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[u/mrichter/AliRoot.git] / PHOS / AliPHOSv1.cxx

/**************************************************************************
 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
 *                                                                        *
 * Author: The ALICE Off-line Project.                                    *
 * Contributors are mentioned in the code where appropriate.              *
 *                                                                        *
 * Permission to use, copy, modify and distribute this software and its   *
 * documentation strictly for non-commercial purposes is hereby granted   *
 * without fee, provided that the above copyright notice appears in all   *
 * copies and that both the copyright notice and this permission notice   *
 * appear in the supporting documentation. The authors make no claims     *
 * about the suitability of this software for any purpose. It is          *
 * provided "as is" without express or implied warranty.                  *
 **************************************************************************/

/* $Id$ */

/* History of cvs commits:
 *
 * $Log$
 * Revision 1.111  2007/07/24 09:41:19  morsch
 * AliStack included for kKeepBit.
 *
 * Revision 1.110  2007/03/10 08:58:52  kharlov
 * Protection for noCPV geometry
 *
 * Revision 1.109  2007/03/01 11:37:37  kharlov
 * Strip units changed from 8x1 to 8x2 (T.Pocheptsov)
 *
 * Revision 1.108  2007/02/02 09:40:50  alibrary
 * Includes required by ROOT head
 *
 * Revision 1.107  2007/02/01 10:34:47  hristov
 * Removing warnings on Solaris x86
 *
 * Revision 1.106  2006/11/14 17:11:15  hristov
 * Removing inheritances from TAttLine, TAttMarker and AliRndm in AliModule. The copy constructor and assignment operators are moved to the private part of the class and not implemented. The corresponding changes are propagated to the detectors
 *
 * Revision 1.105  2006/09/13 07:31:01  kharlov
 * Effective C++ corrections (T.Pocheptsov)
 *
 * Revision 1.104  2005/05/28 14:19:05  schutz
 * Compilation warnings fixed by T.P.
 *
 */

//_________________________________________________________________________
// Implementation version v1 of PHOS Manager class 
//---
//---
// Layout EMC + CPV  has name IHEP:
// Produces hits for CPV, cumulated hits
//---
//---
//*-- Author: Yves Schutz (SUBATECH)


// --- ROOT system ---
#include <TClonesArray.h>
#include <TParticle.h>
#include <TVirtualMC.h>

// --- Standard library ---


// --- AliRoot header files ---
#include "AliPHOSCPVDigit.h"
#include "AliPHOSGeometry.h"
#include "AliPHOSHit.h"
#include "AliPHOSv1.h"
#include "AliRun.h"
#include "AliMC.h"
#include "AliStack.h"
#include "AliPHOSSimParam.h"

ClassImp(AliPHOSv1)

//____________________________________________________________________________
AliPHOSv1::AliPHOSv1() : fCPVDigits("AliPHOSCPVDigit",20)
{
  //Def ctor.
}

//____________________________________________________________________________
AliPHOSv1::AliPHOSv1(const char *name, const char *title):
  AliPHOSv0(name,title), fCPVDigits("AliPHOSCPVDigit",20)
{
  //
  // We store hits :
  //   - fHits (the "normal" one), which retains the hits associated with
  //     the current primary particle being tracked
  //     (this array is reset after each primary has been tracked).
  //



  // We do not want to save in TreeH the raw hits
  // But save the cumulated hits instead (need to create the branch myself)
  // It is put in the Digit Tree because the TreeH is filled after each primary
  // and the TreeD at the end of the event (branch is set in FinishEvent() ). 
  
  fHits= new TClonesArray("AliPHOSHit",1000) ;
//   fCPVDigits("AliPHOSCPVDigit",20);
  gAlice->GetMCApp()->AddHitList(fHits) ; 

  fNhits = 0 ;

  fIshunt     =  2 ; // All hits are associated with primary particles
}

//____________________________________________________________________________
AliPHOSv1::~AliPHOSv1()
{
  // dtor
 if ( fHits) {
    fHits->Delete() ; 
    delete fHits ;
    fHits = 0 ; 
 }
}

//____________________________________________________________________________
void AliPHOSv1::AddHit(Int_t shunt, Int_t primary, Int_t Id, Float_t * hits)
{
  // Add a hit to the hit list.
  // A PHOS hit is the sum of all hits in a single crystal from one primary and within some time gate

