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qfs_new11_sub.f
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qfs_new11_sub.f
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*qfs
subroutine qfs(z,a,e,th,w,delnu,flag,sigma_qfs)
c
implicit real*8 (a-h,o-z)
character*1 dorg
logical*4 flag
common /par/ eps,epsd,pf,spence
common /switch/ dorg
parameter(scale=1.d-26)
parameter (wpi = 1.078d0)
pm=939.0d0
dm=1219.d0
alph=1.d0/137.03604d0
pi=acos(-1.d0)
c
IF(A.EQ.1.) THEN
PF=0.
EPS=0.
EPSD=13.0
dorg='n'
ELSEIF(A.eq.2.) THEN
! PF=77.
! EPS=2.23
PF=74. ! OR 2/04
EPS=2.22
EPSD=13.0
ELSEIF(A.EQ.4.) THEN
PF=180. !152
EPS=20. !8
EPSD=13.0
ELSEIF(A.EQ.9.) THEN
PF=200.
EPS=20.
EPSD=13.0
ELSEIF(A.EQ.12.) THEN
PF=230. !205, 215, 220, 230=5/03
EPS=25.
EPSD=13.
ELSEIF(A.EQ.14 .OR. A.EQ.15) THEN
PF=225.
EPS=25.
EPSD=13.
ELSEIF(A.EQ.27.) THEN
PF=235.
EPS=32.
EPSD=13.
ELSEIF(A.EQ.59.) THEN
PF=260.
EPS=35.
EPSD=13.
ELSEIF(A.EQ.64.) THEN
PF=260.
EPS=35.
EPSD=13.
ELSEIF(A.EQ.184.) THEN
PF=265.
EPS=43.
EPSD=13.
ELSE
WRITE(*,*) 'pf, eps, epsd not specified for this material, stop'
STOP
ENDIF
c
sigqfza=sigqfs(e,th,w,z,a,eps,pf,delnu)*scale
! 6/03 Use Hall C F2 R for proton inelastic sigma
thr = th*pi/180.0d0 ! 6/03
qsq = 4.0d0*e*(e-w)*sin(thr/2.0d0)**2 ! 6/03
wsq = pm*pm + 2.d0*pm*w - qsq ! 6/03
if((a.eq.1.and.z.eq.1).and.(wsq.le.3.9d0)) then ! 6/03
call hcf2r(qsq/1.d6,wsq/1.d6,f2,r) ! 6/03
siginel=sigmot(e,thr)*f2*(1.d0/w+
1 2*w*(1+qsq/w**2)*(tan(thr/2))**2/(qsq*(1+r))) ! 6/03
signinel=siginel*scale ! 6/03
else ! 6/03 A >1
if(a.eq.2.and.z.eq.1) then ! 2/04
! print *,'e ',e,enu,ww,qsq,th
call hallc2h(e,th,w,sigdelc,sigr1c,sigr2c,sigxc) ! 2/04
sigda = sigdelc*scale ! "
sigr1a = sigr1c*scale ! "
sigr2a = sigr2c*scale ! "
sigxa = sigxc*scale ! "
siginel = sigda+sigxa+sigr1a+sigr2a ! "
! if (w.lt.wpi) then
if (w.lt.1140) then !
! sig2na=sig2n(e,th,enu,z,a,pf)*scale*0.7d0
sig2na=sig2n(e,th,enu,z,a,pf)*scale*1.4d0 ! "
else ! "
sig2na = 0.d0 ! "
end if ! No 2N sig if W > W_pi_thr. 2/04
else ! A > 2
sigda=sigdel(e,th,w,a,epsd,pf,z)*scale
sigxa=sigx(e,th,w,a)*scale
sigr1a=sigr1(e,th,w,a,pf,z)*scale
sigr2a=sigr2(e,th,w,a,pf,z)*scale
! sig2na=sig2n(e,th,w,z,a,pf)*scale*0.7
! siginel=sigda+sigxa+sigr1a+sigr2a+sig2na ! 6/03
siginel=sigda+sigxa+sigr1a+sigr2a
sig2na=sig2n(e,th,enu,z,a,pf)*scale*0.7
end if ! hallc 2h
! sig2na=sig2n(e,th,enu,z,a,pf)*scale*0.7
siginel=siginel+sig2na
end if ! hcf2r 2/04
! end if ! 6/03
! sig=sigqfza+sigda+sigxa+sigr1a+sigr2a+sig2na
sig = sigqfza + siginel ! 6/03
sigma_qfs=sig ! nonradiated qfs cross section
c
c thcr=th*pi/180.
