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diffcross.f
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C**********************************************************************
C* *
C* Exact calculation of the total differential e+ e- -pair production *
C* in Relativistic Heavy Ion Collisions for a point particle in an *
C* external field approach. *
C* *
C* For details see the publication: *
C* "Multiple electromagnetic electron positron pair production in *
C* relativistic heavy ion collisions" *
C* Adrian Alscher, Kai Hencken, Dirk Trautmann, and Gerhard Baur *
C* Phys. Rev. A55 (1997) 396. *
C* *
C* Copyright (c) 1997, 1998, 2002, Adrian Alscher and Kai Hencken *
C* *
C* Permission to use, copy and distribute this software and its *
C* documentation strictly for non-commercial purposes is hereby *
C* granted without fee, provided that the above copyright notice *
C* appears in all copies, that both the copyright notice and this *
C* permission notice appear in the supporting documentation and that *
C* the use of this program is acknowledged in scientific *
C* publications (see reference above). The authors make no claims *
C* about the suitability of this software for any purpose. It is *
C* provided "as is" without express or implied warranty. Any change *
C* of the code should be submitted to the authors *
C* *
C* To use this program at LHC energies, please make sure that *
C* "double precision" variables should better be real*16 *
C**********************************************************************
C======================================================================
C
C call this routine first to initialize some parameter needed in the
C function.
C
C gm = Gamma_cm, that is, gm of each ion (~100 for RHIC ~3000 for LHC)
C mass = mass of the produced particle in MeV (~0.511 for e,~100 for mu)
C======================================================================
SUBROUTINE Initdiffcross (gm,mass)
IMPLICIT NONE
DOUBLE PRECISION gm,mass
DOUBLE PRECISION gamma,beta,m,w1xw1,w1xw2,w2xw2,wl,wy
COMMON/PHYSPARAM/gamma,beta,m,w1xw1,w1xw2,w2xw2,wl,wy
DOUBLE PRECISION ARCOSH,x
ARCOSH(x)=LOG(x+SQRT((x-1D0)*(x+1D0)))
gamma=gm
beta=sqrt((1D0-1D0/gamma)*(1D0+1D0/gamma))
m=mass
w1xw1 = 1D0/gamma**2
w2xw2 = 1D0/gamma**2
w1xw2 = 2D0-1D0/gamma**2
wl=SQRT (w1xw1)
wy=ARCOSH (gamma)
RETURN
END
C ============================================================================
C
C Diffcross calculates the fivefold differential cross section
C
C dsigma/ dp+t dp-t dy+ dy- ddeltaphi
C
C the trivial integration over the total phi-dependence is not included
C
C ppvt= absolute value of the positron transverse momentum (MeV)
C pmvt= - " - electron - " -
C dphi= phi-angle between the electron and positron transverse momentum
C yp = rapidity of the positron
C ym = rapidity of the electron
C defined to make E = sqrt(pt^2 + m^2) cosh (y)
C and Pz= sqrt(pt^2 + m^2) sinh (y)
C
C dsigma = differential cross section in kbarn/MeV^4/ (Zalpha)**4
C
C to get the total cross section, you have to integrate over
C
C Integral dsigma dyp dym ddphi 2 pi ppt dppt pmt dpmt
C
C (see also source for sigma.f)
C
C======================================================================
SUBROUTINE Diffcross(ppvt,yp,pmvt,ym,dphi,dsigma)
IMPLICIT NONE
DOUBLE PRECISION ppvt,pmvt,dphi,dsigma,yp,ym
DOUBLE PRECISION ppvl,pmvl
DOUBLE PRECISION k1(2)
DOUBLE PRECISION kd(2)
DOUBLE PRECISION kx(2)
DOUBLE PRECISION pmt(2)
DOUBLE PRECISION ppt(2)
DOUBLE PRECISION qb
