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subroutine eaoxxx(eb,ea,shlf,chlf,phi,nhe,nha , eao)
c
c This subroutine computes an off-shell positron wavefunction after
c emitting a photon from the positron beam, with a special care for the
c small angle region. The momenta are measured in the laboratory frame,
c where the e+ beam is along the negative z axis.
c
c input:
c real eb : energy (GeV) of beam e+
c real ea : energy (GeV) of final photon
c real shlf : sin(theta/2) of final photon
c real chlf : cos(theta/2) of final photon
c real phi : azimuthal angle of final photon
c integer nhe = -1 or 1 : helicity of beam e+
c integer nha = -1 or 1 : helicity of final photon
c
c output:
c complex eao(6) : off-shell positron <e,A,e'|
c
implicit none
double complex eao(6),phs
double precision eb,ea,shlf,chlf,phi,alpha,gal,rnhe,x,c,s,d
double precision coeff,xnnp,xnnm,snp,csp
integer nhe,nha,nn
double precision rHalf, rOne, rTwo, rFour, rOte
double precision rPi, rIalph
parameter( rHalf = 0.5d0, rOne = 1.0d0, rTwo = 2.0d0 )
parameter( rFour = 4.0d0, rOte = 128.9d0 )
parameter( rPi = 3.14159265358979323846d0 )
parameter( rIalph = 137.0359895d0 )
double precision me
parameter( me = 0.510998902d-3 )
#ifdef HELAS_CHECK
double precision zero
double precision rZero
parameter( rZero = 0.0d0 )
double precision epsi
parameter( epsi = 1.0d-5 )
integer stdo
parameter( stdo = 6 )
#endif
c
#ifdef HELAS_CHECK
if ( eb.le.rZero )
& write(stdo,*) ' helas-error : eb in eaoxxx is not positive'
if ( ea.le.rZero )
& write(stdo,*) ' helas-error : ea in eaoxxx is not positive'
if (ea.gt.eb ) then
write(stdo,*) ' helas-error : ea in eaoxxx is greater than eb'
write(stdo,*) ' eb = ',eb,' : ea = ',ea
endif
if ( shlf.lt.rZero .or. shlf.gt.rOne ) then
write(stdo,*) ' helas-error : shlf in eaoxxx is improper'
write(stdo,*) ' shlf = ',shlf
endif
if ( chlf.lt.rZero .or. chlf.gt.rOne ) then
write(stdo,*) ' helas-error : chlf in eaoxxx is improper'
write(stdo,*) ' chlf = ',chlf
endif
zero = abs(shlf**2+chlf**2-rOne)
if ( zero.gt.epsi ) then
write(stdo,*)
& ' helas-error : shlf and chlf in eaoxxx are inconsistent'
write(stdo,*)
& ' : shlf,chlf = ',shlf,chlf
endif
if ( phi.lt.rZero .or. phi.gt.rTwo*rPi ) then
write(stdo,*)
& ' helas-warn : phi in eaoxxx does not lie on 0.0 thru 2.0*pi'
write(stdo,*)
& ' : phi = ',phi
endif
if (abs(nhe).ne.1 ) then
write(stdo,*) ' helas-error : nhe in eaoxxx is not -1,1'
write(stdo,*) ' nhe = ',nhe
endif
if ( abs(nha).ne.1 ) then
write(stdo,*) ' helas-error : nha in eaoxxx is not -1,1'
write(stdo,*) ' nha = ',nha
endif
if ( eb.lt.rOne ) then
write(stdo,*)
& ' helas-warn : use of eaoxxx is not appropriate: eb too low'
write(stdo,*)
& ' : eb = ',eb
endif
#endif
alpha = rOne/rOte
gal = sqrt(alpha*rFour*rPi)
nn = nha*nhe
rnhe = nhe
x = ea/eb
c = (chlf+shlf)*(chlf-shlf)
s = rTwo*chlf*shlf
d = -rOne/(ea*eb*(rFour*chlf**2-(me/eb)**2*c))
coeff = nn*gal*sqrt(eb)*d
xnnp = x*(1+nn)
xnnm = x*(1-nn)
snp = sin(phi)
csp = cos(phi)
phs = dcmplx( csp, -rnhe*snp )
eao((5-3*nhe)/2) = coeff*me*s*(rOne+xnnp*rHalf)
eao((5-nhe)/2) = rnhe*xnnp *coeff*me*shlf**2*phs
eao((5+nhe)/2) = coeff*eb*s*(-rTwo+xnnm)
eao((5+3*nhe)/2) = real(nha-nhe)*coeff*eb*x*chlf**2*phs*rTwo
eao(5) = eb*dcmplx( x-rOne, x*c+rOne )
eao(6) = eb*x*s*dcmplx( csp, snp )
c
return
end
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