug
174  G4cout<<"---G4QNMNCrossSec::GetCrosSec:pPDG="<<pPDG<<",j="<<j<<",N="<<colN[i]
175  <<",Z["<<i<<"]="<<colZ[i]<<",cPDG="<<colPDG[i]<<G4endl;
176  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
177 #endif
178  j++; // Increment a#0f records found in DB for this pPDG
179  }
180  if(!in) // This nucleus has not been calculated previously
181  {
182 #ifdef pdebug
183  G4cout<<"G4QNMNCS::GetCrSec: CalcNew P="<<pMom<<",f="<<fCS<<",lastI="<<lastI<<G4endl;
184 #endif
185  lastCS=CalculateCrossSection(fCS,0,j,lastPDG,lastZ,lastN,pMom); //calculate & create
187  if(lastCS<=0.)
188  {
189  lastTH = ThresholdEnergy(tgZ, tgN); // The Threshold Energy which is now the last
190 #ifdef pdebug
191  G4cout<<"G4QNMNCrossSection::GetCrossSect:NewThresh="<<lastTH<<",T="<<pEn<<G4endl;
192 #endif
193  if(pEn>lastTH)
194  {
195 #ifdef pdebug
196  G4cout<<"G4QNMNCS::GetCS: First T="<<pEn<<"(CS=0) > Threshold="<<lastTH<<G4endl;
197 #endif
198  lastTH=pEn;
199  }
200  }
201 #ifdef pdebug
202  G4cout<<"G4QNMNCS::GetCrosSec:New CS="<<lastCS<<",lZ="<<lastN<<",lN="<<lastZ<<G4endl;
203  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
204 #endif
205  colN.push_back(tgN);
206  colZ.push_back(tgZ);
207  colPDG.push_back(pPDG);
208  colP.push_back(pMom);
209  colTH.push_back(lastTH);
210  colCS.push_back(lastCS);
211 #ifdef pdebug
212  G4cout<<"G4QNMNCS::GetCS:1st,P="<<pMom<<"(MeV),X="<<lastCS*millibarn<<"(mb)"<<G4endl;
213  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
214 #endif
215  return lastCS*millibarn;
216  } // End of creation of the new set of parameters
217  else
218  {
219 #ifdef pdebug
220  G4cout<<"G4QNMNCS::GetCS: Update lastI="<<lastI<<",j="<<j<<G4endl;
221 #endif
222  colP[lastI]=pMom;
223  colPDG[lastI]=pPDG;
224  colCS[lastI]=lastCS;
225  }
226  } // End of parameters udate
227  else if(pEn<=lastTH)
228  {
229 #ifdef pdebug
230  G4cout<<"G4QNMNCS::GetCS: Current T="<<pEn<<" < Threshold="<<lastTH<<", CS=0"<<G4endl;
231  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
232 #endif
233  return 0.; // Momentum is below the Threshold Value -> CS=0
234  }
235  else if(std::fabs(lastP/pMom-1.)<tolerance)
236  {
237 #ifdef pdebug
238  G4cout<<"G4QNMNCS::GetCS:OldCur P="<<pMom<<"="<<pMom<<",CS="<<lastCS*millibarn<<G4endl;
239  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
240 #endif
241  return lastCS*millibarn; // Use theLastCS
242  }
243  else
244  {
245 #ifdef pdebug
246  G4cout<<"G4QNMNCS::GetCS:UpdaCur P="<<pMom<<",f="<<fCS<<",I="<<lastI<<",j="<<j<<G4endl;
247 #endif
248  lastCS=CalculateCrossSection(fCS,1,j,lastPDG,lastZ,lastN,pMom); // Only UpdateDB
249  lastP=pMom;
250  }
251 #ifdef pdebug
252  G4cout<<"G4QNMNCS::GetCrSec:End,P="<<pMom<<"(MeV),CS="<<lastCS*millibarn<<"(mb)"<<G4endl;
253  //CalculateCrossSection(fCS,-27,j,lastPDG,lastZ,lastN,pMom); // DUMMY TEST
254 #endif
255  return lastCS*millibarn;
256 }
257 
258 // Gives the threshold energy = the same for all nuclei (@@ can be reduced for hevy nuclei)
259 G4double G4QNuMuNuclearCrossSection::ThresholdEnergy(G4int Z, G4int N, G4int)
260 {
261  //static const G4double mNeut = G4NucleiProperties::GetNuclearMass(1,0)/GeV;
262  //static const G4double mProt = G4NucleiProperties::GetNuclearMass(1,1)/GeV;
263  //static const G4double mDeut = G4NucleiProperties::GetNuclearMass(2,1)/GeV/2.;
264  static const G4double mN=.931494043;// Nucleon mass (inside nucleus, AtomicMassUnit, GeV)
265  static const G4double dmN=mN+mN; // Doubled nucleon mass (2*AtomicMassUnit, GeV)
266  static const G4double mmu=.105658369; // Mass of a muon in GeV
267  static const G4double mmu2=mmu*mmu; // Squared mass of a muon in GeV^2
268  static const G4double thresh=mmu+mmu2/dmN; // Universal threshold in GeV
269  // ---------
270  //static const G4double infEn = 9.e27;
271  G4double dN=0.;
272  if(Z>0||N>0) dN=thresh*GeV; // @@ if upgraded, change it in a total cross section
273  //@@ "dN=mmu+mmu2/G4NucleiProperties::GetNuclearMass(<G4double>(Z+N),<G4double>(Z)/GeV"
274  return dN;
275 }
276 
277 // The main member function giving the gamma-A cross section (E_kin in MeV, CS in mb)
278 G4double G4QNuMuNuclearCrossSection::CalculateCrossSection(G4bool CS, G4int F, G4int I,
279  G4int, G4int targZ, G4int targN, G4double Momentum)
280 {
281  static const G4double mb38=1.E-11; // Conversion 10^-38 cm^2 to mb=10^-27 cm^2
282  static const G4int nE=65; // !! If change this, change it in GetFunctions() (*.hh) !!