DOUBLE PRECISION mk1(2),mk1d(2),mk1x(2)
DOUBLE PRECISION mkd(2),mkd1(2)
DOUBLE PRECISION mkx(2),mkx1(2)
DOUBLE PRECISION Iz2,Id1,Id2,Id3,Iv1,Iv2
DOUBLE PRECISION PI
PARAMETER (PI=3.141592653589793238462643D0)
DOUBLE PRECISION gamma,beta,m,w1xw1,w1xw2,w2xw2,wl,wy
COMMON/PHYSPARAM/gamma,beta,m,w1xw1,w1xw2,w2xw2,wl,wy
DOUBLE PRECISION m0,m1,md,mx
DOUBLE PRECISION N1,N2,N3,N4,N5
DOUBLE PRECISION N6,N7,N8,N9,N10
DOUBLE PRECISION N11,N12,N13,N14,N15
DOUBLE PRECISION N16,N17,N18,NT
DOUBLE PRECISION pmlxpml,pmlxppl,pmlxql
DOUBLE PRECISION pmtxpmt,pmtxppt,pptxppt
DOUBLE PRECISION pplxppl,pplxql,qlxql
DOUBLE PRECISION w1xpml,w1xppl,w1xql
DOUBLE PRECISION w2xpml,w2xppl,w2xql
DOUBLE PRECISION r1,rd,rx
INTEGER setzero
COMMON /SETZPARAM/ setzero
INTEGER badcount
COMMON/badpar/badcount
setzero=0
ppt(1)=ppvt
ppt(2)=0D0
ppvl=SQRT(ppvt**2+m**2)
pmt(1)=pmvt*cos(dphi)
pmt(2)=pmvt*sin(dphi)
pmvl=SQRT(pmvt**2+m**2)
pmlxpml = pmvl**2
pplxppl = ppvl**2
pmlxppl = pmvl*ppvl*COSH(yp-ym)
w2xpml = wl*pmvl*COSH(ym+wy)
w2xppl = wl*ppvl*COSH(yp+wy)
w1xpml = wl*pmvl*COSH(ym-wy)
w1xppl = wl*ppvl*COSH(yp-wy)
w1xql=0D0
w2xql=w2xpml+w2xppl
qb=gamma*(w2xppl+w2xpml)/SINH(2D0*wy)
qlxql=-qb**2
pmlxql = qb*pmvl*SINH(wy-ym)
pplxql = qb*ppvl*SINH(wy-yp)
pmtxpmt =-pmvt**2
pmtxppt =-pmvt*ppvt*cos(dphi)
pptxppt =-ppvt**2
C======================================================================
C
C Definition of propagatorterms
C
m0 = -qlxql
k1(1) = -ppt(1) -pmt(1)
k1(2) = -pmt(2)
m1=-qlxql-pplxppl-pmlxpml+2D0*(pplxql+pmlxql-pmlxppl)
kd(1)= -pmt(1)
kd(2)= -pmt(2)
md= m**2 - (qlxql+pmlxpml-2D0*pmlxql)
kx(1)= -ppt(1)
kx(2)=0D0
mx= m**2 - (qlxql+pplxppl-2D0*pplxql)
r1 = m1 - m0 + k1(1)*k1(1)+k1(2)*k1(2)
rd = md - m0 + kd(1)*kd(1)+kd(2)*kd(2)
rx = mx - m0 + kx(1)*kx(1)+kx(2)*kx(2)
mk1(1)= -k1(1)
mk1(2)= -k1(2)
mkd(1)= -kd(1)
mkd(2)= -kd(2)
mkx(1)= -kx(1)
mkx(2)= -kx(2)
mk1d(1)= k1(1)-kd(1)
mk1d(2)= k1(2)-kd(2)
mk1x(1)= k1(1)-kx(1)
mk1x(2)= k1(2)-kx(2)
mkd1(1)= kd(1)-k1(1)
mkd1(2)= kd(2)-k1(2)
mkx1(1)= kx(1)-k1(1)
mkx1(2)= kx(2)-k1(2)
C
C calculate all different integrals
C
N1 = Id1(mkd,mk1d,md,m0,m1) * ( - 2*w1xw1*w2xw2 )
N2 = Id1(mkx,mk1x,mx,m0,m1) * ( - 2*w1xw1*w2xw2 )
N3 = Iv1(mk1,mkd1,mkx1,m1,m0,md,mx) * ( 4*w1xw1*w2xw2*
& pmlxpml + 8*w1xw1*w2xw2*pmlxppl - 8*w1xw1*w2xw2*pmlxql + 4*
& w1xw1*w2xw2*pmtxpmt + 8*w1xw1*w2xw2*pmtxppt + 4*w1xw1*w2xw2*
& pplxppl - 8*w1xw1*w2xw2*pplxql + 4*w1xw1*w2xw2*pptxppt + 4*
& w1xw1*w2xw2*rd + 4*w1xw1*w2xw2*rx - 16*w1xw1*w2xpml*w2xppl +
& 8*w1xw1*w2xpml*w2xql + 8*w1xw1*w2xppl*w2xql - 8*w1xw2**2*
& pmlxpml - 16*w1xw2**2*pmlxppl + 16*w1xw2**2*pmlxql - 8*
& w1xw2**2*pmtxpmt - 16*w1xw2**2*pmtxppt - 8*w1xw2**2*pplxppl
& + 16*w1xw2**2*pplxql - 8*w1xw2**2*pptxppt - 8*w1xw2**2*rd -
& 8*w1xw2**2*rx + 16*w1xw2*w1xpml*w2xpml + 16*w1xw2*w1xpml*
& w2xppl - 16*w1xw2*w1xpml*w2xql + 16*w1xw2*w1xppl*w2xpml + 16*
& w1xw2*w1xppl*w2xppl - 16*w1xw2*w1xppl*w2xql - 16*w1xw2*w1xql*
& w2xpml - 16*w1xw2*w1xql*w2xppl - 8*w1xpml**2*w2xw2 + 8*w1xpml
& *w1xql*w2xw2 - 8*w1xppl**2*w2xw2 + 8*w1xppl*w1xql*w2xw2 )
N4 = Id1(mk1,mkd1,m1,m0,md) * ( - 2*w1xw1*w2xw2 + 8*
& w1xw2**2 )
N5 = Id2(mk1d,mkd,md,m1,m0) * ( 4*w1xw1*w2xw2*pmlxppl + 4*
& w1xw1*w2xw2*pmtxppt - 4*w1xw1*w2xw2*pplxql + 4*w1xw1*w2xw2*
& m**2 + 2*w1xw1*w2xw2*r1 - 2*w1xw1*w2xw2*rd - 8*w1xw1*w2xpml*
& w2xppl + 8*w1xw1*w2xppl*w2xql )
N6 = Id1(mk1,mkx1,m1,m0,mx) * ( - 2*w1xw1*w2xw2 + 8*
& w1xw2**2 )
N7 = Id2(mk1x,mkx,mx,m1,m0) * ( 4*w1xw1*w2xw2*pmlxppl - 4*
& w1xw1*w2xw2*pmlxql + 4*w1xw1*w2xw2*pmtxppt + 4*w1xw1*w2xw2*
