1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
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 **************************************************************************/
18 Revision 1.13 1999/09/29 09:24:35 fca
19 Introduction of the Copyright and cvs Log
23 ///////////////////////////////////////////////////////////////////////////////
25 // Transition Radiation Detector version 2 -- detailed simulation //
29 <img src="picts/AliTRDv2Class.gif">
34 ///////////////////////////////////////////////////////////////////////////////
41 #include "AliTRDmatrix.h"
48 //_____________________________________________________________________________
49 AliTRDv2::AliTRDv2(const char *name, const char *title)
53 // Standard constructor for Transition Radiation Detector version 2
73 for (iplan = 0; iplan < kNplan; iplan++) {
74 for (Int_t icham = 0; icham < kNcham; icham++) {
75 fRowMax[iplan][icham] = 0;
97 SetBufferSize(128000);
101 //_____________________________________________________________________________
102 AliTRDv2::~AliTRDv2()
105 if (fDeltaE) delete fDeltaE;
109 //_____________________________________________________________________________
110 void AliTRDv2::CreateGeometry()
113 // Create the GEANT geometry for the Transition Radiation Detector - Version 2
114 // This version covers the full azimuth.
116 // Author: Christoph Blume (C.Blume@gsi.de) 20/07/99
119 Float_t xpos, ypos, zpos;
121 // Check that FRAME is there otherwise we have no place where to put the TRD
122 AliModule* FRAME = gAlice->GetModule("FRAME");
125 // Define the chambers
126 AliTRD::CreateGeometry();
128 // Position the the TRD-sectors in all TRD-volumes in the spaceframe
132 gMC->Gspos("TRD ",1,"BTR1",xpos,ypos,zpos,0,"ONLY");
133 gMC->Gspos("TRD ",2,"BTR2",xpos,ypos,zpos,0,"ONLY");
134 gMC->Gspos("TRD ",3,"BTR3",xpos,ypos,zpos,0,"ONLY");
138 //_____________________________________________________________________________
139 void AliTRDv2::CreateMaterials()
142 // Create materials for the Transition Radiation Detector version 2
145 AliTRD::CreateMaterials();
149 //_____________________________________________________________________________
150 void AliTRDv2::Diffusion(Float_t driftlength, Float_t *xyz)
153 // Applies the diffusion smearing to the position of a single electron
156 if ((driftlength > 0) &&
157 (driftlength < kDrThick)) {
158 Float_t driftSqrt = TMath::Sqrt(driftlength);
159 Float_t sigmaT = driftSqrt * fDiffusionT;
160 Float_t sigmaL = driftSqrt * fDiffusionL;
161 xyz[0] = gRandom->Gaus(xyz[0], sigmaL);
162 xyz[1] = gRandom->Gaus(xyz[1], sigmaT);
163 xyz[2] = gRandom->Gaus(xyz[2], sigmaT);
173 //_____________________________________________________________________________
174 void AliTRDv2::Hits2Digits()
177 // Creates TRD digits from hits. This procedure includes the following:
179 // - Gas gain including fluctuations
180 // - Pad-response (simple Gaussian approximation)
181 // - Electronics noise
182 // - Electronics gain
185 // The corresponding parameter can be adjusted via the various Set-functions.
186 // If these parameters are not explicitly set, default values are used (see
188 // To produce digits from a galice.root file with TRD-hits use the
189 // digitsCreate.C macro.
192 printf(" Start creating digits\n");
194 ///////////////////////////////////////////////////////////////
196 ///////////////////////////////////////////////////////////////
198 // Converts number of electrons to fC
199 const Float_t el2fC = 1.602E-19 * 1.0E15;
201 ///////////////////////////////////////////////////////////////
210 // Position of pad 0,0,0
212 // chambers seen from the top:
213 // +----------------------------+
219 // +----------------------------+ +------>
221 // chambers seen from the side: ^
222 // +----------------------------+ time|
225 // +----------------------------+ +------>
228 // The pad row (z-direction)
229 Float_t row0[kNplan][kNcham];
230 for (iplan = 0; iplan < kNplan; iplan++) {
231 row0[iplan][0] = -fClengthI[iplan]/2. - fClengthM[iplan] - fClengthO[iplan]
233 row0[iplan][1] = -fClengthI[iplan]/2. - fClengthM[iplan]
235 row0[iplan][2] = -fClengthI[iplan]/2.