283  static const G4int mL=nE-1;
284  static const G4double mN=.931494043;// Nucleon mass (inside nucleus, AtomicMassUnit, GeV)
285  static const G4double dmN=mN+mN; // Doubled nucleon mass (2*AtomicMassUnit, GeV)
286  static const G4double mmu=.105658369; // Mass of a muon in GeV
287  static const G4double mmu2=mmu*mmu;// Squared mass of a muon in GeV^2
288  static const G4double EMi=mmu+mmu2/dmN; // Universal threshold of the reaction in GeV
289  static const G4double EMa=300.; // Maximum tabulated Energy of nu_mu in GeV
290  // *** Begin of the Associative memory for acceleration of the cross section calculations
291  static std::vector <G4double> colH;//?? Vector of HighEnergyCoefficients (functional)
292  static G4bool first=true; // Flag of initialization of the energy axis
293  // *** End of Static Definitions (Associative Memory) ***
294  //const G4double Energy = aPart->GetKineticEnergy()/MeV; // Energy of the Muon
295  //G4double TotEnergy2=Momentum;
296  onlyCS=CS; // Flag to calculate only CS (not TX & QE)
297  lastE=Momentum/GeV; // Kinetic energy of the muon neutrino (in GeV!)
298  if (lastE<=EMi) // Energy is below the minimum energy in the table
299  {
300  lastE=0.;
301  lastSig=0.;
302  return 0.;
303  }
304  G4int Z=targZ; // New Z, which can change the sign
305  if(F<=0) // This isotope was not the last used isotop
306  {
307  if(F<0) // This isotope was found in DAMDB =-------=> RETRIEVE
308  {
309  lastTX =(*TX)[I]; // Pointer to the prepared TX function (same isotope)
310  lastQE =(*QE)[I]; // Pointer to the prepared QE function (same isotope)
311  }
312  else // This isotope wasn't calculated previously => CREATE
313  {
314  if(first)
315  {
316  lastEN = new G4double[nE]; // This must be done only once!
317  Z=-Z; // To explain GetFunctions that E-axis must be filled
318  first=false; // To make it only once
319  }
320  lastTX = new G4double[nE]; // Allocate memory for the new TX function
321  lastQE = new G4double[nE]; // Allocate memory for the new QE function
322  G4int res=GetFunctions(Z,targN,lastTX,lastQE,lastEN);//@@analize(0=first,-1=bad,1=OK)
323  if(res<0) G4cerr<<"*W*G4NuMuNuclearCS::CalcCrossSect:Bad Function Retrieve"<<G4endl;
324  // *** The synchronization check ***
325  G4int sync=TX->size();
326  if(sync!=I) G4cerr<<"***G4NuMuNuclearCS::CalcCrossSect:Sync.="<<sync<<"#"<<I<<G4endl;
327  TX->push_back(lastTX);
328  QE->push_back(lastQE);
329  } // End of creation of the new set of parameters
330  } // End of parameters udate
331  // =--------------------= NOW Calculate the Cross Section =-------------------=
332  if (lastE<=EMi) // Check that the neutrinoEnergy is higher than ThreshE
333  {
334  lastE=0.;
335  lastSig=0.;
336  return 0.;
337  }
338  if(lastE<EMa) // Linear fit is made explicitly to fix the last bin for the randomization
339  {
340  G4int chk=1;
341  G4int ran=mL/2;
342  G4int sep=ran; // as a result = an index of the left edge of the interval
343  while(ran>=2)
344  {
345  G4int newran=ran/2;
346  if(lastE<=lastEN[sep]) sep-=newran;
347  else sep+=newran;
348  ran=newran;
349  chk=chk+chk;
350  }
351  if(chk+chk!=mL) G4cerr<<"*Warn*G4NuMuNuclearCS::CalcCS:Table! mL="<<mL<<G4endl;
352  G4double lowE=lastEN[sep];
353  G4double highE=lastEN[sep+1];
354  G4double lowTX=lastTX[sep];
355  if(lastE<lowE||sep>=mL||lastE>highE)
356  G4cerr<<"*Warn*G4NuMuNuclearCS::CalcCS:Bin! "<<lowE<<" < "<<lastE<<" < "<<highE
357  <<", sep="<<sep<<", mL="<<mL<<G4endl;
358  lastSig=lastE*(lastE-lowE)*(lastTX[sep+1]-lowTX)/(highE-lowE)+lowTX; // Recover *E
359  if(!onlyCS) // Skip the differential cross-section parameters
360  {
361  G4double lowQE=lastQE[sep];
362  lastQEL=(lastE-lowE)*(lastQE[sep+1]-lowQE)/(highE-lowE)+lowQE;
363 #ifdef pdebug
364  G4cout<<"G4NuMuNuclearCS::CalcCS: T="<<lastSig<<",Q="<<lastQEL<<",E="<<lastE<<G4endl;
365 #endif
366  }
367  }
368  else
369  {
370  lastSig=lastTX[mL]; // @@ No extrapolation, just a const, while it looks shrinking...