& m**2 + 2*w1xw1*w2xw2*r1 - 2*w1xw1*w2xw2*rx - 8*w1xw1*w2xpml*
& w2xppl + 8*w1xw1*w2xpml*w2xql )
N8 = Id1(k1,kd,m0,m1,md) * ( 2*w1xw1*w2xw2 )
N9 = Id2(kd,k1,m0,md,m1) * ( - 4*w1xw1*w2xw2*pmlxpml
& + 4*w1xw1*w2xw2*pmlxql - 4*w1xw1*w2xw2*pmtxpmt + 4*w1xw1*
& w2xw2*m**2 - 2*w1xw1*w2xw2*rd + 8*w1xpml**2*w2xw2 - 8*w1xpml*
& w1xql*w2xw2 )
N10 = Id1(k1,kx,m0,m1,mx) * ( 2*w1xw1*w2xw2 )
N11 = Id2(kx,k1,m0,mx,m1) * ( - 4*w1xw1*w2xw2*pplxppl
& + 4*w1xw1*w2xw2*pplxql - 4*w1xw1*w2xw2*pptxppt + 4*w1xw1*
& w2xw2*m**2 - 2*w1xw1*w2xw2*rx + 8*w1xppl**2*w2xw2 - 8*w1xppl*
& w1xql*w2xw2 )
N12 = Iv2(k1,kd,kx,m0,m1,md,mx) * ( 8*w1xw1*w2xw2*
& pmlxpml*pplxppl - 8*w1xw1*w2xw2*pmlxpml*pplxql + 8*w1xw1*
& w2xw2*pmlxpml*pptxppt - 8*w1xw1*w2xw2*pmlxpml*m**2 + 4*w1xw1*
& w2xw2*pmlxpml*rx - 8*w1xw1*w2xw2*pmlxppl*qlxql - 8*w1xw1*
& w2xw2*pmlxppl*m0 - 8*w1xw1*w2xw2*pmlxql*pplxppl + 16*w1xw1
& *w2xw2*pmlxql*pplxql - 8*w1xw1*w2xw2*pmlxql*pptxppt + 8*w1xw1
& *w2xw2*pmlxql*m**2 - 8*w1xw1*w2xw2*pmlxql*rx + 8*w1xw1*w2xw2*
& pmtxpmt*pplxppl - 8*w1xw1*w2xw2*pmtxpmt*pplxql + 8*w1xw1*
& w2xw2*pmtxpmt*pptxppt - 8*w1xw1*w2xw2*pmtxpmt*m**2 + 4*w1xw1*
& w2xw2*pmtxpmt*rx - 8*w1xw1*w2xw2*pmtxppt*qlxql - 8*w1xw1*
& w2xw2*pmtxppt*m0 - 8*w1xw1*w2xw2*pplxppl*m**2 + 4*w1xw1*
& w2xw2*pplxppl*rd + 8*w1xw1*w2xw2*pplxql*m**2 - 8*w1xw1*w2xw2*
& pplxql*rd - 8*w1xw1*w2xw2*pptxppt*m**2 + 4*w1xw1*w2xw2*
& pptxppt*rd - 8*w1xw1*w2xw2*qlxql*m**2 + 8*w1xw1*w2xw2*m**4 -
& 8*w1xw1*w2xw2*m**2*m0 - 4*w1xw1*w2xw2*m**2*rd - 4*w1xw1*
& w2xw2*m**2*rx + 4*w1xw1*w2xw2*rd*rx + 16*w1xw1*w2xpml*w2xppl*
& qlxql + 16*w1xw1*w2xpml*
& w2xppl*m0 - 16*w1xw1*w2xpml*w2xql*pplxql + 8*w1xw1*w2xpml*
& w2xql*rx - 16*w1xw1*w2xppl*w2xql*pmlxql + 8*w1xw1*w2xppl*
& w2xql*rd + 16*w1xw1*w2xql**2*pmlxppl + 16*w1xw1*w2xql**2*
& pmtxppt + 16*w1xw1*w2xql**2*m**2 - 16*w1xw2**2*pmlxpml*
& pplxppl + 16*w1xw2**2*pmlxpml*pplxql - 16*w1xw2**2*pmlxpml*
& pptxppt + 16*w1xw2**2*pmlxpml*m**2 - 8*w1xw2**2*pmlxpml*rx +
& 16*w1xw2**2*pmlxppl*qlxql + 16*w1xw2**2*pmlxppl*m0 + 16*
& w1xw2**2*pmlxql*pplxppl - 32*w1xw2**2*pmlxql*pplxql + 16*
& w1xw2**2*pmlxql*pptxppt - 16*w1xw2**2*pmlxql*m**2 + 16*
& w1xw2**2*pmlxql*rx - 16*w1xw2**2*pmtxpmt*pplxppl + 16*
& w1xw2**2*pmtxpmt*pplxql - 16*w1xw2**2*pmtxpmt*pptxppt + 16*
& w1xw2**2*pmtxpmt*m**2 - 8*w1xw2**2*pmtxpmt*rx + 16*w1xw2**2*
& pmtxppt*qlxql + 16*w1xw2**2*pmtxppt*m0 + 16*w1xw2**2*
& pplxppl*m**2 - 8*w1xw2**2*pplxppl*rd - 16*w1xw2**2*pplxql*
& m**2 + 16*w1xw2**2*pplxql*rd + 16*w1xw2**2*pptxppt*m**2 - 8*
& w1xw2**2*pptxppt*rd + 16*w1xw2**2*qlxql
& *m**2 - 16*w1xw2**2*m**4 + 16*w1xw2**2*m**2*m0 + 8*
& w1xw2**2*m**2*rd + 8*w1xw2**2*m**2*rx - 8*w1xw2**2*rd*rx + 32
& *w1xw2*w1xpml*w2xpml*pplxppl - 32*w1xw2*w1xpml*w2xpml*pplxql
& + 32*w1xw2*w1xpml*w2xpml*pptxppt - 32*w1xw2*w1xpml*w2xpml*
& m**2 + 16*w1xw2*w1xpml*w2xpml*rx - 16*w1xw2*w1xpml*w2xppl*
& qlxql - 16*w1xw2*w1xpml*w2xppl*m0 - 16*w1xw2*w1xpml*w2xql*
& pplxppl + 32*w1xw2*w1xpml*w2xql*pplxql - 16*w1xw2*w1xpml*
& w2xql*pptxppt + 16*w1xw2*w1xpml*w2xql*m**2 - 16*w1xw2*w1xpml*
& w2xql*rx - 16*w1xw2*w1xppl*w2xpml*qlxql - 16*w1xw2*w1xppl*
& w2xpml*m0 + 32*w1xw2*w1xppl*w2xppl*pmlxpml - 32*w1xw2*
& w1xppl*w2xppl*pmlxql + 32*w1xw2*w1xppl*w2xppl*pmtxpmt - 32*
& w1xw2*w1xppl*w2xppl*m**2 + 16*w1xw2*w1xppl*w2xppl*rd - 16*
& w1xw2*w1xppl*w2xql*pmlxpml + 32*w1xw2*w1xppl*w2xql*pmlxql -
& 16*w1xw2*w1xppl*w2xql*pmtxpmt + 16*w1xw2*w1xppl*w2xql*m**2 -
& 16*w1xw2*w1xppl*w2xql*rd - 16*w1xw2*w1xql*w2xpml*pplxppl + 32
& *w1xw2*w1xql*w2xpml*pplxql - 16*w1xw2*w1xql