237 row0[iplan][3] = fClengthI[iplan]/2.
239 row0[iplan][4] = fClengthI[iplan]/2. + fClengthM[iplan]
242 // The pad column (rphi-direction)
243 Float_t col0[kNplan];
244 for (iplan = 0; iplan < kNplan; iplan++) {
245 col0[iplan] = -fCwidth[iplan]/2. + kCcthick;
248 Float_t time0[kNplan];
249 for (iplan = 0; iplan < kNplan; iplan++) {
250 time0[iplan] = kRmin + kCcframe/2. + kDrZpos - 0.5 * kDrThick
251 + iplan * (kCheight + kCspace);
254 // Get the pointer to the hit tree
255 TTree *HitTree = gAlice->TreeH();
256 // Get the pointer to the digits tree
257 TTree *DigitsTree = gAlice->TreeD();
259 // Get the number of entries in the hit tree
260 // (Number of primary particles creating a hit somewhere)
261 Int_t nTrack = (Int_t) HitTree->GetEntries();
264 Int_t chamEnd = kNcham;
265 if (fSensChamber) chamEnd = chamBeg = fSensChamber;
267 Int_t planEnd = kNplan;
268 if (fSensPlane) planEnd = planBeg = fSensPlane;
270 Int_t sectEnd = kNsect;
271 if (fSensSector) sectEnd = sectBeg = fSensSector;
273 // Loop through all the chambers
274 for (Int_t icham = chamBeg; icham < chamEnd; icham++) {
275 for (iplan = planBeg; iplan < planEnd; iplan++) {
276 for (Int_t isect = sectBeg; isect < sectEnd; isect++) {
278 printf(" Digitizing chamber %d, plane %d, sector %d\n"
279 ,icham+1,iplan+1,isect+1);
281 // Create a detector matrix to keep the signal and track numbers
282 AliTRDmatrix *matrix = new AliTRDmatrix(fRowMax[iplan][icham]
285 ,isect+1,icham+1,iplan+1);
287 // Loop through all entries in the tree
288 for (Int_t iTrack = 0; iTrack < nTrack; iTrack++) {
291 nBytes += HitTree->GetEvent(iTrack);
293 // Get the number of hits in the TRD created by this particle
294 Int_t nHit = fHits->GetEntriesFast();
296 // Loop through the TRD hits
297 for (Int_t iHit = 0; iHit < nHit; iHit++) {
299 if (!(TRDhit = (AliTRDhit *) fHits->UncheckedAt(iHit)))
302 Float_t x = TRDhit->fX;
303 Float_t y = TRDhit->fY;
304 Float_t z = TRDhit->fZ;
305 Float_t q = TRDhit->fQ;
306 Int_t track = TRDhit->fTrack;
307 Int_t plane = TRDhit->fPlane;
308 Int_t sector = TRDhit->fSector;
309 Int_t chamber = TRDhit->fChamber;
311 if ((sector != isect+1) ||
312 (plane != iplan+1) ||
313 (chamber != icham+1))
316 // Rotate the sectors on top of each other
317 Float_t phi = 2.0 * kPI / (Float_t) kNsect
318 * ((Float_t) sector - 0.5);
319 Float_t xRot = -x * TMath::Cos(phi) + y * TMath::Sin(phi);
320 Float_t yRot = x * TMath::Sin(phi) + y * TMath::Cos(phi);
323 // The hit position in pad coordinates (center pad)
324 // The pad row (z-direction)
325 Int_t rowH = (Int_t) ((zRot - row0[iplan][icham]) / fRowPadSize);
326 // The pad column (rphi-direction)
327 Int_t colH = (Int_t) ((yRot - col0[iplan] ) / fColPadSize);
329 Int_t timeH = (Int_t) ((xRot - time0[iplan] ) / fTimeBinSize);
331 // Array to sum up the signal in a box surrounding the
333 const Int_t timeBox = 5;
334 const Int_t colBox = 7;
335 const Int_t rowBox = 5;
336 Float_t signalSum[rowBox][colBox][timeBox];
337 for (iRow = 0; iRow < rowBox; iRow++ ) {
338 for (Int_t iCol = 0; iCol < colBox; iCol++ ) {
339 for (Int_t iTime = 0; iTime < timeBox; iTime++) {
340 signalSum[iRow][iCol][iTime] = 0;
345 // Loop over all electrons of this hit
346 Int_t nEl = (Int_t) q;
347 for (Int_t iEl = 0; iEl < nEl; iEl++) {
349 // Apply the diffusion smearing
350 Float_t driftlength = xRot - time0[iplan];
355 Diffusion(driftlength,xyz);
357 // At this point absorption effects that depend on the
358 // driftlength could be taken into account.