c qms=4.*e*(e-w)*sin(thr/2.)**2
c qvs=qms+w**2
c ekappa=w-qms/2./pm
c if(ekappa.gt.-pm/2.)then
c cmtot=sqrt(pm**2+2.*pm*ekappa)
c else
c cmtot=pm
c endif
c flux=(alph/2./pi**2)*((e-w)/e)*((2.*pm*w-qms)/2./pm/qms)
c polari=1./(1.+2.*qvs*tan(thr/2.)**2/qms)
c flux=flux/(1.-polari)
c if(ekappa.lt.0.) photsig=0.
c photsig=sig/flux
c radiate
sigrad=0.
if(sig.gt.0.0d0.and.flag) then
call radiate(e,th,w,z,a,sig,sigrad)
sigma_qfs=sigrad
end if
c
return
end
*fd
real*8 function fd(qms,a)
implicit real*8 (a-h,o-z)
fd=1./(1.+qms/a**2)**2
return
end
*fm
real*8 function fm(qms,a)
implicit real*8 (a-h,o-z)
fm=1./(1.+qms/a**2)
return
end
*fphenom
real*8 function fphenom(qms)
implicit real*8 (a-h,o-z)
a1=.55d0
a2=20.d0/1.d6
! a2=10.d0/1.d6
b1=.45d0
! b2=.45d0/1.d6
b2=.45d0/1.d6*1.1d0
! c1=0.03d0
c1 = 0.00d0
! c2=0.2d0/1.d12
c2=0.1d0/1.d12
! c3=4.5d6
c3=4.0d6
fphenom=a1*exp(-a2*qms)+b1*exp(-b2*qms)
! fphenom=fphenom+c1*exp(-c2*(qms-4.5e6)**2)
fphenom=fphenom+c1*exp(-c2*(qms-c3)**2)
fphenom=sqrt(fphenom)
return
end
*fyukawa
real*8 function fyukawa(qms,a)
implicit real*8 (a-h,o-z)
if(qms.lt.1.e-5.or.a.lt.1.e-5)then
fyukawa=0.
else
arg=sqrt(qms/2.)/a
fyukawa=atan(arg)/arg
endif
return
end
*sigmot
real*8 function sigmot(e,thr)
implicit real*8 (a-h,o-z)
alph=1./137.03604
hbarc=197.3286
sigmot=(alph*hbarc*cos(thr/2.)/2./e/sin(thr/2.)**2)**2
c fm**2/sr
return
end
*recoil
real*8 function recoil(e,thr,tm)
implicit real*8 (a-h,o-z)
recoil=1./(1.+2.*e*sin(thr/2.)**2/tm)
return
end
*sigqfs
real*8 function sigqfs(e,th,w,z,a,eps,pf,delnu)
implicit real*8 (a-h,o-z)
character*1 dorg
common /switch/dorg
c Needed to save delnu for later calls to sigqfs
c Saving of delsav between calls done by -fno-automatic
! if(icall.ne.1) then
delsav = delnu
! icall = 1
! else
! delnu = delsav
! end if
pm=939.0d0
up=2.7928456
un=-1.91304184
ap0=840.
! ap1=750.