& *w2xpml*pptxppt + 16*w1xw2*w1xql*w2xpml*m**2 - 16*w1xw2*w1xql
& *w2xpml*rx - 16*w1xw2*w1xql*w2xppl*pmlxpml + 32*w1xw2*w1xql*
& w2xppl*pmlxql - 16*w1xw2*w1xql*w2xppl*pmtxpmt + 16*w1xw2*
& w1xql*w2xppl*m**2 - 16*w1xw2*w1xql*w2xppl*rd - 32*w1xw2*w1xql
& *w2xql*pmlxppl - 32*w1xw2*w1xql*w2xql*pmtxppt - 32*w1xw2*
& w1xql*w2xql*m**2 - 16*w1xpml**2*w2xw2*pplxppl + 16*w1xpml**2*
& w2xw2*pplxql - 16*w1xpml**2*w2xw2*pptxppt + 16*w1xpml**2*
& w2xw2*m**2 - 8*w1xpml**2*w2xw2*rx + 32*w1xpml*w1xppl*w2xw2*
& pmlxppl - 16*w1xpml*w1xppl*w2xw2*pmlxql + 32*w1xpml*w1xppl*
& w2xw2*pmtxppt - 16*w1xpml*w1xppl*w2xw2*pplxql + 16*w1xpml*
& w1xppl*w2xw2*qlxql + 32*w1xpml*w1xppl*w2xw2*m**2 + 16*w1xpml*
& w1xppl*w2xw2*m0 + 8*w1xpml*w1xppl*w2xw2*rd + 8*w1xpml*
& w1xppl*w2xw2*rx - 64*w1xpml*w1xppl*w2xpml*w2xppl + 32*w1xpml*
& w1xppl*w2xpml*w2xql + 32*w1xpml*w1xppl*w2xppl*w2xql - 32*
& w1xpml*w1xppl*w2xql**2 - 16*w1xpml*w1xql*w2xw2*pmlxppl - 16*
& w1xpml*w1xql*w2xw2*pmtxppt + 16*w1xpml*w1xql*
& w2xw2*pplxppl - 16*w1xpml*w1xql*w2xw2*pplxql + 16*w1xpml*
& w1xql*w2xw2*pptxppt - 32*w1xpml*w1xql*w2xw2*m**2 + 8*w1xpml*
& w1xql*w2xw2*rx + 32*w1xpml*w1xql*w2xpml*w2xppl - 16*w1xppl**2
& *w2xw2*pmlxpml + 16*w1xppl**2*w2xw2*pmlxql - 16*w1xppl**2*
& w2xw2*pmtxpmt + 16*w1xppl**2*w2xw2*m**2 - 8*w1xppl**2*w2xw2*
& rd + 16*w1xppl*w1xql*w2xw2*pmlxpml - 16*w1xppl*w1xql*w2xw2*
& pmlxppl - 16*w1xppl*w1xql*w2xw2*pmlxql + 16*w1xppl*w1xql*
& w2xw2*pmtxpmt - 16*w1xppl*w1xql*w2xw2*pmtxppt - 32*w1xppl*
& w1xql*w2xw2*m**2 + 8*w1xppl*w1xql*w2xw2*rd + 32*w1xppl*w1xql*
& w2xpml*w2xppl + 16*w1xql**2*w2xw2*pmlxppl + 16*w1xql**2*w2xw2
& *pmtxppt + 16*w1xql**2*w2xw2*m**2 - 32*w1xql**2*w2xpml*w2xppl
& )
N13 = Id2(k1,kd,m0,m1,md) * ( 4*w1xw1*w2xw2*pmlxql + 4*
& w1xw1*w2xw2*pplxql - 2*w1xw1*w2xw2*r1 - 8*w1xw1*w2xpml*w2xql
& - 8*w1xw1*w2xppl*w2xql + 8*w1xw2**2*pmlxpml - 16*w1xw2**2*
& pmlxql + 8*w1xw2**2*pmtxpmt - 8*w1xw2**2*m**2 + 8*w1xw2**2*rd
& - 16*w1xw2*w1xpml*w2xpml + 16*w1xw2*w1xpml*w2xppl + 16*w1xw2
& *w1xpml*w2xql + 16*w1xw2*w1xql*w2xpml - 16*w1xpml*w1xppl*
& w2xw2 )
N14 = Id3(k1,kd,m0,m1,md) * ( 4*w1xw1*w2xw2*pmlxpml*
& pmlxppl + 4*w1xw1*w2xw2*pmlxpml*pmtxppt - 8*w1xw1*w2xw2*
& pmlxpml*pplxql + 4*w1xw1*w2xw2*pmlxpml*m**2 + 4*w1xw1*w2xw2*
& pmlxpml*r1 - 4*w1xw1*w2xw2*pmlxpml*rd + 4*w1xw1*w2xw2*pmlxppl
& *pmtxpmt - 4*w1xw1*w2xw2*pmlxppl*qlxql - 4*w1xw1*w2xw2*
& pmlxppl*m**2 - 4*w1xw1*w2xw2*pmlxppl*m0 + 8*w1xw1*w2xw2*
& pmlxql*pplxql - 4*w1xw1*w2xw2*pmlxql*r1 + 4*w1xw1*w2xw2*
& pmlxql*rd + 4*w1xw1*w2xw2*pmtxpmt*pmtxppt - 8*w1xw1*w2xw2*
& pmtxpmt*pplxql + 4*w1xw1*w2xw2*pmtxpmt*m**2 + 4*w1xw1*w2xw2*
& pmtxpmt*r1 - 4*w1xw1*w2xw2*pmtxpmt*rd - 4*w1xw1*w2xw2*pmtxppt
& *qlxql - 4*w1xw1*w2xw2*pmtxppt*m**2 - 4*w1xw1*w2xw2*pmtxppt*
& m0 + 8*w1xw1*w2xw2*pplxql*m**2 - 4*w1xw1*w2xw2*pplxql*rd
& - 4*w1xw1*w2xw2*qlxql*m**2 - 4*w1xw1*w2xw2*m**4 - 4*w1xw1*
& w2xw2*m**2*m0 - 4*w1xw1*w2xw2*m**2*r1 + 4*w1xw1*w2xw2*m**2
& *rd + 2*w1xw1*w2xw2*r1*rd - 2*w1xw1*w2xw2*rd**2 - 8*w1xw1*
& w2xpml*w2xppl*pmlxpml - 8*w1xw1*w2xpml*w2xppl*pmtxpmt + 8*
& w1xw1*w2xpml*w2xppl*qlxql + 8*w1xw1*w2xpml*w2xppl*m**2
& + 8*w1xw1*w2xpml*w2xppl*m0 + 16*w1xw1*w2xppl*w2xql*
& pmlxpml - 16*w1xw1*w2xppl*w2xql*pmlxql + 16*w1xw1*w2xppl*
& w2xql*pmtxpmt - 16*w1xw1*w2xppl*w2xql*m**2 + 8*w1xw1*w2xppl*
& w2xql*rd - 16*w1xw2*w1xpml*w2xppl*pmlxpml + 32*w1xw2*w1xpml*
& w2xppl*pmlxql - 16*w1xw2*w1xpml*w2xppl*pmtxpmt - 16*w1xw2*
& w1xpml*w2xppl*qlxql + 16*w1xw2*w1xpml*w2xppl*m**2 - 16*w1xw2*
& w1xpml*w2xppl*m0 - 16*w1xw2*w1xpml*w2xppl*rd - 16*