371  lastQEL=lastQE[mL];
372  }
373  if(lastQEL<0.) lastQEL = 0.;
374  if(lastSig<0.) lastSig = 0.;
375  // The cross-sections are expected to be in mb
376  lastSig*=mb38;
377  if(!onlyCS) lastQEL*=mb38;
378  return lastSig;
379 }
380 
381 // Calculate the cros-section functions
382 // ****************************************************************************************
383 // *** This tables are the same for all lepto-nuclear reactions, only mass is different ***
384 // ***@@ IT'S REASONABLE TO MAKE ADDiTIONAL VIRTUAL CLASS FOR LEPTO-NUCLEAR WITH THIS@@ ***
385 // ****************************************************************************************
386 G4int G4QNuMuNuclearCrossSection::GetFunctions(G4int z, G4int n,
387  G4double* t, G4double* q, G4double* e)
388 {
389  static const G4double mN=.931494043;// Nucleon mass (inside nucleus, AtomicMassUnit, GeV)
390  static const G4double dmN=mN+mN; // Doubled nucleon mass (2*AtomicMassUnit, GeV)
391  static const G4double mmu=.105658369; // Mass of a muon in GeV
392  static const G4double mmu2=mmu*mmu; // Squared mass of a muon in GeV^2
393  static const G4double thresh=mmu+mmu2/dmN; // Universal threshold in GeV
394  static const G4int nE=65; // !! If change this, change it in GetCrossSection() (*.cc) !!
395  static const G4double nuEn[nE]={thresh,
396  .112039,.116079,.120416,.125076,.130090,.135494,.141324,.147626,.154445,.161838,
397  .169864,.178594,.188105,.198485,.209836,.222272,.235923,.250941,.267497,.285789,
398  .306045,.328530,.353552,.381466,.412689,.447710,.487101,.531538,.581820,.638893,
399  .703886,.778147,.863293,.961275,1.07445,1.20567,1.35843,1.53701,1.74667,1.99390,
400  2.28679,2.63542,3.05245,3.55386,4.15990,4.89644,5.79665,6.90336,8.27224,9.97606,
401  12.1106,14.8029,18.2223,22.5968,28.2351,35.5587,45.1481,57.8086,74.6682,97.3201,
402  128.036,170.085,228.220,309.420};
403  static const G4double TOTX[nE]={0.,
404  .108618,.352160,.476083,.566575,.639014,.699871,.752634,.799407,.841524,.879844,
405  .914908,.947050,.976456,1.00321,1.02734,1.04881,1.06755,1.08349,1.09653,1.10657,
406  1.11355,1.11739,1.11806,1.11556,1.10992,1.10124,1.08964,1.07532,1.05851,1.03950,
407  1.01859,.996169,.972593,.948454,.923773,.899081,.874713,.850965,.828082,.806265,
408  .785659,.766367,.748450,.731936,.716824,.703098,.690723,.679652,.669829,.661187,
409  .653306,.646682,.640986,.636125,.631993,.628479,.625458,.622800,.620364,.616231,
410  .614986,.612563,.609807,.606511};
411  static const G4double QELX[nE]={0.,
412  .012170,.040879,.057328,.070865,.083129,.094828,.106366,.118013,.129970,.142392,
413  .155410,.169138,.183676,.199123,.215573,.233120,.251860,.271891,.293317,.316246,
414  .340796,.367096,.395292,.425547,.458036,.491832,.524989,.556457,.585692,.612377,
415  .636544,.657790,.676260,.692007,.705323,.716105,.724694,.731347,.736340,.740172,
416  .742783,.744584,.745804,.746829,.747479,.747995,.748436,.749047,.749497,.749925,
417  .750486,.750902,.751268,.751566,.752026,.752266,.752428,.752761,.752873,.753094,
418  .753161,.753164,.753340,.753321};
419  // --------------------------------
420  G4int first=0;
421  if(z<0.)
422  {
423  first=1;
424  z=-z;
425  }
426  if(z<1 || z>92) // neutron and plutonium are forbidden
427  {
428  G4cout<<"***G4QNuMuNuclearCrossSection::GetFunctions:Z="<<z<<".No CS returned"<<G4endl;
429  return -1;
430  }
431  for(G4int k=0; k<nE; k++)
432  {
433  G4double a=n+z;
434  G4double na=n+a;
435  G4double dn=n+n;
436  G4double da=a+a;
437  G4double ta=da+a;
438  if(first) e[k]=nuEn[k]; // Energy of neutrino E (first bin k=0 can be modified)
439  t[k]=TOTX[k]*nuEn[k]*(na+na)/ta+QELX[k]*(dn+dn-da)/ta; // TotalCrossSection
440  q[k]=QELX[k]*dn/a; // QuasiElasticCrossSection
441  }
442  return first;
443 }
444 
445 // Randomize Q2 from neutrino to the scattered muon when the scattering is quasi-elastic
446 G4double G4QNuMuNuclearCrossSection::GetQEL_ExchangeQ2()
447 {
448  static const G4double mmu=.105658369;// Mass of muon in GeV
449  static const G4double mmu2=mmu*mmu; // Squared Mass of muon in GeV^2
450  static const double hmmu2=mmu2/2; // .5*m_mu^2 in GeV^2