  Int_t hitCounter ;
  AliPHOSHit *newHit ;
  AliPHOSHit *curHit ;
  Bool_t deja = kFALSE ;
  AliPHOSGeometry * geom = GetGeometry() ; 

  newHit = new AliPHOSHit(shunt, primary, Id, hits) ;

  for ( hitCounter = fNhits-1 ; hitCounter >= 0 && !deja ; hitCounter-- ) {
    curHit = dynamic_cast<AliPHOSHit*>((*fHits)[hitCounter]) ;
    if(curHit->GetPrimary() != primary) break ; 
           // We add hits with the same primary, while GEANT treats primaries succesively 
    if( *curHit == *newHit ) {
      *curHit + *newHit ;
      deja = kTRUE ;
    }
  }
         
  if ( !deja ) {
    new((*fHits)[fNhits]) AliPHOSHit(*newHit) ;
    // get the block Id number
    Int_t relid[4] ;
    geom->AbsToRelNumbering(Id, relid) ;

    fNhits++ ;
  }
  
  delete newHit;
}

//____________________________________________________________________________
void AliPHOSv1::FinishPrimary() 
{
  // called at the end of each track (primary) by AliRun
  // hits are reset for each new track
  // accumulate the total hit-multiplicity

}

//____________________________________________________________________________
void AliPHOSv1::FinishEvent() 
{
  // called at the end of each event by AliRun
  // accumulate the hit-multiplicity and total energy per block 
  // if the values have been updated check it
  
  AliDetector::FinishEvent(); 
}
//____________________________________________________________________________
void AliPHOSv1::StepManager(void)
{
   // Accumulates hits as long as the track stays in a single crystal or CPV gas Cell

  Int_t          relid[4] ;           // (box, layer, row, column) indices
  Int_t          absid    ;           // absolute cell ID number
  Float_t        xyzte[5]={-1000.,-1000.,-1000.,0.,0.}  ; // position wrt MRS, time and energy deposited
  TLorentzVector pos      ;           // Lorentz vector of the track current position
  Int_t          copy     ;

  Int_t moduleNumber ;
  
  static Int_t idPCPQ = -1;
  if (strstr(fTitle.Data(),"noCPV") == 0) 
    idPCPQ = gMC->VolId("PCPQ");

  if( gMC->CurrentVolID(copy) == idPCPQ &&
     (gMC->IsTrackEntering() ) &&
      gMC->TrackCharge() != 0) {      
    
    gMC -> TrackPosition(pos);

    Float_t xyzm[3], xyzd[3] ;
    Int_t i;
    for (i=0; i<3; i++) xyzm[i] = pos[i];
    gMC -> Gmtod (xyzm, xyzd, 1);    // transform coordinate from master to daughter system    


    Float_t        xyd[3]={0,0,0}   ;   //local position of the entering
    xyd[0]  = xyzd[0];
    xyd[1]  =-xyzd[2];
    xyd[2]  =-xyzd[1];
    
    // Current momentum of the hit's track in the local ref. system
    TLorentzVector pmom     ;        //momentum of the particle initiated hit
    gMC -> TrackMomentum(pmom);
    Float_t pm[3], pd[3];
    for (i=0; i<3; i++)  
      pm[i]   = pmom[i];
    
    gMC -> Gmtod (pm, pd, 2);        // transform 3-momentum from master to daughter system
    pmom[0] = pd[0];
    pmom[1] =-pd[1];
    pmom[2] =-pd[2];

    // Digitize the current CPV hit:
    
    // 1. find pad response and    
    gMC->CurrentVolOffID(3,moduleNumber);
    moduleNumber--;
    
//     TClonesArray *cpvDigits = new TClonesArray("AliPHOSCPVDigit",0);   // array of digits for current hit
    CPVDigitize(pmom,xyd,&fCPVDigits);
      
    Float_t xmean = 0;
    Float_t zmean = 0;
    Float_t qsum  = 0;
    Int_t   idigit,ndigits;
    
