1 /**************************************************************************
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4 * Author: The ALICE Off-line Project. *
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14 **************************************************************************/
17 // ******************************************************************
19 // Class for nuclear fragments formation
21 // ******************************************************************
23 // --- Standard libraries
30 // --- AliRoot classes
31 #include "AliZDCFragment.h"
33 ClassImp(AliZDCFragment)
35 int comp(const void *i,const void *j) {return *(int *)i - *(int *)j;}
38 //_____________________________________________________________________________
39 AliZDCFragment::AliZDCFragment()
42 // Default constructor
47 //_____________________________________________________________________________
48 AliZDCFragment::AliZDCFragment(Float_t b)
52 // Standard constructor
59 for(Int_t i=0; i<=99; i++){
69 //_____________________________________________________________________________
70 void AliZDCFragment::GenerateIMF(Int_t* fZZ, Int_t &fNalpha)
76 // Coefficients of polynomial for average number of IMF
77 const Float_t kParamNimf[5]={0.011236,1.8364,56.572,-116.24,58.289};
78 // Coefficients of polynomial for fluctuations on average number of IMF
79 const Float_t kParamFluctNimf[4]={-0.13176,2.9392,-5.2147,2.3092};
80 // Coefficients of polynomial for average maximum Z of fragments
81 const Float_t kParamZmax[4]={0.16899,14.203,-2.8284,65.036};
82 // Coefficients of polynomial for fluctuations on maximum Z of fragments
83 const Float_t kParamFluctZmax[5]={0.013782,-0.17282,1.5065,1.0654,-2.4317};
84 // Coefficients of polynomial for exponent tau of fragments Z distribution
85 const Float_t kParamTau[3]={6.7233,-15.85,13.047};
86 //Coefficients of polynomial for average number of alphas
87 const Float_t kParamNalpha[4]={-0.68554,39.605,-68.311,30.165};
88 // Coefficients of polynomial for fluctuations on average number of alphas
89 const Float_t kParamFluctNalpha[5]={0.283,6.2141,-17.113,17.394,-6.6084};
90 // Coefficients of function for Pb nucleus skin
91 const Float_t kParamSkinPb[2]={0.93,11.05};
93 // Thickness of nuclear surface
94 const Float_t kNuclearThick = 0.52;
95 // Maximum impact parameter for U [r0*A**(1/3)]
96 const Float_t kbMaxU = 14.87;
97 // Maximum impact parameter for Pb [r0*A**(1/3)]
98 const Float_t kbMaxPb = 14.22;
99 // Z of the projectile
100 const Float_t kZProj = 82.;
102 // From b(Pb) to b(U)
103 Float_t bU = fB*kbMaxU/kbMaxPb;
105 // From b(U) to Zbound(U)
106 // --- A.Schuttauf et al, Nuc.Phys. A607 (1996) 457 ---------------
107 // From geometrical consideration and from dsigma/dZbound for U+U,
108 // which is approx. constant, the constant value is found
109 // integrating the nucleus cross surface from 0 to bmax=R1+R2 where
110 // R = 1.2*A**(1/3). This value has been measured in Aladin (U+U).
111 Float_t zbU = bU*bU*TMath::Pi()/7.48;
113 // Rescale Zbound for Pb
114 fZbAverage = kZProj/92.*zbU;
116 // Zbound is proportional to b**2 up to b < kbMaxPb-2*kNuclearThick
117 // and then it is an increasing exponential, imposing that at
118 // b=kbMaxPb-2kNuclearThick the two functions have the same derivative
119 Float_t bCore = kbMaxPb-2*kNuclearThick;
121 fZbAverage=kZProj*(1.-TMath::Exp(-kParamSkinPb[0]*(fB-kParamSkinPb[1])));
123 if(fZbAverage>kZProj) fZbAverage = kZProj;
124 Float_t zbNorm = fZbAverage/kZProj;
125 Float_t bNorm = fB/kbMaxPb;
127 // From Zbound to <Nimf>,<Zmax>,tau
128 // Polinomial fits to Aladin distribution
129 // --- A.Schuttauf et al, Nuc.Phys. A607 (1996) 457.