451  static const double MN=.931494043; // Nucleon mass (inside nucleus, atomicMassUnit,GeV)
452  static const double MN2=MN*MN; // M_N^2 in GeV^2
453  static const G4double power=-3.5; // direct power for the magic variable
454  static const G4double pconv=1./power;// conversion power for the magic variable
455  static const G4int nQ2=101; // #Of point in the Q2l table (in GeV^2)
456  static const G4int lQ2=nQ2-1; // index of the last in the Q2l table
457  static const G4int bQ2=lQ2-1; // index of the before last in the Q2 ltable
458  // Reversed table
459  static const G4double Xl[nQ2]={1.87905e-10,
460  .005231, .010602, .016192, .022038, .028146, .034513, .041130, .047986, .055071, .062374,
461  .069883, .077587, .085475, .093539, .101766, .110150, .118680, .127348, .136147, .145069,
462  .154107, .163255, .172506, .181855, .191296, .200825, .210435, .220124, .229886, .239718,
463  .249617, .259578, .269598, .279675, .289805, .299986, .310215, .320490, .330808, .341169,
464  .351568, .362006, .372479, .382987, .393527, .404099, .414700, .425330, .435987, .446670,
465  .457379, .468111, .478866, .489643, .500441, .511260, .522097, .532954, .543828, .554720,
466  .565628, .576553, .587492, .598447, .609416, .620398, .631394, .642403, .653424, .664457,
467  .675502, .686557, .697624, .708701, .719788, .730886, .741992, .753108, .764233, .775366,
468  .786508, .797658, .808816, .819982, .831155, .842336, .853524, .864718, .875920, .887128,
469  .898342, .909563, .920790, .932023, .943261, .954506, .965755, .977011, .988271, .999539};
470  // Direct table
471  static const G4double Xmax=Xl[lQ2];
472  static const G4double Xmin=Xl[0];
473  static const G4double dX=(Xmax-Xmin)/lQ2; // step in X(Q2, GeV^2)
474  static const G4double inl[nQ2]={0,
475  1.88843, 3.65455, 5.29282, 6.82878, 8.28390, 9.67403, 11.0109, 12.3034, 13.5583, 14.7811,
476  15.9760, 17.1466, 18.2958, 19.4260, 20.5392, 21.6372, 22.7215, 23.7933, 24.8538, 25.9039,
477  26.9446, 27.9766, 29.0006, 30.0171, 31.0268, 32.0301, 33.0274, 34.0192, 35.0058, 35.9876,
478  36.9649, 37.9379, 38.9069, 39.8721, 40.8337, 41.7920, 42.7471, 43.6992, 44.6484, 45.5950,
479  46.5390, 47.4805, 48.4197, 49.3567, 50.2916, 51.2245, 52.1554, 53.0846, 54.0120, 54.9377,
480  55.8617, 56.7843, 57.7054, 58.6250, 59.5433, 60.4603, 61.3761, 62.2906, 63.2040, 64.1162,
481  65.0274, 65.9375, 66.8467, 67.7548, 68.6621, 69.5684, 70.4738, 71.3784, 72.2822, 73.1852,
482  74.0875, 74.9889, 75.8897, 76.7898, 77.6892, 78.5879, 79.4860, 80.3835, 81.2804, 82.1767,
483  83.0724, 83.9676, 84.8622, 85.7563, 86.6499, 87.5430, 88.4356, 89.3277, 90.2194, 91.1106,
484  92.0013, 92.8917, 93.7816, 94.6711, 95.5602, 96.4489, 97.3372, 98.2252, 99.1128, 100.000};
485  G4double Enu=lastE; // Get energy of the last calculated cross-section
486  G4double dEnu=Enu+Enu; // doubled energy of nu/anu
487  G4double Enu2=Enu*Enu; // squared energy of nu/anu
488  G4double ME=Enu*MN; // M*E
489  G4double dME=ME+ME; // 2*M*E
490  G4double dEMN=(dEnu+MN)*ME;
491  G4double MEm=ME-hmmu2;
492  G4double sqE=Enu*std::sqrt(MEm*MEm-mmu2*MN2);
493  G4double E2M=MN*Enu2-(Enu+MN)*hmmu2;
494  G4double ymax=(E2M+sqE)/dEMN;
495  G4double ymin=(E2M-sqE)/dEMN;
496  G4double rmin=1.-ymin;
497  G4double rhm2E=hmmu2/Enu2;
498  G4double Q2mi=(Enu2+Enu2)*(rmin-rhm2E-std::sqrt(rmin*rmin-rhm2E-rhm2E)); // Q2_min(E_nu)
499  G4double Q2ma=dME*ymax; // Q2_max(E_nu)
500  G4double Xma=std::pow((1.+Q2mi),power); // X_max(E_nu)
501  G4double Xmi=std::pow((1.+Q2ma),power); // X_min(E_nu)
502  // Find the integral values integ(Xmi) & integ(Xma) using the direct table
503  G4double rXi=(Xmi-Xmin)/dX;
504  G4int iXi=static_cast<int>(rXi);
505  if(iXi<0) iXi=0;
506  if(iXi>bQ2) iXi=bQ2;
507  G4double dXi=rXi-iXi;
508  G4double bnti=inl[iXi];
509  G4double inti=bnti+dXi*(inl[iXi+1]-bnti);
510  //
511  G4double rXa=(Xma-Xmin)/dX;
512  G4int iXa=static_cast<int>(rXa);
513  if(iXa<0) iXa=0;
514  if(iXa>bQ2) iXa=bQ2;
515  G4double dXa=rXa-iXa;
516  G4double bnta=inl[iXa];
517  G4double inta=bnta+dXa*(inl[iXa+1]-bnta);
518  // *** Find X using the reversed table ***