    // 2. go through the current digit list and sum digits in pads
    
    ndigits = fCPVDigits.GetEntriesFast();
    for (idigit=0; idigit<ndigits-1; idigit++) {
      AliPHOSCPVDigit  *cpvDigit1 = dynamic_cast<AliPHOSCPVDigit*>(fCPVDigits.UncheckedAt(idigit));
      Float_t x1 = cpvDigit1->GetXpad() ;
      Float_t z1 = cpvDigit1->GetYpad() ;
      for (Int_t jdigit=idigit+1; jdigit<ndigits; jdigit++) {
	AliPHOSCPVDigit  *cpvDigit2 = dynamic_cast<AliPHOSCPVDigit*>(fCPVDigits.UncheckedAt(jdigit));
	Float_t x2 = cpvDigit2->GetXpad() ;
	Float_t z2 = cpvDigit2->GetYpad() ;
	if (x1==x2 && z1==z2) {
	  Float_t qsumpad = cpvDigit1->GetQpad() + cpvDigit2->GetQpad() ;
	  cpvDigit2->SetQpad(qsumpad) ;
	  fCPVDigits.RemoveAt(idigit) ;
	}
      }
    }
    fCPVDigits.Compress() ;
    
    // 3. add digits to temporary hit list fTmpHits
    
    ndigits = fCPVDigits.GetEntriesFast();
    for (idigit=0; idigit<ndigits; idigit++) {
      AliPHOSCPVDigit  *cpvDigit = dynamic_cast<AliPHOSCPVDigit*>(fCPVDigits.UncheckedAt(idigit));
      relid[0] = moduleNumber + 1 ;                             // CPV (or PHOS) module number
      relid[1] =-1 ;                                            // means CPV
      relid[2] = cpvDigit->GetXpad() ;                          // column number of a pad
      relid[3] = cpvDigit->GetYpad() ;                          // row    number of a pad
      
      // get the absolute Id number
      GetGeometry()->RelToAbsNumbering(relid, absid) ; 
      
      // add current digit to the temporary hit list

      xyzte[3] = gMC->TrackTime() ;
      xyzte[4] = cpvDigit->GetQpad() ;                          // amplitude in a pad

      Int_t primary  =  gAlice->GetMCApp()->GetPrimary( gAlice->GetMCApp()->GetCurrentTrackNumber() ); 
      AddHit(fIshunt, primary, absid, xyzte);  
      
      if (cpvDigit->GetQpad() > 0.02) {
	xmean += cpvDigit->GetQpad() * (cpvDigit->GetXpad() + 0.5);
	zmean += cpvDigit->GetQpad() * (cpvDigit->GetYpad() + 0.5);
	qsum  += cpvDigit->GetQpad();
      }
    }
    fCPVDigits.Clear();
  }

 
  static Int_t idPXTL = gMC->VolId("PXTL");  
  if(gMC->CurrentVolID(copy) == idPXTL ) { //  We are inside a PBWO crystal

    gMC->TrackPosition(pos) ;
    xyzte[0] = pos[0] ;
    xyzte[1] = pos[1] ;
    xyzte[2] = pos[2] ;

    Float_t lostenergy = gMC->Edep(); 
    
    //Put in the TreeK particle entering PHOS and all its parents
    if ( gMC->IsTrackEntering() ){
      Float_t xyzd[3] ;
      gMC -> Gmtod (xyzte, xyzd, 1);    // transform coordinate from master to daughter system    
      if (xyzd[1] < -GetGeometry()->GetCrystalSize(1)/2.+0.1){   //Entered close to forward surface  
	Int_t parent = gAlice->GetMCApp()->GetCurrentTrackNumber() ; 
	TParticle * part = gAlice->GetMCApp()->Particle(parent) ; 
	Float_t vert[3],vertd[3] ;
	vert[0]=part->Vx() ;
	vert[1]=part->Vy() ;
	vert[2]=part->Vz() ;
	gMC -> Gmtod (vert, vertd, 1);    // transform coordinate from master to daughter system
	if(vertd[1]<-GetGeometry()->GetCrystalSize(1)/2.-0.1){ //Particle is created in foront of PHOS 
	                                                       //0.1 to get rid of numerical errors 
	  part->SetBit(kKeepBit);
	  while ( parent != -1 ) {
	    part = gAlice->GetMCApp()->Particle(parent) ; 
	    part->SetBit(kKeepBit);
	    parent = part->GetFirstMother() ; 
	  }
	}
      }
    }
    if ( lostenergy != 0 ) {  // Track is inside the crystal and deposits some energy 
      xyzte[3] = gMC->TrackTime() ;     
      
      gMC->CurrentVolOffID(10, moduleNumber) ; // get the PHOS module number ;
      
      Int_t strip ;
      gMC->CurrentVolOffID(3, strip);
      Int_t cell ;
      gMC->CurrentVolOffID(2, cell);

