Initial energy density as function of impact parameter added.
[u/mrichter/AliRoot.git] / FASTSIM / AliFastGlauber.cxx
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5b3a5a5d 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
88cb7938 16/* $Id$ */
5b3a5a5d 17
18// from AliRoot
19#include "AliFastGlauber.h"
20// from root
21#include <TH1F.h>
22#include <TF1.h>
23#include <TF2.h>
24#include <TCanvas.h>
25#include <TRandom.h>
26#include <TFile.h>
27
28ClassImp(AliFastGlauber)
29
2a103154 30TF1* AliFastGlauber::fWSb = NULL;
31TF2* AliFastGlauber::fWSbz = NULL;
32TF1* AliFastGlauber::fWSz = NULL;
33TF1* AliFastGlauber::fWSta = NULL;
34TF2* AliFastGlauber::fWStarfi = NULL;
35TF2* AliFastGlauber::fWAlmond = NULL;
36TF1* AliFastGlauber::fWStaa = NULL;
37TF1* AliFastGlauber::fWSgeo = NULL;
38TF1* AliFastGlauber::fWSbinary = NULL;
39TF1* AliFastGlauber::fWSN = NULL;
40TF1* AliFastGlauber::fWPathLength0 = NULL;
41TF1* AliFastGlauber::fWPathLength = NULL;
42TF1* AliFastGlauber::fWEnergyDensity = NULL;
43TF1* AliFastGlauber::fWIntRadius = NULL;
44Float_t AliFastGlauber::fbMax = 0.;
5b3a5a5d 45
46AliFastGlauber::AliFastGlauber()
47{
48// Default Constructor
49//
50// Defaults for Pb
51 SetWoodSaxonParameters(6.624, 0.549, 0.00, 7.69e-4);
52 SetHardCrossSection();
53 SetMaxImpact();
54}
55
56void AliFastGlauber::Init(Int_t mode)
57{
58// Initialisation
59//
60// Wood-Saxon
61//
62 fWSb = new TF1("WSb", WSb, 0, fbMax, 4);
63 fWSb->SetParameter(0, fWSr0);
64 fWSb->SetParameter(1, fWSd);
65 fWSb->SetParameter(2, fWSw);
66 fWSb->SetParameter(3, fWSn);
67
68 fWSbz = new TF2("WSbz", WSbz, 0, fbMax, 4);
69 fWSbz->SetParameter(0, fWSr0);
70 fWSbz->SetParameter(1, fWSd);
71 fWSbz->SetParameter(2, fWSw);
72 fWSbz->SetParameter(3, fWSn);
73
74 fWSz = new TF1("WSz", WSz, 0, fbMax, 5);
75 fWSz->SetParameter(0, fWSr0);
76 fWSz->SetParameter(1, fWSd);
77 fWSz->SetParameter(2, fWSw);
78 fWSz->SetParameter(3, fWSn);
79
80//
81// Thickness
82//
83 fWSta = new TF1("WSta", WSta, 0., fbMax, 0);
84
85//
86// Overlap Kernel
87//
88 fWStarfi = new TF2("WStarfi", WStarfi, 0., fbMax, 0., TMath::Pi(), 1);
89 fWStarfi->SetParameter(0, 0.);
90 fWStarfi->SetNpx(200);
91 fWStarfi->SetNpy(20);
92//
f3a04204 93// Almond shaped interaction region
94//
95 fWAlmond = new TF2("WAlmond", WAlmond, -fbMax, fbMax, -fbMax, fbMax, 1);
96 fWAlmond->SetParameter(0, 0.);
97 fWAlmond->SetNpx(200);
98 fWAlmond->SetNpy(200);
99//
100// Path Length as a function of Phi
101//
102 fWPathLength0 = new TF1("WPathLength0", WPathLength0, -TMath::Pi(), TMath::Pi(), 1);
103 fWPathLength0->SetParameter(0, 0.);
104 fWPathLength = new TF1("WPathLength", WPathLength, -TMath::Pi(), TMath::Pi(), 2);
105// Impact Parameter
106 fWPathLength->SetParameter(0, 0.);
107// Number of interactions used for average
108 fWPathLength->SetParameter(1, 1000.);
109
110 fWIntRadius = new TF1("WIntRadius", WIntRadius, 0., fbMax, 1);
2a103154 111 fWIntRadius->SetParameter(0, 0.);
112
113