130 Float_t averageNimf = kParamNimf[0]+kParamNimf[1]*zbNorm+kParamNimf[2]*
131 TMath::Power(zbNorm,2)+kParamNimf[3]*TMath::Power(zbNorm,3)+
132 kParamNimf[4]*TMath::Power(zbNorm,4);
134 // Add fluctuation: from Singh et al.
135 Float_t fluctNimf = kParamFluctNimf[0]+kParamFluctNimf[1]*zbNorm+
136 kParamFluctNimf[2]*TMath::Power(zbNorm,2)+kParamFluctNimf[3]
137 *TMath::Power(zbNorm,3);
138 Float_t xx = gRandom->Gaus(0.0,1.0);
139 fluctNimf = fluctNimf*xx;
140 fNimf = Int_t(averageNimf+fluctNimf);
141 Float_t y = gRandom->Rndm();
142 if(y < ((averageNimf+fluctNimf)-fNimf)) fNimf += 1;
143 if(fNimf ==0 && zbNorm>0.75) fNimf = 1;
145 Float_t averageZmax = kParamZmax[0]+kParamZmax[1]*zbNorm+kParamZmax[2]*
146 TMath::Power(zbNorm,2)+kParamZmax[3]*TMath::Power(zbNorm,3);
147 fTau = kParamTau[0]+kParamTau[1]*zbNorm+kParamTau[2]*TMath::Power(zbNorm,2);
149 // Add fluctuation to mean value of Zmax (see Hubele)
150 Float_t fluctZmax = kParamFluctZmax[0]+kParamFluctZmax[1]*zbNorm+
151 kParamFluctZmax[2]*TMath::Power(zbNorm,2)+kParamFluctZmax[3]*
152 TMath::Power(zbNorm,3)+kParamFluctZmax[4]*TMath::Power(zbNorm,4);
153 fluctZmax = fluctZmax*kZProj/6.;
154 Float_t xg = gRandom->Gaus(0.0,1.0);
155 fluctZmax = fluctZmax*xg;
156 fZmax = averageZmax+fluctZmax;
157 if(fZmax>kZProj) fZmax = kZProj;
159 // printf("\n\n ------------------------------------------------------------");
160 // printf("\n Generation of nuclear fragments\n");
161 // printf("\n fNimf = %d\n", fNimf);
162 // printf("\n fZmax = %f\n", fZmax);
164 // Find the number of alpha particles
165 // from Singh et al. : Pb+emulsion
166 Float_t averageAlpha = kParamNalpha[0]+kParamNalpha[1]*zbNorm+
167 kParamNalpha[2]*TMath::Power(zbNorm,2)+kParamNalpha[3]*
168 TMath::Power(zbNorm,3);
169 Float_t fluctAlpha = kParamFluctNalpha[0]+kParamFluctNalpha[1]*
170 zbNorm+kParamFluctNalpha[2]*TMath::Power(zbNorm,2)+
171 kParamFluctNalpha[3]*TMath::Power(zbNorm,3)+
172 kParamFluctNalpha[4]*TMath::Power(zbNorm,4);
173 Float_t xxx = gRandom->Gaus(0.0,1.0);
174 fluctAlpha = fluctAlpha*xxx;
175 fNalpha = Int_t(averageAlpha+fluctAlpha);
176 Float_t yy = gRandom->Rndm();
177 if(yy < ((averageAlpha+fluctAlpha)-fNalpha)) fNalpha += 1;
180 // 1) for bNorm < 0.9 ==> first remove alphas, then fragments
181 // 2) for bNorm > 0.9 ==> first remove fragments, then alphas
184 Float_t zbFrag = 0, sumZ = 0.;
187 // remove alpha from zbound to find zbound for fragments (Z>=3)
188 zbFrag = fZbAverage-fNalpha*2;
195 // printf("\n choice = %d, fZbAverage = %f, zbFrag = %f \n", choice, fZbAverage, zbFrag);
198 // Check if zbFrag < fZmax
200 if(fNimf>0 && zbFrag>=2){