      //Old formula for row is wrong. For example, I have strip 56 (28 for 2 x 8), row must be 1.
      //But row == 1 + 56 - 56 % 56 == 57 (row == 1 + 28 - 28 % 28 == 29)
      //Int_t row = 1 + GetGeometry()->GetEMCAGeometry()->GetNStripZ() - strip % (GetGeometry()->GetEMCAGeometry()->GetNStripZ()) ;
      Int_t row = GetGeometry()->GetEMCAGeometry()->GetNStripZ() - (strip - 1) % (GetGeometry()->GetEMCAGeometry()->GetNStripZ()) ;
      Int_t col = (Int_t) TMath::Ceil((Double_t) strip/(GetGeometry()->GetEMCAGeometry()->GetNStripZ())) -1 ;

      // Absid for 8x2-strips. Looks nice :) 
      absid = (moduleNumber-1)*GetGeometry()->GetNCristalsInModule() + 
	            row * 2 + (col*GetGeometry()->GetEMCAGeometry()->GetNCellsXInStrip() + (cell - 1) / 2)*GetGeometry()->GetNZ() - (cell & 1 ? 1 : 0);

      
      //Calculates the light yield, the number of photons produced in the
      //crystal 
      //There is no dependence of reponce on distance from energy deposition to APD
      Float_t lightYield = gRandom->Poisson(AliPHOSSimParam::GetInstance()->GetLightFactor() * lostenergy) ;

      //Calculates de energy deposited in the crystal  
      xyzte[4] = AliPHOSSimParam::GetInstance()->GetAPDFactor() * lightYield ;
      
      Int_t primary ;
      if(fIshunt == 2){
	primary = gAlice->GetMCApp()->GetCurrentTrackNumber() ;
	TParticle * part = gAlice->GetMCApp()->Particle(primary) ;
	while ( !part->TestBit(kKeepBit) ) {
	  primary = part->GetFirstMother() ;
	  if(primary == -1){	    
	    primary  =  gAlice->GetMCApp()->GetPrimary( gAlice->GetMCApp()->GetCurrentTrackNumber() ); 
	    break ; //there is a possibility that particle passed e.g. thermal isulator and hits a side 
	  //surface of the crystal. In this case it may have no primary at all. 
	  //We can not easily separate this case from the case when this is part of the shower, 
	  //developed in the neighboring crystal.
	  }
	  part = gAlice->GetMCApp()->Particle(primary) ;
	}
      }
      else{
	primary  =  gAlice->GetMCApp()->GetPrimary( gAlice->GetMCApp()->GetCurrentTrackNumber() ); 
      }
      
      // add current hit to the hit list
      // Info("StepManager","%d %d", primary, tracknumber) ; 
      AddHit(fIshunt, primary, absid, xyzte);
        
    } // there is deposited energy
  } // we are inside a PHOS Xtal
  
}

//____________________________________________________________________________
void AliPHOSv1::CPVDigitize (TLorentzVector p, Float_t *zxhit, TClonesArray *cpvDigits)
{
  // ------------------------------------------------------------------------
  // Digitize one CPV hit:
  // On input take exact 4-momentum p and position zxhit of the hit,
  // find the pad response around this hit and
  // put the amplitudes in the pads into array digits
  //
  // Author: Yuri Kharlov (after Serguei Sadovsky)
  // 2 October 2000
  // ------------------------------------------------------------------------

  const Float_t kCelWr  = GetGeometry()->GetPadSizePhi()/2;  // Distance between wires (2 wires above 1 pad)
  const Float_t kDetR   = 0.1;     // Relative energy fluctuation in track for 100 e-
  const Float_t kdEdx   = 4.0;     // Average energy loss in CPV;
  const Int_t   kNgamz  = 5;       // Ionization size in Z
  const Int_t   kNgamx  = 9;       // Ionization size in Phi
  const Float_t kNoise = 0.03;    // charge noise in one pad

  Float_t rnor1,rnor2;

  // Just a reminder on axes notation in the CPV module:
  // axis Z goes along the beam
  // axis X goes across the beam in the module plane
  // axis Y is a normal to the module plane showing from the IP

  Float_t hitX  = zxhit[0];
  Float_t hitZ  =-zxhit[1];
  Float_t pX    = p.Px();
  Float_t pZ    =-p.Pz();
  Float_t pNorm = p.Py();
  Float_t eloss = kdEdx;