519  G4double intx=inti+(inta-inti)*G4UniformRand();
520  G4int intc=static_cast<int>(intx);
521  if(intc<0) intc=0;
522  if(intc>bQ2) intc=bQ2; // If it is more than max, then the BAD extrapolation
523  G4double dint=intx-intc;
524  G4double mX=Xl[intc];
525  G4double X=mX+dint*(Xl[intc+1]-mX);
526  G4double Q2=std::pow(X,pconv)-1.;
527  return Q2*GeV*GeV;
528 }
529 
530 // Randomize Q2 from neutrino to the scattered muon when the scattering is not quasiElastic
531 G4double G4QNuMuNuclearCrossSection::GetNQE_ExchangeQ2()
532 {
533  static const double mpi=.13957018; // charged pi meson mass in GeV
534  static const G4double mmu=.105658369; // Mass of muon in GeV
535  static const G4double mmu2=mmu*mmu; // Squared Mass of muon in GeV^2
536  static const double hmmu2=mmu2/2; // .5*m_mu^2 in GeV^2
537  static const double MN=.931494043; // Nucleon mass (inside nucleus,atomicMassUnit,GeV)
538  static const double MN2=MN*MN; // M_N^2 in GeV^2
539  static const double dMN=MN+MN; // 2*M_N in GeV
540  static const double mcV=(dMN+mpi)*mpi;// constant of W>M+mc cut for Quasi-Elastic
541  static const G4int power=7; // direct power for the magic variable
542  static const G4double pconv=1./power; // conversion power for the magic variable
543  static const G4int nX=21; // #Of point in the Xl table (in GeV^2)
544  static const G4int lX=nX-1; // index of the last in the Xl table
545  static const G4int bX=lX-1; // @@ index of the before last in the Xl table
546  static const G4int nE=20; // #Of point in the El table (in GeV^2)
547  static const G4int bE=nE-1; // index of the last in the El table
548  static const G4int pE=bE-1; // index of the before last in the El table
549  // Reversed table
550  static const G4double X0[nX]={6.14081e-05,
551  .413394, .644455, .843199, 1.02623, 1.20032, 1.36916, 1.53516, 1.70008, 1.86539, 2.03244,
552  2.20256, 2.37723, 2.55818, 2.74762, 2.94857, 3.16550, 3.40582, 3.68379, 4.03589, 4.77419};
553  static const G4double X1[nX]={.00125268,
554  .861178, 1.34230, 1.75605, 2.13704, 2.49936, 2.85072, 3.19611, 3.53921, 3.88308, 4.23049,
555  4.58423, 4.94735, 5.32342, 5.71700, 6.13428, 6.58447, 7.08267, 7.65782, 8.38299, 9.77330};
556  static const G4double X2[nX]={.015694,
557  1.97690, 3.07976, 4.02770, 4.90021, 5.72963, 6.53363, 7.32363, 8.10805, 8.89384, 9.68728,
558  10.4947, 11.3228, 12.1797, 13.0753, 14.0234, 15.0439, 16.1692, 17.4599, 19.0626, 21.7276};
559  static const G4double X3[nX]={.0866877,
560  4.03498, 6.27651, 8.20056, 9.96931, 11.6487, 13.2747, 14.8704, 16.4526, 18.0351, 19.6302,
561  21.2501, 22.9075, 24.6174, 26.3979, 28.2730, 30.2770, 32.4631, 34.9243, 37.8590, 41.9115};
562  static const G4double X4[nX]={.160483,
563  5.73111, 8.88884, 11.5893, 14.0636, 16.4054, 18.6651, 20.8749, 23.0578, 25.2318, 27.4127,
564  29.6152, 31.8540, 34.1452, 36.5074, 38.9635, 41.5435, 44.2892, 47.2638, 50.5732, 54.4265};
565  static const G4double X5[nX]={.0999307,
566  5.25720, 8.11389, 10.5375, 12.7425, 14.8152, 16.8015, 18.7296, 20.6194, 22.4855, 24.3398,
567  26.1924, 28.0527, 29.9295, 31.8320, 33.7699, 35.7541, 37.7975, 39.9158, 42.1290, 44.4649};
568  static const G4double X6[nX]={.0276367,
569  3.53378, 5.41553, 6.99413, 8.41629, 9.74057, 10.9978, 12.2066, 13.3796, 14.5257, 15.6519,
570  16.7636, 17.8651, 18.9603, 20.0527, 21.1453, 22.2411, 23.3430, 24.4538, 25.5765, 26.7148};
571  static const G4double X7[nX]={.00472383,
572  2.08253, 3.16946, 4.07178, 4.87742, 5.62140, 6.32202, 6.99034, 7.63368, 8.25720, 8.86473,
573  9.45921, 10.0430, 10.6179, 11.1856, 11.7475, 12.3046, 12.8581, 13.4089, 13.9577, 14.5057};
574  static const G4double X8[nX]={.000630783,
575  1.22723, 1.85845, 2.37862, 2.84022, 3.26412, 3.66122, 4.03811, 4.39910, 4.74725, 5.08480,
576  5.41346, 5.73457, 6.04921, 6.35828, 6.66250, 6.96250, 7.25884, 7.55197, 7.84232, 8.13037};
577  static const G4double X9[nX]={7.49179e-05,
578  .772574, 1.16623, 1.48914, 1.77460, 2.03586, 2.27983, 2.51069, 2.73118, 2.94322, 3.14823,
579  3.34728, 3.54123, 3.73075, 3.91638, 4.09860, 4.27779, 4.45428, 4.62835, 4.80025, 4.97028};