360 // The electron position and the distance to the hit position
362 // The pad row (z-direction)
363 Int_t rowE = (Int_t) ((xyz[2] - row0[iplan][icham]) / fRowPadSize);
364 Int_t rowD = rowH - rowE;
365 // The pad column (rphi-direction)
366 Int_t colE = (Int_t) ((xyz[1] - col0[iplan] ) / fColPadSize);
367 Int_t colD = colH - colE;
369 Int_t timeE = (Int_t) ((xyz[0] - time0[iplan] ) / fTimeBinSize);
370 Int_t timeD = timeH - timeE;
372 // Apply the gas gain including fluctuations
373 Int_t signal = (Int_t) (-fGasGain * TMath::Log(gRandom->Rndm()));
375 // The distance of the electron to the center of the pad
376 // in units of pad width
377 Float_t dist = (xyz[1] - col0[iplan] - (colE + 0.5) * fColPadSize)
380 // Sum up the signal in the different pixels
381 // and apply the pad response
382 Int_t rowIdx = rowD + (Int_t) ( rowBox / 2);
383 Int_t colIdx = colD + (Int_t) ( colBox / 2);
384 Int_t timeIdx = timeD + (Int_t) (timeBox / 2);
385 signalSum[rowIdx][colIdx-1][timeIdx] += PadResponse(dist-1.) * signal;
386 signalSum[rowIdx][colIdx ][timeIdx] += PadResponse(dist ) * signal;
387 signalSum[rowIdx][colIdx+1][timeIdx] += PadResponse(dist+1.) * signal;
391 // Add the padcluster to the detector matrix
392 for (iRow = 0; iRow < rowBox; iRow++ ) {
393 for (Int_t iCol = 0; iCol < colBox; iCol++ ) {
394 for (Int_t iTime = 0; iTime < timeBox; iTime++) {
396 Int_t rowB = rowH + iRow - (Int_t) ( rowBox / 2);
397 Int_t colB = colH + iCol - (Int_t) ( colBox / 2);
398 Int_t timeB = timeH + iTime - (Int_t) (timeBox / 2);
400 Float_t signalB = signalSum[iRow][iCol][iTime];
402 matrix->AddSignal(rowB,colB,timeB,signalB);
403 if (!(matrix->AddTrack(rowB,colB,timeB,track)))
404 printf("More than three tracks in a pixel!\n");
415 // Create the hits for this chamber
416 for (Int_t iRow = 0; iRow < fRowMax[iplan][icham]; iRow++ ) {
417 for (Int_t iCol = 0; iCol < fColMax[iplan] ; iCol++ ) {
418 for (Int_t iTime = 0; iTime < fTimeMax ; iTime++) {
420 Float_t signalAmp = matrix->GetSignal(iRow,iCol,iTime);
423 signalAmp = TMath::Max(gRandom->Gaus(signalAmp,fNoise),(Float_t) 0.0);
427 signalAmp *= fChipGain;
428 // Convert to ADC counts
429 Int_t adc = (Int_t) (signalAmp * (fADCoutRange / fADCinRange));
431 // Apply threshold on ADC value
432 if (adc > fADCthreshold) {
435 for (Int_t ii = 0; ii < 3; ii++) {
436 trackSave[ii] = matrix->GetTrack(iRow,iCol,iTime,ii);
440 digits[0] = matrix->GetSector();
441 digits[1] = matrix->GetChamber();
442 digits[2] = matrix->GetPlane();
448 // Add this digit to the TClonesArray
449 AddDigit(trackSave,digits);
464 // Fill the digits-tree
469 //_____________________________________________________________________________
470 void AliTRDv2::Init()
473 // Initialise Transition Radiation Detector after geometry has been built.
474 // Includes the default settings of all parameter for the digitization.