f3a04204 114//
5b3a5a5d 115// Overlap
116//
117 if (! mode) {
118 fWStaa = new TF1("WStaa", WStaa, 0., fbMax, 0);
119 fWStaa->SetNpx(100);
120 } else {
121 TFile* f = new TFile("$(ALICE_ROOT)/FASTSIM/data/glauberPbPb.root");
122 fWStaa = (TF1*) f->Get("WStaa");
123 }
124
2a103154 125//
126 fWEnergyDensity = new TF1("WEnergyDensity", WEnergyDensity, 0., 2. * fWSr0, 1);
127 fWEnergyDensity->SetParameter(0, fWSr0 + 1.);
128
5b3a5a5d 129//
130// Geometrical Cross-Section
131//
132 fWSgeo = new TF1("WSgeo", WSgeo, 0., fbMax, 0);
133 fWSgeo->SetNpx(100);
134//
135// Hard cross section (~ binary collisions)
136//
137 fWSbinary = new TF1("WSbinary", WSbinary, 0., fbMax, 1);
138 fWSbinary->SetParameter(0, fSigmaHard); // mb
139 fWSbinary->SetNpx(100);
140//
141// Hard collisions per event
142//
143 fWSN = new TF1("WSN", WSN, 0., fbMax, 1);
144 fWSN->SetNpx(100);
145}
146
147void AliFastGlauber::DrawWSb()
148{
149//
150// Draw Wood-Saxon Nuclear Density Function
151//
152 TCanvas *c1 = new TCanvas("c1","Wood Saxon",400,10,600,700);
153 c1->cd();
154 fWSb->Draw();
155}
156
157void AliFastGlauber::DrawOverlap()
158{
159//
160// Draw Overlap Function
161//
162 TCanvas *c2 = new TCanvas("c2","Overlap",400,10,600,700);
163 c2->cd();
164 fWStaa->Draw();
165}
166
167void AliFastGlauber::DrawThickness()
168{
169//
170// Draw Thickness Function
171//
172 TCanvas *c3 = new TCanvas("c3","Thickness",400,10,600,700);
173 c3->cd();
174 fWSta->Draw();
175}
176
177void AliFastGlauber::DrawGeo()
178{
179//
180// Draw Geometrical Cross-Section
181//
182 TCanvas *c3 = new TCanvas("c3","Geometrical Cross-Section",400,10,600,700);
183 c3->cd();
184 fWSgeo->Draw();
185}
186
187void AliFastGlauber::DrawBinary()
188{
189//
190// Draw Wood-Saxon Nuclear Density Function
191//
192 TCanvas *c4 = new TCanvas("c4","Binary Cross-Section",400,10,600,700);
193 c4->cd();
194 fWSbinary->Draw();
195}
196
197void AliFastGlauber::DrawN()
198{
199//
200// Draw Binaries per event
201//
202 TCanvas *c5 = new TCanvas("c5","Binaries per event",400,10,600,700);
203 c5->cd();
204 fWSN->Draw();
205}
206
f3a04204 207void AliFastGlauber::DrawKernel(Double_t b)
5b3a5a5d 208{
209//
210// Draw Kernel
211//
212 TCanvas *c6 = new TCanvas("c6","Kernel",400,10,600,700);
213 c6->cd();
f3a04204 214 fWStarfi->SetParameter(0, b);
5b3a5a5d 215 fWStarfi->Draw();
216}
217
f3a04204 218void AliFastGlauber::DrawAlmond(Double_t b)
219{
220//
2a103154 221// Draw Interaction Almond
f3a04204 222//
223 TCanvas *c7 = new TCanvas("c7","Almond",400,10,600,700);
224 c7->cd();
225 fWAlmond->SetParameter(0, b);
226 fWAlmond->Draw();
227}
228
229void AliFastGlauber::DrawPathLength0(Double_t b)
230{
231//
2a103154 232// Draw Path Length
f3a04204 233//
234 TCanvas *c8 = new TCanvas("c8","Path Length",400,10,600,700);
235 c8->cd();
236 fWPathLength0->SetParameter(0, b);
237 fWPathLength0->SetMinimum(0.);
238 fWPathLength0->SetMaximum(10.);
239 fWPathLength0->Draw();
240}
241