& w1xpml**2*w2xw2*pmlxppl - 16*w1xpml**2*w2xw2*pmtxppt + 16*
& w1xpml**2*w2xw2*pplxql - 16*w1xpml**2*w2xw2*m**2 - 8*
& w1xpml**2*w2xw2*r1 + 8*w1xpml**2*w2xw2*rd + 32*w1xpml**2*
& w2xpml*w2xppl - 32*w1xpml**2*w2xppl*w2xql + 8*w1xpml*w1xppl*
& w2xw2*pmlxpml - 16*w1xpml*w1xppl*w2xw2*pmlxql + 8*w1xpml*
& w1xppl*w2xw2*pmtxpmt + 8*w1xpml*w1xppl*w2xw2*qlxql - 8*w1xpml
& *w1xppl*w2xw2*m**2 + 8*w1xpml*w1xppl*w2xw2*m0 + 8*w1xpml*
& w1xppl*w2xw2*rd + 16*w1xpml*w1xql*w2xw2*pmlxppl + 16*w1xpml*
& w1xql*w2xw2*pmtxppt - 16*w1xpml*w1xql*w2xw2*
& pplxql + 16*w1xpml*w1xql*w2xw2*m**2 + 8*w1xpml*w1xql*w2xw2*r1
& - 8*w1xpml*w1xql*w2xw2*rd - 32*w1xpml*w1xql*w2xpml*w2xppl +
& 32*w1xpml*w1xql*w2xppl*w2xql )
N15 = Id2(k1,kx,m0,m1,mx) * ( 4*w1xw1*w2xw2*pmlxql + 4*
& w1xw1*w2xw2*pplxql - 2*w1xw1*w2xw2*r1 - 8*w1xw1*w2xpml*w2xql
& - 8*w1xw1*w2xppl*w2xql + 8*w1xw2**2*pplxppl - 16*w1xw2**2*
& pplxql + 8*w1xw2**2*pptxppt - 8*w1xw2**2*m**2 + 8*w1xw2**2*rx
& + 16*w1xw2*w1xppl*w2xpml - 16*w1xw2*w1xppl*w2xppl + 16*w1xw2
& *w1xppl*w2xql + 16*w1xw2*w1xql*w2xppl - 16*w1xpml*w1xppl*
& w2xw2 )
N16 = Id3(k1,kx,m0,m1,mx) * ( 4*w1xw1*w2xw2*pmlxppl*
& pplxppl + 4*w1xw1*w2xw2*pmlxppl*pptxppt - 4*w1xw1*w2xw2*
& pmlxppl*qlxql - 4*w1xw1*w2xw2*pmlxppl*m**2 - 4*w1xw1*w2xw2*
& pmlxppl*m0 - 8*w1xw1*w2xw2*pmlxql*pplxppl + 8*w1xw1*w2xw2*
& pmlxql*pplxql - 8*w1xw1*w2xw2*pmlxql*pptxppt + 8*w1xw1*w2xw2*
& pmlxql*m**2 - 4*w1xw1*w2xw2*pmlxql*rx + 4*w1xw1*w2xw2*pmtxppt
& *pplxppl + 4*w1xw1*w2xw2*pmtxppt*pptxppt - 4*w1xw1*w2xw2*
& pmtxppt*qlxql - 4*w1xw1*w2xw2*pmtxppt*m**2 - 4*w1xw1*w2xw2*
& pmtxppt*m0 + 4*w1xw1*w2xw2*pplxppl*m**2 + 4*w1xw1*w2xw2*
& pplxppl*r1 - 4*w1xw1*w2xw2*pplxppl*rx - 4*w1xw1*w2xw2*pplxql*
& r1 + 4*w1xw1*w2xw2*pplxql*rx + 4*w1xw1*w2xw2*pptxppt*m**2 + 4
& *w1xw1*w2xw2*pptxppt*r1 - 4*w1xw1*w2xw2*pptxppt*rx - 4*w1xw1*
& w2xw2*qlxql*m**2 - 4*w1xw1*w2xw2*m**4 - 4*w1xw1*w2xw2*m**2*
& m0 - 4*w1xw1*w2xw2*m**2*r1 + 4*w1xw1*w2xw2*m**2*rx + 2*
& w1xw1*w2xw2*r1*rx - 2*w1xw1*w2xw2*rx**2 - 8*w1xw1*w2xpml*
& w2xppl*pplxppl - 8*w1xw1*w2xpml*w2xppl*pptxppt + 8*w1xw1*
& w2xpml*w2xppl*qlxql + 8*w1xw1*w2xpml*w2xppl*m**2
& + 8*w1xw1*w2xpml*w2xppl*m0 + 16*w1xw1*w2xpml*w2xql*
& pplxppl - 16*w1xw1*w2xpml*w2xql*pplxql + 16*w1xw1*w2xpml*
& w2xql*pptxppt - 16*w1xw1*w2xpml*w2xql*m**2 + 8*w1xw1*w2xpml*
& w2xql*rx - 16*w1xw2*w1xppl*w2xpml*pplxppl + 32*w1xw2*w1xppl*
& w2xpml*pplxql - 16*w1xw2*w1xppl*w2xpml*pptxppt - 16*w1xw2*
& w1xppl*w2xpml*qlxql + 16*w1xw2*w1xppl*w2xpml*m**2 - 16*w1xw2*
& w1xppl*w2xpml*m0 - 16*w1xw2*w1xppl*w2xpml*rx + 8*w1xpml*
& w1xppl*w2xw2*pplxppl - 16*w1xpml*w1xppl*w2xw2*pplxql + 8*
& w1xpml*w1xppl*w2xw2*pptxppt + 8*w1xpml*w1xppl*w2xw2*qlxql - 8
& *w1xpml*w1xppl*w2xw2*m**2 + 8*w1xpml*w1xppl*w2xw2*m0 + 8*
& w1xpml*w1xppl*w2xw2*rx - 16*w1xppl**2*w2xw2*pmlxppl + 16*
& w1xppl**2*w2xw2*pmlxql - 16*w1xppl**2*w2xw2*pmtxppt - 16*
& w1xppl**2*w2xw2*m**2 - 8*w1xppl**2*w2xw2*r1 + 8*w1xppl**2*
& w2xw2*rx + 32*w1xppl**2*w2xpml*w2xppl - 32*w1xppl**2*w2xpml*
& w2xql + 16*w1xppl*w1xql*w2xw2*pmlxppl - 16*w1xppl*w1xql*w2xw2
& *pmlxql + 16*w1xppl*w1xql*w2xw2*
& pmtxppt + 16*w1xppl*w1xql*w2xw2*m**2 + 8*w1xppl*w1xql*w2xw2*
& r1 - 8*w1xppl*w1xql*w2xw2*rx - 32*w1xppl*w1xql*w2xpml*w2xppl
& + 32*w1xppl*w1xql*w2xpml*w2xql )
N17 = Iz2(k1,m0,m1) * ( - 8*w1xw2**2 )
N18 = Id1(mkd1,mkx1,m1,md,mx) * ( 4*w1xw1*w2xw2 - 8*w1xw2**2 )
C
C dsigma is summ of all terms
C
NT=N1+N2+N3+N4+N5+N6+N7+N8+N9+N10+N11+N12+N13+N14+
& N15+N16+N17+N18
C
C correction from w/u
NT=NT*4D0/beta**2
C 1/(2pi)**6 from d3p, (2*pi)**2 from F.T.