480 printf(" Only plane %d is sensitive\n",fSensPlane);
482 printf(" Only chamber %d is sensitive\n",fSensChamber);
484 printf(" Only sector %d is sensitive\n",fSensSector);
486 for (Int_t i = 0; i < 80; i++) printf("*");
489 // First ionization potential (eV) for the gas mixture (90% Xe + 10% CO2)
490 const Float_t kPoti = 12.1;
491 // Maximum energy (50 keV);
492 const Float_t kEend = 50000.0;
493 // Ermilova distribution for the delta-ray spectrum
494 Float_t Poti = TMath::Log(kPoti);
495 Float_t Eend = TMath::Log(kEend);
496 fDeltaE = new TF1("deltae",Ermilova,Poti,Eend,0);
498 // Identifier of the sensitive volume (drift region)
499 fIdSens = gMC->VolId("UL05");
501 // Identifier of the TRD-spaceframe volumina
502 fIdSpace1 = gMC->VolId("B028");
503 fIdSpace2 = gMC->VolId("B029");
504 fIdSpace3 = gMC->VolId("B030");
506 // Identifier of the TRD-driftchambers
507 fIdChamber1 = gMC->VolId("UCIO");
508 fIdChamber2 = gMC->VolId("UCIM");
509 fIdChamber3 = gMC->VolId("UCII");
511 // The default pad dimensions
512 if (!(fRowPadSize)) fRowPadSize = 4.5;
513 if (!(fColPadSize)) fColPadSize = 1.0;
514 if (!(fTimeBinSize)) fTimeBinSize = 0.1;
516 // The maximum number of pads
517 for (Int_t iplan = 0; iplan < kNplan; iplan++) {
519 fRowMax[iplan][0] = 1 + TMath::Nint((fClengthO[iplan] - 2. * kCcthick)
520 / fRowPadSize - 0.5);
521 fRowMax[iplan][1] = 1 + TMath::Nint((fClengthM[iplan] - 2. * kCcthick)
522 / fRowPadSize - 0.5);
523 fRowMax[iplan][2] = 1 + TMath::Nint((fClengthI[iplan] - 2. * kCcthick)
524 / fRowPadSize - 0.5);
525 fRowMax[iplan][3] = 1 + TMath::Nint((fClengthM[iplan] - 2. * kCcthick)
526 / fRowPadSize - 0.5);
527 fRowMax[iplan][4] = 1 + TMath::Nint((fClengthO[iplan] - 2. * kCcthick)
528 / fRowPadSize - 0.5);
530 fColMax[iplan] = 1 + TMath::Nint((fCwidth[iplan] - 2. * kCcthick)
531 / fColPadSize - 0.5);
534 fTimeMax = 1 + TMath::Nint(kDrThick / fTimeBinSize - 0.5);
536 // The default parameter for the digitization
537 if (!(fGasGain)) fGasGain = 2.0E3;
538 if (!(fNoise)) fNoise = 3000.;
539 if (!(fChipGain)) fChipGain = 10.;
540 if (!(fADCoutRange)) fADCoutRange = 255.;
541 if (!(fADCinRange)) fADCinRange = 2000.;
542 if (!(fADCthreshold)) fADCthreshold = 0;
544 // Transverse and longitudinal diffusion coefficients (Xe/Isobutane)
545 if (!(fDiffusionT)) fDiffusionT = 0.060;
546 if (!(fDiffusionL)) fDiffusionL = 0.017;
550 //_____________________________________________________________________________
551 void AliTRDv2::MakeBranch(Option_t* option)
554 // Create Tree branches for the TRD digits.
557 Int_t buffersize = 4000;
558 Char_t branchname[10];
560 sprintf(branchname,"%s",GetName());
562 AliDetector::MakeBranch(option);
564 Char_t *D = strstr(option,"D");
565 if (fDigits && gAlice->TreeD() && D) {
566 gAlice->TreeD()->Branch(branchname,&fDigits, buffersize);
567 printf("Making Branch %s for digits\n",branchname);
572 //_____________________________________________________________________________
573 Float_t AliTRDv2::PadResponse(Float_t x)
576 // The pad response for the chevron pads.
577 // We use a simple Gaussian approximation which should be good
578 // enough for our purpose.