! ap1=840.
ap1=815. ! 5/2003
alph=1./137.03604
hbarc=197.32858
pi=acos(-1.0d0)
gamr=120.
pfr=230.
qmsrq=4.*730.*(730.-115.)*sin(37.1*pi/180./2.)**2
qvsrq=qmsrq+115.**2
na=int(a)
if(na.eq.1)then
ap=ap0
elseif(na.lt.4)then
ap=ap0+(a-1.)*(ap1-ap0)/3.
else
ap=ap1
endif
c print 200
200 format(' enter de-e[MeV],domega-e[sr],b-luminosity[cm-2*s-1]')
c read *,dee,dwe,blum
thr=th*pi/180.0d0
qms=4.0d0*e*(e-w)*sin(thr/2.0d0)**2
qvs=qms+w**2
ekappa=w-qms/2./pm
if(ekappa.gt.-pm/2.)then
cmtot=sqrt(pm**2+2.*pm*ekappa)
else
cmtot=pm
endif
c start qfs section
signs=sigmot(e,thr)*recoil(e,thr,pm)
formp=1.+qms*up**2/4./pm**2
formp=formp/(1.+qms/4./pm**2)
formp=formp+qms*up**2*tan(thr/2.)**2/2./pm**2
formp=formp*fd(qms,ap)**2
sigep=signs*formp
falloff=(1.+5.6*qms/4./pm**2)**2
formn=(qms*un/4./pm**2)**2/falloff+qms*un**2/4./pm**2
formn=formn/(1.+qms/4./pm**2)
formn=formn+qms*un**2*tan(thr/2.)**2/2./pm**2
formn=formn*fd(qms,ap)**2
sigen=signs*formn
epq=4.0d0*e**2*sin(thr/2.0d0)**2/2.0d0/pm
epq=epq/(1.+2.*e*sin(thr/2.)**2/pm)+eps
epq=e-epq
if(int(a).eq.1)then
c Get sig_el as ds2/(dE'dOmega) [nb/(sr MeV)]
if(dorg.ne.'y') then ! Gauusian elastic peak
! arg=(e-w-epq)/sqrt(2.)/1. ! Old qfs's wrong form of ds/dOmega
! den=2.51
siggauss = delnu/2.354d0 ! sigma_gauss = FWHM(=delnu)/2.354
showw = w
arg=(e-w-epq)/sqrt(2.0d0)/siggauss
den=2.51d0*siggauss ! 2.51 = sqrt(2*Pi)
else
c This is option for ds/dOmega
wel=e - e/(1+2.0d0*e*sin(thr/2.)**2/pm)
winv=pm*(pm+2.0d0*w)-qms
if(abs(w-wel).le.delnu.and.(w.le.wel))then
sigq=(z*sigep+(a-z)*sigen)
else
sigq=0.0d0
endif
sigqfs=sigq
return
end if ! end dorg
else
gamq=gamr*pf*sqrt(qvs)/pfr/sqrt(qvsrq)
arg=(e-w-epq)/1.20d0/(gamq/2.0d0)
den=2.13d0*(gamq/2.d0)
! sigq=(z*sigep+(a-z)*sigen)*exp(-arg**2)/den
endif
nq=int(arg)
! if(abs(nq).gt.10)then
if(abs(nq).gt.20)then ! needed for delw =1
sigq=0.d0
else
sigq=(z*sigep+(a-z)*sigen)*exp(-arg**2)/den
endif
sigqfs=sigq
return
end
*sigdel
real*8 function sigdel(e,th,w,a,epsd,pf,z)
implicit real*8 (a-h,o-z)
pm=939.0d0
pimass=140.
dm=1219.
! ad1=700.
! ad1=700. ! 2H
! ad1=774. ! 12C
ad1=750. ! 12C
! ad0=700.
ad0=774.
pi=acos(-1.d0)
alph=1./137.03604
hbarc=197.32858
! gamdp=110.
gamdp=110.
! gamsprd=140.
gamsprd=20.
! gamr=120.
gamr=100.
! gampi=5.
gampi=50.
qfdp=1.02d-7
pfr=230.
qmsr=4.*730.*(730.-390.)*sin(37.1*pi/180./2.)**2
qvsr=qmsr+390.**2
qmsrq=4.*730.*(730.-115.)*sin(37.1*pi/180./2.)**2
qvsrq=qmsrq+115.**2
na=int(a)
if(na.eq.1)then
qfd=qfdp
gsprda=0.
ad=ad0
! elseif(na.lt.4)then
elseif(na.eq.2)then
qfd=qfdp
gsprda=(a-1.)*gamsprd/3.