  Float_t dZY   = pZ/pNorm * GetGeometry()->GetCPVGasThickness();
  Float_t dXY   = pX/pNorm * GetGeometry()->GetCPVGasThickness();
  gRandom->Rannor(rnor1,rnor2);
  eloss *= (1 + kDetR*rnor1) *
           TMath::Sqrt((1 + ( pow(dZY,2) + pow(dXY,2) ) / pow(GetGeometry()->GetCPVGasThickness(),2)));
  Float_t zhit1 = hitZ + GetGeometry()->GetCPVActiveSize(1)/2 - dZY/2;
  Float_t xhit1 = hitX + GetGeometry()->GetCPVActiveSize(0)/2 - dXY/2;
  Float_t zhit2 = zhit1 + dZY;
  Float_t xhit2 = xhit1 + dXY;

  Int_t   iwht1 = (Int_t) (xhit1 / kCelWr);           // wire (x) coordinate "in"
  Int_t   iwht2 = (Int_t) (xhit2 / kCelWr);           // wire (x) coordinate "out"

  Int_t   nIter;
  Float_t zxe[3][5];
  if (iwht1==iwht2) {                      // incline 1-wire hit
    nIter = 2;
    zxe[0][0] = (zhit1 + zhit2 - dZY*0.57735) / 2;
    zxe[1][0] = (iwht1 + 0.5) * kCelWr;
    zxe[2][0] =  eloss/2;
    zxe[0][1] = (zhit1 + zhit2 + dZY*0.57735) / 2;
    zxe[1][1] = (iwht1 + 0.5) * kCelWr;
    zxe[2][1] =  eloss/2;
  }
  else if (TMath::Abs(iwht1-iwht2) != 1) { // incline 3-wire hit
    nIter = 3;
    Int_t iwht3 = (iwht1 + iwht2) / 2;
    Float_t xwht1 = (iwht1 + 0.5) * kCelWr; // wire 1
    Float_t xwht2 = (iwht2 + 0.5) * kCelWr; // wire 2
    Float_t xwht3 = (iwht3 + 0.5) * kCelWr; // wire 3
    Float_t xwr13 = (xwht1 + xwht3) / 2;   // center 13
    Float_t xwr23 = (xwht2 + xwht3) / 2;   // center 23
    Float_t dxw1  = xhit1 - xwr13;
    Float_t dxw2  = xhit2 - xwr23;
    Float_t egm1  = TMath::Abs(dxw1) / ( TMath::Abs(dxw1) + TMath::Abs(dxw2) + kCelWr );
    Float_t egm2  = TMath::Abs(dxw2) / ( TMath::Abs(dxw1) + TMath::Abs(dxw2) + kCelWr );
    Float_t egm3  =           kCelWr / ( TMath::Abs(dxw1) + TMath::Abs(dxw2) + kCelWr );
    zxe[0][0] = (dXY*(xwr13-xwht1)/dXY + zhit1 + zhit1) / 2;
    zxe[1][0] =  xwht1;
    zxe[2][0] =  eloss * egm1;
    zxe[0][1] = (dXY*(xwr23-xwht1)/dXY + zhit1 + zhit2) / 2;
    zxe[1][1] =  xwht2;
    zxe[2][1] =  eloss * egm2;
    zxe[0][2] =  dXY*(xwht3-xwht1)/dXY + zhit1;
    zxe[1][2] =  xwht3;
    zxe[2][2] =  eloss * egm3;
  }
  else {                                   // incline 2-wire hit
    nIter = 2;
    Float_t xwht1 = (iwht1 + 0.5) * kCelWr;
    Float_t xwht2 = (iwht2 + 0.5) * kCelWr;
    Float_t xwr12 = (xwht1 + xwht2) / 2;
    Float_t dxw1  = xhit1 - xwr12;
    Float_t dxw2  = xhit2 - xwr12;
    Float_t egm1  = TMath::Abs(dxw1) / ( TMath::Abs(dxw1) + TMath::Abs(dxw2) );
    Float_t egm2  = TMath::Abs(dxw2) / ( TMath::Abs(dxw1) + TMath::Abs(dxw2) );
    zxe[0][0] = (zhit1 + zhit2 - dZY*egm1) / 2;
    zxe[1][0] =  xwht1;
    zxe[2][0] =  eloss * egm1;
    zxe[0][1] = (zhit1 + zhit2 + dZY*egm2) / 2;
    zxe[1][1] =  xwht2;
    zxe[2][1] =  eloss * egm2;
  }