202 fZZ[0] = Int_t(zbFrag);
211 // Prepare the exponential charge distribution dN/dZ
221 TF1 *funTau = new TF1("funTau","1./(x**[0])",0.01,fZmax);
222 funTau->SetParameter(0,fTau);
224 // Extract randomly the charge of the fragments from the distribution
226 Float_t * zz = new Float_t[fNimf];
227 for(j=0; j<fNimf; j++){
230 for(i=0; i<fNimf; i++){
231 zz[i] = Float_t(funTau->GetRandom());
232 // printf("\n zz[%d] = %f \n",i,zz[i]);
236 // Sorting vector in ascending order with C function QSORT
237 qsort((void*)zz,fNimf,sizeof(Float_t),comp);
240 // for(Int_t i=0; i<fNimf; i++){
241 // printf("\n After sorting -> zz[%d] = %f \n",i,zz[i]);
244 // Rescale the maximum charge to fZmax
245 for(j=0; j<fNimf; j++){
246 fZZ[j] = Int_t (zz[j]*fZmax/zz[fNimf-1]);
247 if(fZZ[j]<3) fZZ[j] = 3;
248 // printf("\n fZZ[%d] = %d \n",j,fZZ[j]);
253 // Check that the sum of the bound charges is not > than Zbound-Zalfa
255 for(Int_t ii=0; ii<fNimf; ii++){
261 for(i=0; i< fNimf; i++){
271 if(choice == 1) return;
272 Int_t iDiff = Int_t((zbFrag-sumZ)/2);
283 for(i=0; i<fNimf; i++){
289 for(i=0; i<fNimf; i++){
295 //_____________________________________________________________________________
296 void AliZDCFragment::AttachNeutrons(Int_t *fZZ, Int_t *fNN, Int_t &fZtot,Int_t &fNtot)
299 // Prepare nuclear fragment by attaching a suitable number of neutrons
301 const Float_t kAIon[68]={1.87612,2.80943,3.7284,5.60305,6.53536,
302 6.53622,8.39479,9.32699,10.2551,11.17793,
303 13.04378,14.89917,17.6969,18.62284,21.41483,
304 22.34193,25.13314,26.06034,28.85188,29.7818,
305 32.57328,33.50356,36.29447,37.22492,41.87617,
306 44.66324,47.45401,48.38228,51.17447,52.10307,
307 54.89593,53.96644,58.61856,59.54963,68.85715,
308 74.44178,78.16309,81.88358,83.74571,91.19832,
309 98.64997,106.10997,111.68821,122.86796,
312 141.55,146.477,148.033,152.699,153.631,
313 155.802,157.357,162.022,162.984,166.2624,
314 168.554,171.349,173.4536,177.198,179.0518,
315 180.675,183.473,188.1345,190.77,193.729,
317 const Int_t kZIon[68]={1,1,2,3,3,
334 // printf("\n fNimf=%d\n",fNimf);
336 for(Int_t i=0; i<fNimf; i++) {
337 for(Int_t j=0; j<68; j++) {
339 if((fZZ[i]-iZ) == 0){
340 iA = Int_t(kAIon[j]/0.93149432+0.5);
344 else if((fZZ[i]-iZ) < 0){
346 iA = Int_t (kAIon[j-1]/0.93149432+0.5);
347 fNN[i] = iA - kZIon[j-1];
358 //_____________________________________________________________________________
359 Float_t AliZDCFragment::DeuteronNumber()
361 // Calculates the fraction of deuterum nucleus produced
363 Float_t deuteronProdPar[2] = {-0.068,0.0385};
364 Float_t deutNum = deuteronProdPar[0] + deuteronProdPar[1]*fB;
365 if(deutNum<0.) deutNum = 0.;