242void AliFastGlauber::DrawPathLength(Double_t b , Int_t ni)
243{
244//
2a103154 245// Draw Path Length
f3a04204 246//
247 TCanvas *c9 = new TCanvas("c9","Path Length",400,10,600,700);
248 c9->cd();
249 fWAlmond->SetParameter(0, b);
250
251 fWPathLength->SetParameter(0, b);
252 fWPathLength->SetParameter(1, Double_t (ni));
253 fWPathLength->SetMinimum(0.);
254 fWPathLength->SetMaximum(10.);
255 fWPathLength->Draw();
256}
257
258void AliFastGlauber::DrawIntRadius(Double_t b)
259{
260//
2a103154 261// Draw Interaction Radius
f3a04204 262//
263 TCanvas *c10 = new TCanvas("c10","Interaction Radius",400,10,600,700);
264 c10->cd();
265 fWIntRadius->SetParameter(0, b);
266 fWIntRadius->SetMinimum(0.);
267 fWIntRadius->Draw();
268}
269
2a103154 270void AliFastGlauber::DrawEnergyDensity()
271{
272//
273// Draw energy density
274//
275 TCanvas *c11 = new TCanvas("c11","Energy Density",400, 10, 600, 700);
276 c11->cd();
277 fWEnergyDensity->SetMinimum(0.);
278 fWEnergyDensity->Draw();
279}
280
5b3a5a5d 281Double_t AliFastGlauber::WSb(Double_t* x, Double_t* par)
282{
283//
284// Woods-Saxon Parameterisation
285// as a function of radius
286//
287 Double_t xx = x[0];
288 Double_t r0 = par[0];
289 Double_t d = par[1];
290 Double_t w = par[2];
291 Double_t n = par[3];
292
293 Double_t y = n * (1.+w*(xx/r0)*(xx/r0))/(1.+TMath::Exp((xx-r0)/d));
2a103154 294
5b3a5a5d 295 return y;
296}
297
298Double_t AliFastGlauber::WSbz(Double_t* x, Double_t* par)
299{
300//
301// Wood Saxon Parameterisation
302// as a function of z and b
303//
304 Double_t bb = x[0];
305 Double_t zz = x[1];
306 Double_t r0 = par[0];
307 Double_t d = par[1];
308 Double_t w = par[2];
309 Double_t n = par[3];
310 Double_t xx = TMath::Sqrt(bb*bb+zz*zz);
311 Double_t y = n * (1.+w*(xx/r0)*(xx/r0))/(1.+TMath::Exp((xx-r0)/d));
2a103154 312
5b3a5a5d 313 return y;
314}
315
316Double_t AliFastGlauber::WSz(Double_t* x, Double_t* par)
317{
318//
319// Wood Saxon Parameterisation
320// as a function of z for fixed b
321//
322 Double_t bb = par[4];
323 Double_t zz = x[0];
324 Double_t r0 = par[0];
325 Double_t d = par[1];
326 Double_t w = par[2];
327 Double_t n = par[3];
328 Double_t xx = TMath::Sqrt(bb*bb+zz*zz);
329 Double_t y = n * (1.+w*(xx/r0)*(xx/r0))/(1.+TMath::Exp((xx-r0)/d));
2a103154 330
5b3a5a5d 331 return y;
332}
333
f86dad79 334Double_t AliFastGlauber::WSta(Double_t* x, Double_t* /*par*/)
5b3a5a5d 335{
336//
337// Thickness function
338//
339 Double_t b = x[0];
340 fWSz->SetParameter(4, b);
341 Double_t y = 2. * fWSz->Integral(0., fbMax);
342 return y;
343}
344
345
346
347Double_t AliFastGlauber::WStarfi(Double_t* x, Double_t* par)
348{
349//
350// Kernel for overlap function
351//
352 Double_t b = par[0];
353 Double_t r1 = x[0];
354 Double_t phi = x[1];
355 Double_t r2 = TMath::Sqrt(r1 * r1 + b * b - 2. * r1 * b * TMath::Cos(phi));
356 Double_t y = r1 * fWSta->Eval(r1) * fWSta->Eval(r2);
357 return y;
358}
359
360
f3a04204 361Double_t AliFastGlauber::WAlmond(Double_t* x, Double_t* par)