NT=NT/(2*pi)**6*(2*pi)**2
C from 1/2E+ 1/2E-
NT=NT/4D0
C transform from MeV^-2 to kbarn
NT=NT*(1.9733D0)**2/10D0
dsigma=NT
IF((setzero.EQ.1).OR.(dsigma.LT.0)) THEN
dsigma=0D0
badcount=badcount+1
ENDIF
END
C========================================================================
C All the differential integral forms are calculated here
C
DOUBLE PRECISION FUNCTION Iz0(x,u,v)
IMPLICIT NONE
DOUBLE PRECISION x(2)
DOUBLE PRECISION u,v
DOUBLE PRECISION s,arg
INTEGER setzero
COMMON /SETZPARAM/ setzero
DOUBLE PRECISION tepxx
DOUBLE PRECISION PI
PARAMETER (PI=3.141592653589793238462643D0)
tepxx=x(1)*x(1)+x(2)*x(2)
s=SQRT((tepxx+u+v)**2 - 4*u*v)
arg=(tepxx+u+v+s)**2/(4*u*v)
IF(arg.lt.0D0) THEN
setzero=1
Iz0=0D0
ELSE
Iz0=pi * LOG((tepxx+u+v+s)**2/(4*u*v)) / s
ENDIF
END
C ---------------------------------------------------------------
DOUBLE PRECISION FUNCTION Iz1(x,u,v)
IMPLICIT NONE
DOUBLE PRECISION Iz0
EXTERNAL Iz0
DOUBLE PRECISION x(2)
DOUBLE PRECISION u,v
DOUBLE PRECISION a,b,s
DOUBLE PRECISION tepxx
DOUBLE PRECISION PI
PARAMETER (PI=3.141592653589793238462643D0)
tepxx=x(1)*x(1)+x(2)*x(2)
s=SQRT((tepxx+u+v)**2 - 4*u*v)
A= (2*(tepxx+u-v+s)) / (s**2*(tepxx+u+v+s))
& - 1/(s*u)
B= -Iz0(x,u,v)/pi * (tepxx+u-v)/s**2
Iz1=(-1)*pi*(A + B)
END
C -----------------------------------------------------------
DOUBLE PRECISION FUNCTION Iz2(x,u,v)
IMPLICIT NONE
DOUBLE PRECISION Iz0,Iz1
EXTERNAL Iz0,Iz1
DOUBLE PRECISION x(2)
DOUBLE PRECISION u,v
DOUBLE PRECISION s,A,B,C,D,E
DOUBLE PRECISION tepxx
DOUBLE PRECISION PI
PARAMETER (PI=3.141592653589793238462643D0)
tepxx=x(1)*x(1)+x(2)*x(2)
s=SQRT((tepxx+u+v)**2 - 4*u*v)
A= (2*(tepxx-u+v-s))/(s**3*(tepxx+u+v+s))
B= -2*(tepxx+u-v+s)*(
& 2*(tepxx-u+v)*(tepxx+u+v+s) +
& s*(tepxx-u+v+s) ) /
& (s**4*(tepxx+u+v+s)**2)
C= (tepxx-u+v)/(u*s**3)
D= (Iz1(x,v,u)/pi)*(tepxx+u-v)/(s**2)
E= (Iz0(x,u,v)/pi)*(
& 1/s**2 + (tepxx+u-v)*2*(tepxx-u+v) /
& (s**4) )
Iz2= pi*(A + B + C +D + E)
END
C -------------------------------------------------------------
DOUBLE PRECISION FUNCTION Id0(x,y,u,v,w)
IMPLICIT NONE
DOUBLE PRECISION Iz0,Iz1
EXTERNAL Iz0,Iz1
DOUBLE PRECISION x(2),y(2),dyx(2)
DOUBLE PRECISION u,v,w
DOUBLE PRECISION A,AXY,B,C,D,E,RX,RY
DOUBLE PRECISION tepxx,tepxy,tepyy
tepxx=x(1)*x(1)+x(2)*x(2)
tepyy=y(1)*y(1)+y(2)*y(2)
tepxy=x(1)*y(1)+x(2)*y(2)
rx= v-u+tepxx
ry= w-u+tepyy
axy= x(1)*y(2)-x(2)*y(1)
A= rx**2*tepyy - 2*rx*ry*tepxy + ry**2*tepxx
B= 4*u*axy**2 + A
C= 2*axy**2 + (rx+ry)*tepxy - rx*tepyy - ry*tepxx
D= rx*tepyy - ry*tepxy
E= ry*tepxx - rx*tepxy
dyx(1)= y(1)-x(1)
dyx(2)= y(2)-x(2)
Id0=1/B*(C*Iz0(dyx,v,w) + D*Iz0(y,u,w) + E*Iz0(x,u,v))
END
C -------------------------------------------------------------
DOUBLE PRECISION FUNCTION Id1(x,y,u,v,w)
IMPLICIT NONE
DOUBLE PRECISION Id0,Iz0,Iz1
EXTERNAL Id0,Iz0,Iz1
DOUBLE PRECISION x(2),y(2),dyx(2)
DOUBLE PRECISION u,v,w
DOUBLE PRECISION A,AXY,B,C,D,E,F,G,H,RX,RY
DOUBLE PRECISION tepxx,tepxy,tepyy
tepxx=x(1)*x(1)+x(2)*x(2)
tepxy=x(1)*y(1)+x(2)*y(2)
tepyy=y(1)*y(1)+y(2)*y(2)
rx= v-u+tepxx
ry= w-u+tepyy
axy= x(1)*y(2)-x(2)*y(1)
A= rx**2*tepyy - 2*rx*ry*tepxy + ry**2*tepxx
B= 4*u*axy**2 + A
C= -4*axy**2 -2*(-rx*tepyy+(rx+ry)*tepxy-ry*tepxx)
D= -2*tepxy + tepxx + tepyy
E= -tepyy + tepxy
F= rx*tepyy - ry*tepxy
G= -tepxx + tepxy
H= ry*tepxx - rx*tepxy
dyx(1)= y(1)-x(1)
dyx(2)= y(2)-x(2)
Id1= -( (C/B)*Id0(x,y,u,v,w) + (1/B)*(
& D*Iz0(dyx,v,w) +
& E*Iz0(y,u,w) - F*Iz1(y,u,w) +
& G*Iz0(x,u,v) - H*Iz1(x,u,v) ) )
END
C --------------------------------------------------------
DOUBLE PRECISION FUNCTION Id2(x,y,u,v,w)
IMPLICIT NONE
DOUBLE PRECISION Id1,Id0,Iz0,Iz1,Iz2
EXTERNAL Id1,Id0,Iz0,Iz1,Iz2
DOUBLE PRECISION x(2),y(2),mx(2),dyx(2)