580  static const G4double XA[nX]={8.43437e-06,
581  .530035, .798454, 1.01797, 1.21156, 1.38836, 1.55313, 1.70876, 1.85712, 1.99956, 2.13704,
582  2.27031, 2.39994, 2.52640, 2.65007, 2.77127, 2.89026, 3.00726, 3.12248, 3.23607, 3.34823};
583  static const G4double XB[nX]={9.27028e-07,
584  .395058, .594211, .756726, .899794, 1.03025, 1.15167, 1.26619, 1.37523, 1.47979, 1.58059,
585  1.67819, 1.77302, 1.86543, 1.95571, 2.04408, 2.13074, 2.21587, 2.29960, 2.38206, 2.46341};
586  static const G4double XC[nX]={1.00807e-07,
587  .316195, .474948, .604251, .717911, .821417, .917635, 1.00829, 1.09452, 1.17712, 1.25668,
588  1.33364, 1.40835, 1.48108, 1.55207, 1.62150, 1.68954, 1.75631, 1.82193, 1.88650, 1.95014};
589  static const G4double XD[nX]={1.09102e-08,
590  .268227, .402318, .511324, .606997, .694011, .774803, .850843, .923097, .992243, 1.05878,
591  1.12309, 1.18546, 1.24613, 1.30530, 1.36313, 1.41974, 1.47526, 1.52978, 1.58338, 1.63617};
592  static const G4double XE[nX]={1.17831e-09,
593  .238351, .356890, .453036, .537277, .613780, .684719, .751405, .814699, .875208, .933374,
594  .989535, 1.04396, 1.09685, 1.14838, 1.19870, 1.24792, 1.29615, 1.34347, 1.38996, 1.43571};
595  static const G4double XF[nX]={1.27141e-10,
596  .219778, .328346, .416158, .492931, .562525, .626955, .687434, .744761, .799494, .852046,
597  .902729, .951786, .999414, 1.04577, 1.09099, 1.13518, 1.17844, 1.22084, 1.26246, 1.30338};
598  static const G4double XG[nX]={1.3713e-11,
599  .208748, .310948, .393310, .465121, .530069, .590078, .646306, .699515, .750239, .798870,
600  .845707, .890982, .934882, .977559, 1.01914, 1.05973, 1.09941, 1.13827, 1.17637, 1.21379};
601  static const G4double XH[nX]={1.47877e-12,
602  .203089, .301345, .380162, .448646, .510409, .567335, .620557, .670820, .718647, .764421,
603  .808434, .850914, .892042, .931967, .970812, 1.00868, 1.04566, 1.08182, 1.11724, 1.15197};
604  static const G4double XI[nX]={1.59454e-13,
605  .201466, .297453, .374007, .440245, .499779, .554489, .605506, .653573, .699213, .742806,
606  .784643, .824952, .863912, .901672, .938353, .974060, 1.00888, 1.04288, 1.07614, 1.10872};
607  static const G4double XJ[nX]={1.71931e-14,
608  .202988, .297870, .373025, .437731, .495658, .548713, .598041, .644395, .688302, .730147,
609  .770224, .808762, .845943, .881916, .916805, .950713, .983728, 1.01592, 1.04737, 1.07813};
610  // Direct table
611  static const G4double Xmin[nE]={X0[0],X1[0],X2[0],X3[0],X4[0],X5[0],X6[0],X7[0],X8[0],
612  X9[0],XA[0],XB[0],XC[0],XD[0],XE[0],XF[0],XG[0],XH[0],XI[0],XJ[0]};
613  static const G4double dX[nE]={
614  (X0[lX]-X0[0])/lX, (X1[lX]-X1[0])/lX, (X2[lX]-X2[0])/lX, (X3[lX]-X3[0])/lX,
615  (X4[lX]-X4[0])/lX, (X5[lX]-X5[0])/lX, (X6[lX]-X6[0])/lX, (X7[lX]-X7[0])/lX,
616  (X8[lX]-X8[0])/lX, (X9[lX]-X9[0])/lX, (XA[lX]-XA[0])/lX, (XB[lX]-XB[0])/lX,
617  (XC[lX]-XC[0])/lX, (XD[lX]-XD[0])/lX, (XE[lX]-XE[0])/lX, (XF[lX]-XF[0])/lX,
618  (XG[lX]-XG[0])/lX, (XH[lX]-XH[0])/lX, (XI[lX]-XI[0])/lX, (XJ[lX]-XJ[0])/lX};
619  static const G4double* Xl[nE]=
620  {X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,XA,XB,XC,XD,XE,XF,XG,XH,XI,XJ};
621  static const G4double I0[nX]={0,
622  .411893, 1.25559, 2.34836, 3.60264, 4.96046, 6.37874, 7.82342, 9.26643, 10.6840, 12.0555,
623  13.3628, 14.5898, 15.7219, 16.7458, 17.6495, 18.4217, 19.0523, 19.5314, 19.8501, 20.0000};
624  static const G4double I1[nX]={0,
625  .401573, 1.22364, 2.28998, 3.51592, 4.84533, 6.23651, 7.65645, 9.07796, 10.4780, 11.8365,
626  13.1360, 14.3608, 15.4967, 16.5309, 17.4516, 18.2481, 18.9102, 19.4286, 19.7946, 20.0000};
627  static const G4double I2[nX]={0,
628  .387599, 1.17339, 2.19424, 3.37090, 4.65066, 5.99429, 7.37071, 8.75427, 10.1232, 11.4586,
629  12.7440, 13.9644, 15.1065, 16.1582, 17.1083, 17.9465, 18.6634, 19.2501, 19.6982, 20.0000};
630  static const G4double I3[nX]={0,
631  .366444, 1.09391, 2.04109, 3.13769, 4.33668, 5.60291, 6.90843, 8.23014, 9.54840, 10.8461,
632  12.1083, 13.3216, 14.4737, 15.5536, 16.5512, 17.4573, 18.2630, 18.9603, 19.5417, 20.0000};
633  static const G4double I4[nX]={0,