! gsprda=gamspr
! ad=ad0+(a-1.)*(ad1-ad0)/3.
ad=700
else
ad=ad1
gsprda=gamsprd
! qfd=qfdp
qfd=qfdp*1.1 ! 5/03
endif
thr=th*pi/180.
qms=4.*e*(e-w)*sin(thr/2.)**2
qvs=qms+w**2
ekappa=w-qms/2./pm
cmtot2=pm**2+2.*pm*ekappa
c begin delta calculation
if(na.gt.1)then
gamq=gamr*pf*sqrt(qvs)/pfr/sqrt(qvsrq)
else
gamq=0.
endif
epd=e-(dm-pm)*(dm+pm)/2./pm
epd=epd/(1.+2.*e*sin(thr/2.)**2/pm)
epd=epd-epsd
wd=e-epd
qmspk=4.*e*epd*sin(thr/2.)**2
qvspk=qmspk+wd**2
c
c note width includes e-dependence,fermi broadening,& spreading
c
wthresh=4.*e**2*sin(thr/2.)**2+pimass**2+2.*pimass*pm
wthresh=wthresh/2./pm
thrshfree=1.+2.*e*sin(thr/2.)**2/pm
threshd=1.+pf/pm+pf**2/2./pm**2+2.*e*sin(thr/2.)**2/pm
wthrfree=wthresh/thrshfree
wthresh=wthresh/threshd
if(w.gt.wthresh)then
if((z.ne.1).and.(a.ne.1)) gampi = wthrfree-wthresh
thresh=1.-exp(-(w-wthresh)/gampi)
else
thresh=0.
endif
gamd=gamdp
gam=sqrt(gamd**2+gamq**2+gsprda**2)
! sigd=qfdp*(gamdp/gam)
sigd=qfd*(gamdp/gam) ! 5/03
sigd=sigd*cmtot2*gam**2
sigd=sigd/((cmtot2-(dm+epsd)**2)**2+cmtot2*gam**2)
sigd=sigd*fd(qms,ad)**2/fd(qmsr,ad)**2
test=qvs/qvsr
sigd=sigd*test
sigd=sigd*(qms/2./qvs+tan(thr/2.)**2)
sigd=sigd/(qmsr/2./qvsr+tan(37.1*pi/180./2.)**2)
sigd=sigd*sigmot(e,thr)/sigmot(730.d0,37.1*pi/180.)
sigd=sigd*a
sigd=sigd*thresh
sigdel=sigd
return
end
*sigx
real*8 function sigx(e,th,w,a)
implicit real*8 (a-h,o-z)
alph=1./137.03604
pi=acos(-1.d0)
c sig0=111.*1.e-30
sig0=100.d-4
! sig0=80.d-4
c sig1=60.*1.e-27
sig1=54.*1.d-1
pimass=140.
pm=939.0d0
c gam0=550.
! gam0=600.
gam0=610.
! gam0=700.
c r=0.10
aq=250.
thr=th*pi/180.
if(w.lt.1.e-5)go to 4
qms=4.*e*(e-w)*sin(thr/2.)**2
arg0=w-qms/2./pm-pimass-pimass**2/2./pm
arg1=arg0/gam0
arg=arg1**2/2.
if(arg1.gt.8.)then
shape=1.+sig1/sig0/arg0
elseif(arg1.lt.1.e-5)then
shape=0.
elseif(arg1.lt.0.1)then
shape=sig1*arg0/2./gam0**2/sig0
else
shape=(1.-exp(-arg))*(1.+sig1/sig0/arg0)
endif
ekappa=w-qms/2./pm
siggam=sig0*shape
qs=qms+w**2
eps=1./(1.+2.*qs*tan(thr/2.)**2/qms)
flux=alph*ekappa*(e-w)/2./pi**2/qms/e/(1.-eps)
if(flux.lt.1.e-20)flux=0.
sigee=flux*siggam*fphenom(qms)**2
c sigee=flux*siggam
! r=0.56*1.e6/(qms+pm**2)
r=min(0.56*1.e6/(qms+pm**2),0.2)
factor1=1.+eps*r
sigee=sigee*factor1
4 sigx=a*sigee
return
end
*sigr1
real*8 function sigr1(e,th,w,a,pf,z)
implicit real*8 (a-h,o-z)
pi=acos(-1.d0)
pm=939.0d0
pimass=140.
thr=th*pi/180.
pfr=230.