362{
363//
364// Almond shaped interaction region
365//
366 Double_t b = par[0];
367 Double_t xx = x[0] + b/2.;
368 Double_t yy = x[1];
369 Double_t r1 = TMath::Sqrt(xx * xx + yy * yy);
370 Double_t phi = TMath::ATan2(yy,xx);
371
372 Double_t r2 = TMath::Sqrt(r1 * r1 + b * b - 2. * r1 * b * TMath::Cos(phi));
373//
374// Interaction probability calculated as product of thicknesses
375//
376 Double_t y = fWSta->Eval(r1) * fWSta->Eval(r2);
377 return y;
378}
379
380Double_t AliFastGlauber::WIntRadius(Double_t* x, Double_t* par)
381{
382//
383// Average radius at which interaction takes place
384//
385// Radius in the Almond
386 Double_t r = x[0];
387// Impact parameter
388 Double_t b = par[0];
389 fWAlmond->SetParameter(0, b);
390// Steps in phi
391 Double_t dphi = 2. * TMath::Pi() / 100.;
392// Average over phi
393 Double_t phi = 0.;
394 Double_t y = 0.;
395
396 for (Int_t i = 0; i < 100; i++) {
397 Double_t xx = r * TMath::Cos(phi);
398 Double_t yy = r * TMath::Sin(phi);
399 y += fWAlmond->Eval(xx,yy);
400 phi += dphi;
401 } // phi loop
402// Result multiplied by Jacobian (2 pi r)
403 return (2. * TMath::Pi() * y * r / 100.);
404}
405
406Double_t AliFastGlauber::WPathLength0(Double_t* x, Double_t* par)
407{
408//
409// Path Length as a function of phi for interaction point fixed at (0,0)
410//
411//
412// Steps in r
413 const Int_t np = 100;
414 const Double_t dr = fbMax/Double_t(np);
415// Impact parameter
416 Double_t b = par[0];
417// Phi direction in Almond
418 Double_t phi0 = x[0];
419 Double_t r = 0.;
420 Double_t rw = 0.;
421 Double_t w = 0.;
422// Step along radial direction phi
423 for (Int_t i = 0; i < np; i++) {
424//
425// Transform into target frame
426//
427 Double_t xx = r * TMath::Cos(phi0) + b / 2.;
428 Double_t yy = r * TMath::Sin(phi0);
429 Double_t phi = TMath::ATan2(yy, xx);
430
431 Double_t r1 = TMath::Sqrt(xx * xx + yy * yy);
432// Radius in projectile frame
433 Double_t r2 = TMath::Sqrt(r1 * r1 + b * b - 2. * r1 * b * TMath::Cos(phi));
434 Double_t y = fWSta->Eval(r1) * fWSta->Eval(r2);
435
436 rw += y * r;
437 w += y;
438 r += dr;
439 } // radial steps
440//
441// My length definition (is exact for hard sphere)
442 return (2. * rw / w);
443}
444
445Double_t AliFastGlauber::WPathLength(Double_t* x, Double_t* par)
446{
447//
448// Path Length as a function of phi
449// Interaction point from random distribution
450//
451//
452// r-steps
453//
454 const Int_t np = 100;
455 const Double_t dr = fbMax/Double_t(np);
456// Number of interactions
457 const Int_t npi = Int_t (par[1]);
458
459//
460// Impact parameter
461 Double_t b = par[0];
462// Phi direction
463 Double_t phi0 = x[0];
464
465 printf("phi0 %f \n", phi0);
466
467// Path length
468 Double_t l = 0.;
469
470 for (Int_t in = 0; in < npi; in ++) {
471 Double_t rw = 0.;
472 Double_t w = 0.;
473
474 // Interaction point
475 Double_t x0, y0;
476 fWAlmond->GetRandom2(x0, y0);
477// Initial radius
478 Double_t r0 = TMath::Sqrt(x0 * x0 + y0 * y0);