581 // The parameters for the response function
582 const Float_t aa = 0.8872;
583 const Float_t bb = -0.00573;
584 const Float_t cc = 0.454;
585 const Float_t cc2 = cc*cc;
587 Float_t pr = aa * (bb + TMath::Exp(-x*x / (2. * cc2)));
589 //TF1 *funPR = new TF1("funPR","[0]*([1]+exp(-x*x /(2.*[2])))",-3,3);
590 //funPR->SetParameter(0,aa );
591 //funPR->SetParameter(1,bb );
592 //funPR->SetParameter(2,cc2);
594 //Float_t pr = funPR->Eval(distance);
602 //_____________________________________________________________________________
603 void AliTRDv2::SetSensPlane(Int_t iplane)
606 // Defines the hit-sensitive plane (1-6)
609 if ((iplane < 0) || (iplane > 6)) {
610 printf("Wrong input value: %d\n",iplane);
611 printf("Use standard setting\n");
622 //_____________________________________________________________________________
623 void AliTRDv2::SetSensChamber(Int_t ichamber)
626 // Defines the hit-sensitive chamber (1-5)
629 if ((ichamber < 0) || (ichamber > 5)) {
630 printf("Wrong input value: %d\n",ichamber);
631 printf("Use standard setting\n");
638 fSensChamber = ichamber;
642 //_____________________________________________________________________________
643 void AliTRDv2::SetSensSector(Int_t isector)
646 // Defines the hit-sensitive sector (1-18)
649 if ((isector < 0) || (isector > 18)) {
650 printf("Wrong input value: %d\n",isector);
651 printf("Use standard setting\n");
658 fSensSector = isector;
662 //_____________________________________________________________________________
663 void AliTRDv2::StepManager()
666 // Called at every step in the Transition Radiation Detector version 2.
667 // Slow simulator. Every charged track produces electron cluster as hits
668 // along its path across the drift volume. The step size is set acording
669 // to Bethe-Bloch. The energy distribution of the delta electrons follows
670 // a spectrum taken from Ermilova et al.
673 Int_t iIdSens, icSens;
674 Int_t iIdSpace, icSpace;
675 Int_t iIdChamber, icChamber;
679 Int_t secMap1[10] = { 3, 7, 8, 9, 10, 11, 2, 1, 18, 17 };
680 Int_t secMap2[ 5] = { 16, 15, 14, 13, 12 };
681 Int_t secMap3[ 3] = { 5, 6, 4 };
691 Double_t betaGamma, pp;
693 TLorentzVector pos, mom;
694 TClonesArray &lhits = *fHits;
696 const Double_t kBig = 1.0E+12;
699 const Float_t kWion = 22.04;
700 // Maximum energy for e+ e- g for the step-size calculation
701 const Float_t kPTotMax = 0.002;
702 // Plateau value of the energy-loss for electron in xenon
703 // taken from: Allison + Comb, Ann. Rev. Nucl. Sci. (1980), 30, 253
704 //const Double_t kPlateau = 1.70;
705 // the averaged value (26/3/99)
706 const Float_t kPlateau = 1.55;
707 // dN1/dx|min for the gas mixture (90% Xe + 10% CO2)
708 const Float_t kPrim = 48.0;
709 // First ionization potential (eV) for the gas mixture (90% Xe + 10% CO2)
710 const Float_t kPoti = 12.1;
712 // Set the maximum step size to a very large number for all
713 // neutral particles and those outside the driftvolume
714 gMC->SetMaxStep(kBig);
716 // Use only charged tracks
717 if (( gMC->TrackCharge() ) &&
718 (!gMC->IsTrackStop() ) &&
719 (!gMC->IsTrackDisappeared())) {
721 // Inside a sensitive volume?