! rm=1500.
rm=1500.
epsr=0.
ar0=1000.
! ar1=1000.
! ar1=940. ! 2H
ar1=1000. ! 12C
! gamqfr=120.
gamqfr=100.
! gamsprd=140.
gamsprd=0.
gamr=110.
! gamr=130.
! gampi=5.
gampi=25.
qfrp=1.20d-7
qmsqfr=4.*730.*(730.-115.)*sin(37.1*pi/180./2.)**2
qvsqfr=qmsqfr+115.**2
qmsrr=4.*10000.*(10000.-1240.)*sin(6.*pi/180./2.)**2
qvsrr=qmsrr+1240.**2
sigref=fd(qmsrr,ar0)**2*qvsrr
sigref=sigref*(qmsrr/2./qvsrr+tan(6.*pi/180./2.)**2)
sigref=sigref*sigmot(10000.d0,6.*pi/180.)
na=int(a)
if(na.eq.1)then
qfr=qfrp
gsprda=0.
ar=ar0
! elseif(na.lt.4)then
elseif(na.eq.2)then
qfr=qfrp
gsprda=(a-1.)*gamsprd/3.
! ar=ar0+(a-1.)*(ar1-ar0)/3.
ar=920
else
ar=ar1
gsprda=gamsprd
qfr=qfrp
endif
qms=4.*e*(e-w)*sin(thr/2.)**2
qvs=qms+w**2
if(na.gt.1)then
gamq=gamqfr*pf*sqrt(qvs)/pfr/sqrt(qvsqfr)
else
gamq=0.
endif
cmtot2=pm**2+2.*pm*w-qms
wthresh=4.*e**2*sin(thr/2.)**2+pimass**2+2.*pimass*pm
wthresh=wthresh/2./pm
thrshfree=1.+2.*e*sin(thr/2.)**2/pm
threshd=1.+pf/pm+pf**2/2./pm**2+2.*e*sin(thr/2.)**2/pm
wthrfree=wthresh/thrshfree
wthresh=wthresh/threshd
if(w.gt.wthresh)then
if((z.ne.1).and.(a.ne.1)) gampi = wthrfree-wthresh
thresh=1.-exp(-(w-wthresh)/gampi)
else
thresh=0.
endif
epr=e-(rm-pm)*(rm+pm)/2./pm
epr=epr/(1.+2.*e*sin(thr/2.)**2/pm)
epr=epr-epsr
wr=e-epr
gam=sqrt(gamr**2+gamq**2+gsprda**2)
sigr=qfr*(gamr/gam)/sigref
sigr=sigr*cmtot2*gam**2
sigr=sigr/((cmtot2-(rm+epsr)**2)**2+cmtot2*gam**2)
sigr=sigr*qvs*fd(qms,ar)**2
sigr=sigr*(qms/2./qvs+tan(thr/2.)**2)
sigr=sigr*sigmot(e,thr)
sigr1=a*thresh*sigr
return
end
*sigr2
real*8 function sigr2(e,th,w,a,pf,z)
implicit real*8 (a-h,o-z)
pi=acos(-1.d0)
pm=939.0d0
pimass=140.
thr=th*pi/180.
pfr=230.
rm=1700.
epsr=0.
ar0=1200.
! ar1=1200.
! ar1=1000. ! 2H
ar1=1200. ! 12C
! gamqfr=120.
gamqfr=100.
! gamsprd=140.
gamsprd=0.
gamr=110.