DOUBLE PRECISION u,v,w
DOUBLE PRECISION A0,A1,A2,A3,A4,AXY
DOUBLE PRECISION B,C1,C2,C3,D1,D2,D3
DOUBLE PRECISION E1,E2,E3,F1,F2,F3
DOUBLE PRECISION G1,G2,G3,RX,RY
DOUBLE PRECISION tepxx,tepxy,tepyy
tepxx=x(1)*x(1)+x(2)*x(2)
tepxy=x(1)*y(1)+x(2)*y(2)
tepyy=y(1)*y(1)+y(2)*y(2)
mx(1)=-x(1)
mx(2)=-x(2)
dyx(1)= y(1)-x(1)
dyx(2)= y(2)-x(2)
rx= v-u+tepxx
ry= w-u+tepyy
axy= x(1)*y(2)-x(2)*y(1)
A0= rx**2*tepyy - 2*rx*ry*tepxy + ry**2*tepxx
B= 4*u*axy**2 + A0
A1= 2*(tepyy-tepxy)*B
A2= (-4*axy**2 +2*(rx*tepyy-(rx+ry)*tepxy+ry*tepxx))*
& 2*2*(rx*tepyy-ry*tepxy)
A3= -4*axy**2 +2*(rx*tepyy-(rx+ry)*tepxy+ry*tepxx)
A4= -2*(rx*tepyy-ry*tepxy)
C1= tepxy-tepyy
D1= 2*axy**2+(rx+ry)*tepxy-rx*tepyy-ry*tepxx
E1= tepyy
F1= -tepxy
G1= ry*tepxx-rx*tepxy
C2= -2*tepxy+tepxx+tepyy
D2= -tepyy + tepxy
E2= rx*tepyy - ry*tepxy
F2= -tepxx + tepxy
G2= ry*tepxx - rx*tepxy
C3= -2*tepxy+tepxx+tepyy
D3= -tepyy
E3= -tepxx+tepxy
F3= tepxy
G3= -(ry*tepxx-rx*tepxy)
Id2= ((A1-A2)/B**2)*Id0(x,y,u,v,w) +
& (A3/B**2)*(
& C1*Iz0(dyx,v,w) - D1*Iz1(dyx,v,w) +
& E1*Iz0(y,u,w) +
& F1*Iz0(x,u,v) - G1*Iz1(mx,v,u) ) +
& (A4/B**2)*(
& C2*Iz0(dyx,v,w) +
& D2*Iz0(y,u,w) - E2*Iz1(y,u,w) +
& F2*Iz0(x,u,v) - G2*Iz1(x,u,v) ) +
& (1/B)*(
& - C3*Iz1(dyx,v,w)
& + D3*Iz1(y,u,w)
& - E3*Iz1(mx,v,u) + F3*Iz1(x,u,v) - G3*Iz2(mx,v,u) )
END
C --------------------------------------------------------
DOUBLE PRECISION FUNCTION Id3(x,y,u,v,w)
IMPLICIT NONE
DOUBLE PRECISION Id2,Id1,Id0,Iz0,Iz1,Iz2
EXTERNAL Id2,Id1,Id0,Iz0,Iz1,Iz2
DOUBLE PRECISION x(2),y(2),dyx(2),mdyx(2),mx(2),my(2)
DOUBLE PRECISION u,v,w
DOUBLE PRECISION A0,A1,A2,A3A,A3B,A3C,A3D
DOUBLE PRECISION A4,A5A,A5B,A5C,A5D,A5E,A5F
DOUBLE PRECISION A6,A8A,A8B,A8C,A9,A10,AXY
DOUBLE PRECISION B,C2,C5,C6,C7,C8,C9,C10,C11
DOUBLE PRECISION D2,D5,D6,D7,D8,D9,D10,D11
DOUBLE PRECISION E2,E5,E6,E7,E8,E9,E10,E11
DOUBLE PRECISION F2,F5,F6,F7,F8,F9,F10
DOUBLE PRECISION G2,G5,G6,G7,G8,G9,G10
DOUBLE PRECISION RX,RY
DOUBLE PRECISION tepxx,tepxy,tepyy
tepxx=x(1)*x(1)+x(2)*x(2)
tepxy=x(1)*y(1)+x(2)*y(2)
tepyy=y(1)*y(1)+y(2)*y(2)
dyx(1)= y(1)-x(1)
dyx(2)= y(2)-x(2)
mdyx(1)=-dyx(1)
mdyx(2)=-dyx(2)
mx(1)=-x(1)
mx(2)=-x(2)
my(1)=-y(1)
my(2)=-y(2)
rx= v-u+tepxx
ry= w-u+tepyy
axy= x(1)*y(2)-x(2)*y(1)
A0= rx**2*tepyy - 2*rx*ry*tepxy + ry**2*tepxx
B= 4*u*axy**2 + A0
A1= 2*(tepyy-tepxy)*(-2)*2*(-rx*tepxy+ry*tepxx)
A2= 2*(tepyy-tepxy)
C2= tepxy-tepxx
D2= 2*axy**2+(rx+ry)*tepxy-rx*tepyy-ry*tepxx
E2= -tepxy
F2= rx*tepyy-ry*tepxy
G2= tepxx
A3a= 2*(-tepxy+tepxx) * 2*(rx*tepyy-ry*tepxy)
A3b= (-4*axy**2 +2*(rx*tepyy-(rx+ry)*tepxy+ry*tepxx))
+ * 2*(-tepxy)
A3c= (-4*axy**2 +2*(rx*tepyy-(rx+ry)*tepxy+ry*tepxx))
& * 2*(rx*tepyy-ry*tepxy)
A3d= 3*2*(-rx*tepxy+ry*tepxx)
A4= A3c
A5a= 2*(-tepxy+tepxx)
A5b= -4*axy**2 +2*(rx*tepyy-(rx+ry)*tepxy+ry*tepxx)
A5c= 2*2*(-rx*tepxy+ ry*tepxx)
A5d= -2*(rx*tepyy-ry*tepxy)
A5e= -2*(-tepxy)
A5f= -2*(rx*tepyy-ry*tepxy)*(2)*(-rx*tepxy+ry*tepxx)
C5= tepxy-tepyy
D5= 2*axy**2+(rx+ry)*tepxy-rx*tepyy-ry*tepxx
E5= tepyy
F5= -tepxy
G5= ry*tepxx-rx*tepxy
A6= -2*(rx*tepyy- ry*tepxy)
C6= tepxy-tepxx
D6= 2*axy**2+(rx+ry)*tepxy-rx*tepyy-ry*tepxx
E6= -tepxy
F6= rx*tepyy-ry*tepxy
G6= tepxx
C7= tepxy-tepyy
D7= -(tepxy-tepxx)
E7= 2*axy**2+(rx+ry)*tepxy-rx*tepyy-ry*tepxx
F7= tepyy
G7= -tepxx
A8a= -2*(-tepxy)
A8b= -2*(rx*tepyy-ry*tepxy)
A8c= 2*2*(-rx*tepxy+ry*tepxx)
C8= -2*tepxy+tepxx+tepyy
D8= -tepyy + tepxy
E8= rx*tepyy - ry*tepxy
F8= -tepxx + tepxy
G8= ry*tepxx - rx*tepxy
A9= -2*(rx*tepyy-ry*tepxy)
C9= -2*tepxy+tepxx+tepyy
D9= -tepyy+tepxy
E9= tepxy
F9= -(rx*tepyy-ry*tepxy)
G9= -tepxx
A10= -2*(-rx*tepxy+ry*tepxx)
C10= -2*tepxy+tepxx+tepyy
D10= -tepyy
E10= -tepxx+tepxy
F10= tepxy