479 Int_t nps = Int_t ((fbMax - r0)/dr) - 1;
480
481 Double_t r = 0.;
482// Radial steps
483 for (Int_t i = 0; (i < nps ); i++) {
484
485// Transform into target frame
486 Double_t xx = x0 + r * TMath::Cos(phi0) + b / 2.;
487 Double_t yy = y0 + r * TMath::Sin(phi0);
488 Double_t phi = TMath::ATan2(yy, xx);
489 Double_t r1 = TMath::Sqrt(xx * xx + yy * yy);
490// Radius in projectile frame
491 Double_t r2 = TMath::Sqrt(r1 * r1 + b * b - 2. * r1 * b * TMath::Cos(phi));
492 Double_t y = fWSta->Eval(r1) * fWSta->Eval(r2);
493
494 rw += y * r;
495 w += y;
496 r += dr;
497 } // steps
498// Average over interactions
499 l += 2. * rw / w;
500 } // interactions
501 return (l / Double_t(npi));
502}
503
f86dad79 504Double_t AliFastGlauber::WStaa(Double_t* x, Double_t* /*par*/)
5b3a5a5d 505{
506//
507// Overlap function
508//
509 Double_t b = x[0];
510 fWStarfi->SetParameter(0, b);
511/*
512 Double_t al[2];
513 Double_t bl[2];
514 al[0] = 0.;
515 al[1] = 0.;
516 bl[0] = 6.6;
517 bl[1] = TMath::Pi();
518 Double_t err;
519
520 Double_t y = 2. * fWStarfi->IntegralMultiple(2, al, bl, 0.001, err);
521 printf("WStaa: %f %f %f\n", b, y, err);
522*/
523//
524// MC Integration
525//
526 Double_t y = 0;
527 for (Int_t i = 0; i < 100000; i++)
528 {
529 Double_t phi = TMath::Pi() * gRandom->Rndm();
530 Double_t b1 = fbMax * gRandom->Rndm();
531 y += fWStarfi->Eval(b1, phi);
532 }
533 y *= 2. * 0.1 * 208. * 208. * TMath::Pi() * fbMax / 100000.;
534 return y;
535}
536
f86dad79 537Double_t AliFastGlauber::WSgeo(Double_t* x, Double_t* /*par*/)
5b3a5a5d 538{
539//
540// Geometrical Cross-Section
541//
542 Double_t b = x[0];
543 Double_t taa = fWStaa->Eval(b);
544 const Double_t sigma = 55.6; // mbarn
545
546 Double_t y = 2. * TMath::Pi() * b * (1. - TMath::Exp(- sigma * taa)); // fm
547 return y;
548}
549
550
551Double_t AliFastGlauber::WSbinary(Double_t* x, Double_t* par)
552{
553//
c2140715 554// Number of binary collisions
5b3a5a5d 555//
556 Double_t b = x[0];
557 Double_t sigma = par[0];
558 Double_t taa = fWStaa->Eval(b);
559
560 Double_t y = 2. * TMath::Pi() * b * sigma * taa; // fm
561 return y;
562}
563
f86dad79 564Double_t AliFastGlauber::WSN(Double_t* x, Double_t* /*par*/)
5b3a5a5d 565{
566//
c2140715 567// Number of hard processes per event
5b3a5a5d 568//
569 Double_t b = x[0];
88cb7938 570 Double_t y = fWSbinary->Eval(b)/fWSgeo->Eval(b);
5b3a5a5d 571 return y;
572}
573
2a103154 574Double_t AliFastGlauber::WEnergyDensity(Double_t* x, Double_t* par)
575{
576//
577// Initial energy density as a function of the impact parameter
578//
579 Double_t b = x[0];
580 Double_t rA = par[0];
581
582 Double_t saa = (TMath::Pi() - 2. * TMath::ASin(b/ 2./ rA)) * rA * rA - b * TMath::Sqrt(rA * rA - b * b/ 4.);
583 Double_t taa = fWStaa->Eval(b);
584
585 return (taa/saa);
586}
587
5b3a5a5d 588void AliFastGlauber::SimulateTrigger(Int_t n)
589{
590 //
591 // Simulates Trigger
592 //
593 TH1F* mbtH = new TH1F("mbtH", "MB Trigger b-Distribution", 100, 0., 20.);