  // Finite size of ionization region

  Int_t nCellZ  = GetGeometry()->GetNumberOfCPVPadsZ();
  Int_t nCellX  = GetGeometry()->GetNumberOfCPVPadsPhi();
  Int_t nz3     = (kNgamz+1)/2;
  Int_t nx3     = (kNgamx+1)/2;
  cpvDigits->Expand(nIter*kNgamx*kNgamz);
  TClonesArray &ldigits = *(static_cast<TClonesArray *>(cpvDigits));

  for (Int_t iter=0; iter<nIter; iter++) {

    Float_t zhit = zxe[0][iter];
    Float_t xhit = zxe[1][iter];
    Float_t qhit = zxe[2][iter];
    Float_t zcell = zhit / GetGeometry()->GetPadSizeZ();
    Float_t xcell = xhit / GetGeometry()->GetPadSizePhi();
    if ( zcell<=0      || xcell<=0 ||
	 zcell>=nCellZ || xcell>=nCellX) return;
    Int_t izcell = (Int_t) zcell;
    Int_t ixcell = (Int_t) xcell;
    Float_t zc = zcell - izcell - 0.5;
    Float_t xc = xcell - ixcell - 0.5;
    for (Int_t iz=1; iz<=kNgamz; iz++) {
      Int_t kzg = izcell + iz - nz3;
      if (kzg<=0 || kzg>nCellZ) continue;
      Float_t zg = (Float_t)(iz-nz3) - zc;
      for (Int_t ix=1; ix<=kNgamx; ix++) {
	Int_t kxg = ixcell + ix - nx3;
	if (kxg<=0 || kxg>nCellX) continue;
	Float_t xg = (Float_t)(ix-nx3) - xc;
	
	// Now calculate pad response
	Float_t qpad = CPVPadResponseFunction(qhit,zg,xg);
	qpad += kNoise*rnor2;
	if (qpad<0) continue;
	
	// Fill the array with pad response ID and amplitude
	new(ldigits[cpvDigits->GetEntriesFast()]) AliPHOSCPVDigit(kxg,kzg,qpad);
      }
    }
  }
}

//____________________________________________________________________________
Float_t AliPHOSv1::CPVPadResponseFunction(Float_t qhit, Float_t zhit, Float_t xhit) {
  // ------------------------------------------------------------------------
  // Calculate the amplitude in one CPV pad using the
  // cumulative pad response function
  // Author: Yuri Kharlov (after Serguei Sadovski)
  // 3 October 2000
  // ------------------------------------------------------------------------

  Double_t dz = GetGeometry()->GetPadSizeZ()   / 2;
  Double_t dx = GetGeometry()->GetPadSizePhi() / 2;
  Double_t z  = zhit * GetGeometry()->GetPadSizeZ();
  Double_t x  = xhit * GetGeometry()->GetPadSizePhi();
  Double_t amplitude = qhit *
    (CPVCumulPadResponse(z+dz,x+dx) - CPVCumulPadResponse(z+dz,x-dx) -
     CPVCumulPadResponse(z-dz,x+dx) + CPVCumulPadResponse(z-dz,x-dx));
  return (Float_t)amplitude;
}

//____________________________________________________________________________
Double_t AliPHOSv1::CPVCumulPadResponse(Double_t x, Double_t y) {
  // ------------------------------------------------------------------------
  // Cumulative pad response function
  // It includes several terms from the CF decomposition in electrostatics
  // Note: this cumulative function is wrong since omits some terms
  //       but the cell amplitude obtained with it is correct because
  //       these omitting terms cancel
  // Author: Yuri Kharlov (after Serguei Sadovski)
  // 3 October 2000
  // ------------------------------------------------------------------------

  const Double_t kA=1.0;
  const Double_t kB=0.7;

  Double_t r2       = x*x + y*y;
  Double_t xy       = x*y;
  Double_t cumulPRF = 0;
  for (Int_t i=0; i<=4; i++) {
    Double_t b1 = (2*i + 1) * kB;
    cumulPRF += TMath::Power(-1,i) * TMath::ATan( xy / (b1*TMath::Sqrt(b1*b1 + r2)) );
  }
  cumulPRF *= kA/(2*TMath::Pi());
  return cumulPRF;
}