722 iIdSens = gMC->CurrentVolID(icSens);
723 if (iIdSens == fIdSens) {
725 iIdSpace = gMC->CurrentVolOffID(4,icSpace );
726 iIdChamber = gMC->CurrentVolOffID(1,icChamber);
728 // Calculate the energy of the delta-electrons
729 eDelta = TMath::Exp(fDeltaE->GetRandom()) - kPoti;
730 eDelta = TMath::Max(eDelta,0.0);
732 // The number of secondary electrons created
733 qTot = (Double_t) ((Int_t) (eDelta / kWion) + 1);
735 // The hit coordinates and charge
736 gMC->TrackPosition(pos);
743 if (iIdSpace == fIdSpace1)
744 vol[0] = secMap1[icSpace-1];
745 else if (iIdSpace == fIdSpace2)
746 vol[0] = secMap2[icSpace-1];
747 else if (iIdSpace == fIdSpace3)
748 vol[0] = secMap3[icSpace-1];
750 // The chamber number
756 if (iIdChamber == fIdChamber1)
757 vol[1] = (hits[2] < 0 ? 1 : 5);
758 else if (iIdChamber == fIdChamber2)
759 vol[1] = (hits[2] < 0 ? 2 : 4);
760 else if (iIdChamber == fIdChamber3)
764 vol[2] = icChamber - TMath::Nint((Float_t) (icChamber / 7)) * 6;
766 // Check on selected volumes
767 Int_t addthishit = 1;
769 if ((fSensPlane) && (vol[2] != fSensPlane )) addthishit = 0;
770 if ((fSensChamber) && (vol[1] != fSensChamber)) addthishit = 0;
771 if ((fSensSector) && (vol[0] != fSensSector )) addthishit = 0;
777 new(lhits[fNhits++]) AliTRDhit(fIshunt,gAlice->CurrentTrack(),vol,hits);
779 // The energy loss according to Bethe Bloch
780 gMC->TrackMomentum(mom);
782 iPid = gMC->TrackPid();
784 ((iPid <= 3) && (pTot < kPTotMax))) {
785 aMass = gMC->TrackMass();
786 betaGamma = pTot / aMass;
787 pp = kPrim * BetheBloch(betaGamma);
788 // Take charge > 1 into account
789 charge = gMC->TrackCharge();
790 if (TMath::Abs(charge) > 1) pp = pp * charge*charge;
792 // Electrons above 20 Mev/c are at the plateau
794 pp = kPrim * kPlateau;
797 // Calculate the maximum step size for the next tracking step
801 while ((random[0] == 1.) || (random[0] == 0.));
802 gMC->SetMaxStep( - TMath::Log(random[0]) / pp);
807 // set step size to maximal value
808 gMC->SetMaxStep(kBig);
817 //_____________________________________________________________________________
818 Double_t AliTRDv2::BetheBloch(Double_t bg)
821 // Parametrization of the Bethe-Bloch-curve
822 // The parametrization is the same as for the TPC and is taken from Lehrhaus.
825 // This parameters have been adjusted to averaged values from GEANT
826 const Double_t kP1 = 7.17960e-02;
827 const Double_t kP2 = 8.54196;
828 const Double_t kP3 = 1.38065e-06;
829 const Double_t kP4 = 5.30972;
830 const Double_t kP5 = 2.83798;
832 // This parameters have been adjusted to Xe-data found in:
833 // Allison & Cobb, Ann. Rev. Nucl. Sci. (1980), 30, 253
834 //const Double_t kP1 = 0.76176E-1;
835 //const Double_t kP2 = 10.632;
836 //const Double_t kP3 = 3.17983E-6;
837 //const Double_t kP4 = 1.8631;
838 //const Double_t kP5 = 1.9479;
841 Double_t yy = bg / TMath::Sqrt(1. + bg*bg);
842 Double_t aa = TMath::Power(yy,kP4);
843 Double_t bb = TMath::Power((1./bg),kP5);
844 bb = TMath::Log(kP3 + bb);
845 return ((kP2 - aa - bb)*kP1 / aa);
852 //_____________________________________________________________________________
853 Double_t Ermilova(Double_t *x, Double_t *)
856 // Calculates the delta-ray energy distribution according to Ermilova.
857 // Logarithmic scale !
868 Float_t vxe[nV] = { 2.3026, 2.9957, 3.4012, 3.6889, 3.9120
869 , 4.0943, 4.2485, 4.3820, 4.4998, 4.6052
870 , 4.7005, 5.0752, 5.2983, 5.7038, 5.9915
871 , 6.2146, 6.5221, 6.9078, 7.3132, 7.6009
872 , 8.0064, 8.5172, 8.6995, 8.9872, 9.2103
873 , 9.4727, 9.9035,10.3735,10.5966,10.8198
876 Float_t vye[nV] = { 80.0 , 31.0 , 23.3 , 21.1 , 21.0
877 , 20.9 , 20.8 , 20.0 , 16.0 , 11.0
878 , 8.0 , 6.0 , 5.2 , 4.6 , 4.0
879 , 3.5 , 3.0 , 1.4 , 0.67 , 0.44
880 , 0.3 , 0.18 , 0.12 , 0.08 , 0.056
881 , 0.04 , 0.023, 0.015, 0.011, 0.01
890 dpos = energy - vxe[pos2++];
894 if (pos2 > nV) pos2 = nV;
897 // Differentiate between the sampling points
898 dnde = (vye[pos1] - vye[pos2]) / (vxe[pos2] - vxe[pos1]);