634  .321962, .959681, 1.79769, 2.77753, 3.85979, 5.01487, 6.21916, 7.45307, 8.69991, 9.94515,
635  11.1759, 12.3808, 13.5493, 14.6720, 15.7402, 16.7458, 17.6813, 18.5398, 19.3148, 20.0000};
636  static const G4double I5[nX]={0,
637  .257215, .786302, 1.49611, 2.34049, 3.28823, 4.31581, 5.40439, 6.53832, 7.70422, 8.89040,
638  10.0865, 11.2833, 12.4723, 13.6459, 14.7969, 15.9189, 17.0058, 18.0517, 19.0515, 20.0000};
639  static const G4double I6[nX]={0,
640  .201608, .638914, 1.24035, 1.97000, 2.80354, 3.72260, 4.71247, 5.76086, 6.85724, 7.99243,
641  9.15826, 10.3474, 11.5532, 12.7695, 13.9907, 15.2117, 16.4275, 17.6337, 18.8258, 20.0000};
642  static const G4double I7[nX]={0,
643  .168110, .547208, 1.07889, 1.73403, 2.49292, 3.34065, 4.26525, 5.25674, 6.30654, 7.40717,
644  8.55196, 9.73492, 10.9506, 12.1940, 13.4606, 14.7460, 16.0462, 17.3576, 18.6767, 20.0000};
645  static const G4double I8[nX]={0,
646  .150652, .497557, .990048, 1.60296, 2.31924, 3.12602, 4.01295, 4.97139, 5.99395, 7.07415,
647  8.20621, 9.38495, 10.6057, 11.8641, 13.1561, 14.4781, 15.8267, 17.1985, 18.5906, 20.0000};
648  static const G4double I9[nX]={0,
649  .141449, .470633, .941304, 1.53053, 2.22280, 3.00639, 3.87189, 4.81146, 5.81837, 6.88672,
650  8.01128, 9.18734, 10.4106, 11.6772, 12.9835, 14.3261, 15.7019, 17.1080, 18.5415, 20.0000};
651  static const G4double IA[nX]={0,
652  .136048, .454593, .912075, 1.48693, 2.16457, 2.93400, 3.78639, 4.71437, 5.71163, 6.77265,
653  7.89252, 9.06683, 10.2916, 11.5631, 12.8780, 14.2331, .625500, 17.0525, 18.5115, 20.0000};
654  static const G4double IB[nX]={0,
655  .132316, .443455, .891741, 1.45656, 2.12399, 2.88352, 3.72674, 4.64660, 5.63711, 6.69298,
656  7.80955, 8.98262, 10.2084, 11.4833, 12.8042, 14.1681, 15.5721, 17.0137, 18.4905, 20.0000};
657  static const G4double IC[nX]={0,
658  .129197, .434161, .874795, 1.43128, 2.09024, 2.84158, 3.67721, 4.59038, 5.57531, 6.62696,
659  7.74084, 8.91291, 10.1395, 11.4173, 12.7432, 14.1143, 15.5280, 16.9817, 18.4731, 20.0000};
660  static const G4double ID[nX]={0,
661  .126079, .424911, .857980, 1.40626, 2.05689, 2.80020, 3.62840, 4.53504, 5.51456, 6.56212,
662  7.67342, 8.84458, 10.0721, 11.3527, 12.6836, 14.0618, 15.4849, 16.9504, 18.4562, 20.0000};
663  static const G4double IE[nX]={0,
664  .122530, .414424, .838964, 1.37801, 2.01931, 2.75363, 3.57356, 4.47293, 5.44644, 6.48949,
665  7.59795, 8.76815, 9.99673, 11.2806, 12.6170, 14.0032, 15.4369, 16.9156, 18.4374, 20.0000};
666  static const G4double IF[nX]={0,
667  .118199, .401651, .815838, 1.34370, 1.97370, 2.69716, 3.50710, 4.39771, 5.36401, 6.40164,
668  7.50673, 8.67581, 9.90572, 11.1936, 12.5367, 13.9326, 15.3790, 16.8737, 18.4146, 20.0000};
669  static const G4double IG[nX]={0,
670  .112809, .385761, .787075, 1.30103, 1.91700, 2.62697, 3.42451, 4.30424, 5.26158, 6.29249,
671  7.39341, 8.56112, 9.79269, 11.0855, 12.4369, 13.8449, 15.3071, 16.8216, 18.3865, 20.0000};
672  static const G4double IH[nX]={0,
673  .106206, .366267, .751753, 1.24859, 1.84728, 2.54062, 3.32285, .189160, 5.13543, 6.15804,
674  7.25377, 8.41975, 9.65334, 10.9521, 12.3139, 13.7367, 15.2184, 16.7573, 18.3517, 20.0000};
675  static const G4double II[nX]={0,
676  .098419, .343194, .709850, 1.18628, 1.76430, 2.43772, 3.20159, 4.05176, 4.98467, 5.99722,
677  7.08663, 8.25043, 9.48633, 10.7923, 12.1663, 13.6067, 15.1118, 16.6800, 18.3099, 20.0000};
678  static const G4double IJ[nX]={0,
679  .089681, .317135, .662319, 1.11536, 1.66960, 2.32002, 3.06260, 3.89397, 4.81126, 5.81196,
680  6.89382, 8.05483, 9.29317, 10.6072, 11.9952, 13.4560, 14.9881, 16.5902, 18.2612, 20.0000};
681  static const G4double* Il[nE]=
682  {I0,I1,I2,I3,I4,I5,I6,I7,I8,I9,IA,IB,IC,ID,IE,IF,IG,IH,II,IJ};
683  static const G4double lE[nE]={
684 -1.98842,-1.58049,-1.17256,-.764638,-.356711, .051215, .459141, .867068, 1.27499, 1.68292,
685  2.09085, 2.49877, 2.90670, 3.31463, 3.72255, 4.13048, 4.53840, 4.94633, 5.35426, 5.76218};
686  static const G4double lEmi=lE[0];
687  static const G4double lEma=lE[nE-1];
688  static const G4double dlE=(lEma-lEmi)/bE;
689  //***************************************************************************************