594 TH1F* hdtH = new TH1F("hdtH", "Hard Trigger b-Distribution", 100, 0., 20.);
595 TH1F* mbmH = new TH1F("mbmH", "MB Trigger Multiplicity Distribution", 100, 0., 8000.);
596 TH1F* hdmH = new TH1F("hdmH", "Hard Trigger Multiplicity Distribution", 100, 0., 8000.);
597
598 mbtH->SetXTitle("b [fm]");
599 hdtH->SetXTitle("b [fm]");
600 mbmH->SetXTitle("Multiplicity");
601 hdmH->SetXTitle("Multiplicity");
602
603 TCanvas *c0 = new TCanvas("c0","Trigger Simulation",400,10,600,700);
604 c0->Divide(2,1);
605 TCanvas *c1 = new TCanvas("c1","Trigger Simulation",400,10,600,700);
606 c1->Divide(1,2);
607
608 //
609 //
610 Init(1);
611 for (Int_t iev = 0; iev < n; iev++)
612 {
613 Float_t b, p, mult;
614 GetRandom(b, p, mult);
615 mbtH->Fill(b,1.);
616 hdtH->Fill(b, p);
617 mbmH->Fill(mult, 1.);
618 hdmH->Fill(mult, p);
619
620 c0->cd(1);
621 mbtH->Draw();
622 c0->cd(2);
623 hdtH->Draw();
624 c0->Update();
625
626 c1->cd(1);
627 mbmH->Draw();
628 c1->cd(2);
629 hdmH->Draw();
630 c1->Update();
631 }
632}
633
634void AliFastGlauber::GetRandom(Float_t& b, Float_t& p, Float_t& mult)
635{
636 //
637 // Gives back a random impact parameter, hard trigger probability and multiplicity
638 //
639 b = fWSgeo->GetRandom();
640 Float_t mu = fWSN->Eval(b);
641 p = 1.-TMath::Exp(-mu);
88cb7938 642 mult = 6000./fWSN->Eval(1.) * mu;
5b3a5a5d 643}
644
c2140715 645void AliFastGlauber::GetRandom(Int_t& bin, Bool_t& hard)
646{
647 //
648 // Gives back a random impact parameter bin, and hard trigger decission
649 //
650 Float_t b = fWSgeo->GetRandom();
651 Float_t mu = fWSN->Eval(b) * fSigmaHard;
652 Float_t p = 1.-TMath::Exp(-mu);
653 if (b < 5.) {
654 bin = 1;
655 } else if (b < 8.6) {
656 bin = 2;
657 } else if (b < 11.2) {
658 bin = 3;
659 } else if (b < 13.2) {
660 bin = 4;
204e011f 661 } else if (b < 15.0) {
c2140715 662 bin = 5;
204e011f 663 } else {
664 bin = 6;
c2140715 665 }
666
667 hard = kFALSE;
668
669 Float_t r = gRandom->Rndm();
670
671 if (r < p) hard = kTRUE;
672}
673
674
5b3a5a5d 675Float_t AliFastGlauber::GetRandomImpactParameter(Float_t bmin, Float_t bmax)
676{
677 //
678 // Gives back a random impact parameter in the range bmin .. bmax
679 //
680
681 Float_t b = -1.;
682 while(b < bmin || b > bmax)
683 b = fWSgeo->GetRandom();
684 return b;
685}
686
687Double_t AliFastGlauber::CrossSection(Double_t b1, Double_t b2)
688{
689 //
690 // Return cross-section integrated from b1 to b2
691 //
692
693 return fWSgeo->Integral(b1, b2)/100.;
694}
695
696Double_t AliFastGlauber::FractionOfHardCrossSection(Double_t b1, Double_t b2)
697{
698 //
699 // Return raction of hard cross-section integrated from b1 to b2
700 //
701
702 return fWSbinary->Integral(b1, b2)/fWSbinary->Integral(0., 100.);
703}
704
705
706Double_t AliFastGlauber::Binaries(Double_t b)
707{
708 //
709 // Return number of binary collisions normalized to 1 at b=0
710 //
711
270181a5 712 return fWSN->Eval(b)/fWSN->Eval(0.);
5b3a5a5d 713}