G10= -(ry*tepxx-rx*tepxy)
C11= -(-2*tepxy+tepyy+tepxx)
D11= -tepyy
E11= tepxx
Id3= -( (A1/B**2)*Id0(x,y,u,v,w) + (A2/B**2)*(
& C2*Iz0(dyx,v,w) - D2*Iz1(mdyx,w,v)+
& E2*Iz0(y,u,w) - F2*Iz1(my,w,u) +
& G2*Iz0(x,u,v) )
& -( ((A3a+A3b)*B - A3c*A3d)/B**3 * Id0(x,y,u,v,w) +
& (A4/B**3)*(
& C2*Iz0(dyx,v,w) - D2*Iz1(mdyx,w,v)+
& E2*Iz0(y,u,w) - F2*Iz1(my,w,u)+
& G2*Iz0(x,u,v) ) ) +
& (A5a*B - A5b*A5c)/B**3*( A5d*Id0(x,y,u,v,w) +
& C5*Iz0(dyx,v,w) - D5*Iz1(dyx,v,w) +
& E5*Iz0(y,u,w) +
& F5*Iz0(x,u,v) - G5*Iz1(mx,v,u) ) +
& A5b/B**2 * ( (A5e - A5f/B) * Id0(x,y,u,v,w) +
& (A6/B)*(
& C6*Iz0(dyx,v,w) - D6*Iz1(mdyx,w,v) +
& E6*Iz0(y,u,w) - F6*Iz1(my,w,u)+
& G6*Iz0(x,u,v) )
& - C7*Iz1(mdyx,w,v) + D7*Iz1(dyx,v,w)
& + E7*Iz2(mdyx,w,v)
& - F7*Iz1(my,w,u)
& + G7*Iz1(mx,v,u) )+
& (A8a*B - A8b*A8c)/B**3*(
& C8*Iz0(dyx,v,w) +
& D8*Iz0(y,u,w) - E8*Iz1(y,u,w) +
& F8*Iz0(x,u,v) - G8*Iz1(x,u,v) ) +
& A9/B**2*(
& - C9*Iz1(mdyx,w,v)
& - D9*Iz1(my,w,u) + E9*Iz1(y,u,w) - F9*Iz2(y,u,w)
& + G9*Iz1(x,u,v) ) +
& A10/B**2*(
& - C10*Iz1(dyx,v,w)
& + D10*Iz1(y,u,w)
& - E10*Iz1(mx,v,u) + F10*Iz1(x,u,v) - G10*Iz2(mx,v,u) )+
& 1/B*(
& - C11*Iz2(dyx,v,w)
& - D11*Iz2(y,u,w)
& + E11*Iz2(x,u,v) ))
END
C --------------------------------------------------------
DOUBLE PRECISION FUNCTION Iv0(x,y,z,u,v,w,w2)
IMPLICIT NONE
DOUBLE PRECISION Id0
EXTERNAL Id0
DOUBLE PRECISION x(2),y(2),z(2),dyx(2),dzx(2)
DOUBLE PRECISION u,v,w,w2
DOUBLE PRECISION rx,ry,rz
DOUBLE PRECISION axy,ayz,azx
DOUBLE PRECISION A
rx= v-u+x(1)*x(1)+x(2)*x(2)
ry= w-u+y(1)*y(1)+y(2)*y(2)
rz= w2-u+z(1)*z(1)+z(2)*z(2)
axy= x(1)*y(2)-x(2)*y(1)
ayz= y(1)*z(2)-y(2)*z(1)
azx= z(1)*x(2)-z(2)*x(1)
dyx(1)= y(1)-x(1)
dyx(2)= y(2)-x(2)
dzx(1)= z(1)-x(1)
dzx(2)= z(2)-x(2)
A= 1/(axy*rz + ayz*rx + azx*ry)
Iv0= A*(-(axy+ayz+azx)*Id0(dyx,dzx,v,w,w2)
& +axy*Id0(x,y,u,v,w)
& +ayz*Id0(y,z,u,w,w2)
& +azx*Id0(x,z,u,v,w2) )
END
C --------------------------------------------------------
DOUBLE PRECISION FUNCTION Iv1(x,y,z,u,v,w,w2)
IMPLICIT NONE
DOUBLE PRECISION Iv0,Id0,Id1
EXTERNAL Iv0,Id0,Id1
DOUBLE PRECISION x(2),y(2),z(2),dyx(2),dzx(2)
DOUBLE PRECISION u,v,w,w2
DOUBLE PRECISION A,B,RX,RY,RZ
DOUBLE PRECISION AXY,AYZ,AZX
dyx(1)= y(1)-x(1)
dyx(2)= y(2)-x(2)
dzx(1)= z(1)-x(1)
dzx(2)= z(2)-x(2)
rx= v-u+x(1)*x(1)+x(2)*x(2)
ry= w-u+y(1)*y(1)+y(2)*y(2)
rz= w2-u+z(1)*z(1)+z(2)*z(2)
axy= x(1)*y(2)-x(2)*y(1)
ayz= y(1)*z(2)-y(2)*z(1)
azx= z(1)*x(2)-z(2)*x(1)
A= 1/(axy*rz + ayz*rx + azx*ry)
B= axy+ayz+azx
Iv1=-((B*A**2)*(-(axy+ayz+azx)*Id0(dyx,dzx,v,w,w2)
& +axy*Id0(x,y,u,v,w)
& +ayz*Id0(y,z,u,w,w2)
& +azx*Id0(x,z,u,v,w2) )+
& A*( -axy*Id1(x,y,u,v,w)
& -ayz*Id1(y,z,u,w,w2)
& -azx*Id1(x,z,u,v,w2) ))
END
C --------------------------------------------------------
DOUBLE PRECISION FUNCTION Iv2(x,y,z,u,v,w,w2)
IMPLICIT NONE
DOUBLE PRECISION Iv1,Iv0,Id0,Id1,Id2
EXTERNAL Iv1,Iv0,Id0,Id1,Id2
DOUBLE PRECISION x(2),mx(2),y(2),z(2),dyx(2)
DOUBLE PRECISION dzx(2)
DOUBLE PRECISION u,v,w,w2
DOUBLE PRECISION axy,azx,ayz
DOUBLE PRECISION rx,ry,rz,A,B
mx(1)=-x(1)
mx(2)=-x(2)
dyx(1)= y(1)-x(1)
dyx(2)= y(2)-x(2)
dzx(1)= z(1)-x(1)
dzx(2)= z(2)-x(2)
rx= v-u+x(1)*x(1)+x(2)*x(2)
ry= w-u+y(1)*y(1)+y(2)*y(2)
rz= w2-u+z(1)*z(1)+z(2)*z(2)
axy= x(1)*y(2)-x(2)*y(1)
azx= z(1)*x(2)-z(2)*x(1)
ayz= y(1)*z(2)-y(2)*z(1)
A= 1/(axy*rz + ayz*rx + azx*ry)
B= axy+ayz+azx
Iv2=(-B*2D0*ayz*A**3)*(
& -B*Id0(dyx,dzx,v,w,w2)
& +axy*Id0(x,y,u,v,w)
& +ayz*Id0(y,z,u,w,w2)
& +azx*Id0(x,z,u,v,w2) )+
& (B*A**2)*(B*Id1(dyx,dzx,v,w,w2)
& -axy*Id1(mx,dyx,v,u,w)
& -azx*Id1(mx,dzx,v,u,w2) )+
& (-ayz*A**2)*(-axy*Id1(x,y,u,v,w)
& -ayz*Id1(y,z,u,w,w2)
& -azx*Id1(x,z,u,v,w2) )+
& A*(axy*Id2(x,y,u,v,w)
& +azx*Id2(x,z,u,v,w2) )
END