690  G4double Enu=lastE; // Get energy of the last calculated cross-section
691  G4double lEn=std::log(Enu); // log(E) for interpolation
692  G4double rE=(lEn-lEmi)/dlE; // Position of the energy
693  G4int fE=static_cast<int>(rE); // Left bin for interpolation
694  if(fE<0) fE=0;
695  if(fE>pE)fE=pE;
696  G4int sE=fE+1; // Right bin for interpolation
697  G4double dE=rE-fE; // relative log shift from the left bin
698  G4double dEnu=Enu+Enu; // doubled energy of nu/anu
699  G4double Enu2=Enu*Enu; // squared energy of nu/anu
700  G4double Emu=Enu-mmu; // Free Energy of neutrino/anti-neutrino
701  G4double ME=Enu*MN; // M*E
702  G4double dME=ME+ME; // 2*M*E
703  G4double dEMN=(dEnu+MN)*ME;
704  G4double MEm=ME-hmmu2;
705  G4double sqE=Enu*std::sqrt(MEm*MEm-mmu2*MN2);
706  G4double E2M=MN*Enu2-(Enu+MN)*hmmu2;
707  G4double ymax=(E2M+sqE)/dEMN;
708  G4double ymin=(E2M-sqE)/dEMN;
709  G4double rmin=1.-ymin;
710  G4double rhm2E=hmmu2/Enu2;
711  G4double Q2mi=(Enu2+Enu2)*(rmin-rhm2E-std::sqrt(rmin*rmin-rhm2E-rhm2E)); // Q2_min(E_nu)
712  G4double Q2ma=dME*ymax; // Q2_max(E_nu)
713  G4double Q2nq=Emu*dMN-mcV;
714  if(Q2ma>Q2nq) Q2ma=Q2nq; // Correction for Non Quasi Elastic
715  // --- now r_min=Q2mi/Q2ma and r_max=1.; when r is randomized -> Q2=r*Q2ma ---
716  G4double Rmi=Q2mi/Q2ma;
717  G4double shift=1.+.9673/(1.+.323/Enu/Enu)/std::pow(Enu,.78); //@@ different for anti-nu
718  // --- E-interpolation must be done in a log scale ---
719  G4double Xmi=std::pow((shift-Rmi),power);// X_min(E_nu)
720  G4double Xma=std::pow((shift-1.),power); // X_max(E_nu)
721  // Find the integral values integ(Xmi) & integ(Xma) using the direct table
722  G4double idX=dX[fE]+dE*(dX[sE]-dX[fE]); // interpolated X step
723  G4double iXmi=Xmin[fE]+dE*(Xmin[sE]-Xmin[fE]); // interpolated X minimum
724  G4double rXi=(Xmi-iXmi)/idX;
725  G4int iXi=static_cast<int>(rXi);
726  if(iXi<0) iXi=0;
727  if(iXi>bX) iXi=bX;
728  G4double dXi=rXi-iXi;
729  G4double bntil=Il[fE][iXi];
730  G4double intil=bntil+dXi*(Il[fE][iXi+1]-bntil);
731  G4double bntir=Il[sE][iXi];
732  G4double intir=bntir+dXi*(Il[sE][iXi+1]-bntir);
733  G4double inti=intil+dE*(intir-intil);// interpolated begin of the integral
734  //
735  G4double rXa=(Xma-iXmi)/idX;
736  G4int iXa=static_cast<int>(rXa);
737  if(iXa<0) iXa=0;
738  if(iXa>bX) iXa=bX;
739  G4double dXa=rXa-iXa;
740  G4double bntal=Il[fE][iXa];
741  G4double intal=bntal+dXa*(Il[fE][iXa+1]-bntal);
742  G4double bntar=Il[sE][iXa];
743  G4double intar=bntar+dXa*(Il[sE][iXa+1]-bntar);
744  G4double inta=intal+dE*(intar-intal);// interpolated end of the integral
745  //
746  // *** Find X using the reversed table ***
747  G4double intx=inti+(inta-inti)*G4UniformRand();
748  G4int intc=static_cast<int>(intx);
749  if(intc<0) intc=0;
750  if(intc>bX) intc=bX;
751  G4double dint=intx-intc;
752  G4double mXl=Xl[fE][intc];
753  G4double Xlb=mXl+dint*(Xl[fE][intc+1]-mXl);
754  G4double mXr=Xl[sE][intc];
755  G4double Xrb=mXr+dint*(Xl[sE][intc+1]-mXr);
756  G4double X=Xlb+dE*(Xrb-Xlb); // interpolated X value
757  G4double R=shift-std::pow(X,pconv);
758  G4double Q2=R*Q2ma;
759  return Q2*GeV*GeV;
760 }
761 
762 // It returns a fraction of the direct interaction of the neutrino with quark-partons
763 G4double G4QNuMuNuclearCrossSection::GetDirectPart(G4double Q2)
764 {
765  G4double f=Q2/4.62;
766  G4double ff=f*f;
767  G4double r=ff*ff;
768  G4double s_value=std::pow((1.+.6/Q2),(-1.-(1.+r)/(12.5+r/.3)));
769  //@@ It is the same for nu/anu, but for nu it is a bit less, and for anu a bit more (par)
770  return 1.-s_value*(1.-s_value/2);
771 }
772 
773 // #of quark-partons in the nonperturbative phase space is the same for neut and anti-neut
774 G4double G4QNuMuNuclearCrossSection::GetNPartons(G4double Q2)
775 {
776  return 3.+.3581*std::log(1.+Q2/.04); // a#of partons in the nonperturbative phase space
777 }
778 
779 // This class can provide only virtual exchange pi+ (a substitute for W+ boson)
780 G4int G4QNuMuNuclearCrossSection::GetExchangePDGCode() {return 211;}
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