! gampi=5.
gampi=25.
qfrp=0.68d-7
qmsqfr=4.*730.*(730.-115.)*sin(37.1*pi/180./2.)**2
qvsqfr=qmsqfr+115.**2
qmsrr=4.*10000.*(10000.-1520.)*sin(6.*pi/180./2.)**2
qvsrr=qmsrr+1520.**2
sigref=fd(qmsrr,ar0)**2*qvsrr
sigref=sigref*(qmsrr/2./qvsrr+tan(6.*pi/180./2.)**2)
sigref=sigref*sigmot(10000.d0,6.*pi/180.)
na=int(a)
if(na.eq.1)then
qfr=qfrp
gsprda=0.
ar=ar0
! elseif(na.lt.4)then
elseif(na.eq.2)then
qfr=qfrp
gsprda=(a-1.)*gamsprd/3.
! ar=ar0+(a-1.)*(ar1-ar0)/3.
ar=980
else
ar=ar1
gsprda=gamsprd
qfr=qfrp
endif
qms=4.*e*(e-w)*sin(thr/2.)**2
qvs=qms+w**2
if(na.gt.1)then
gamq=gamqfr*pf*sqrt(qvs)/pfr/sqrt(qvsqfr)
else
gamq=0.
endif
cmtot2=pm**2+2.*pm*w-qms
wthresh=4.*e**2*sin(thr/2.)**2+pimass**2+2.*pimass*pm
wthresh=wthresh/2./pm
thrshfree=1.+2.*e*sin(thr/2.)**2/pm
threshd=1.+pf/pm+pf**2/2./pm**2+2.*e*sin(thr/2.)**2/pm
wthrfree=wthresh/thrshfree
wthresh=wthresh/threshd
if(w.gt.wthresh)then
if((z.ne.1).and.(a.ne.1)) gampi = wthrfree-wthresh
thresh=1.-exp(-(w-wthresh)/gampi)
else
thresh=0.
endif
epr=e-(rm-pm)*(rm+pm)/2./pm
epr=epr/(1.+2.*e*sin(thr/2.)**2/pm)
epr=epr-epsr
wr=e-epr
gam=sqrt(gamr**2+gamq**2+gsprda**2)
sigr=qfr*(gamr/gam)/sigref
sigr=sigr*cmtot2*gam**2
sigr=sigr/((cmtot2-(rm+epsr)**2)**2+cmtot2*gam**2)
sigr=sigr*qvs*fd(qms,ar)**2
sigr=sigr*(qms/2./qvs+tan(thr/2.)**2)
sigr=sigr*sigmot(e,thr)
sigr2=a*thresh*sigr
return
end
*sig2n
real*8 function sig2n(e,th,w,z,a,pf)
implicit real*8 (a-h,o-z)
pi=acos(-1.d0)
thr=th*pi/180.d0
dm=1219.d0
pimass=140.d0
pm=939.d0
! a2=550.
a2=500.d0
pfr=60.d0
gam2n=20.d0
! gam2n=40.
gamqfr=40.d0
gamref=300.d0
gamr=gamref
sigref=0.20d-7
qmsr=4.d0*596.8d0*(596.8d0-380.d0)*sin(60.d0*pi/180.d0/2.d0)**2
qvsr=qmsr+380.d0**2
sigkin=0.5d0*sigmot(596.8d0,60.d0*pi/180.d0)
sigkin=sigkin*(qmsr/2.d0/qvsr+tan(60.d0*pi/180.d0/2.d0)**2)
sigkin=sigkin*qvsr*fd(qmsr,a2)**2
sigkin=sigkin*gamr/gamref
sigcon=sigref/sigkin
qms=4.d0*e*(e-w)*sin(thr/2.d0)**2
qvs=qms+w**2
gamqf=gamqfr*(pf/pfr)*(sqrt(qvs)/sqrt(qvsr))
effmass=(pm+dm)/2.d0
sig=(z*(a-z)/a)*sigmot(e,thr)
sig=sig*(qms/2.d0/qvs+tan(thr/2.d0)**2)
sig=sig*qvs*fd(qms,a2)**2
ekappa=w-qms/2.d0/pm
cmtot2=pm**2+2.d0*pm*ekappa
c gam=sqrt(gamr**2+gamqf**2)
gam=gamr
sig=sig*cmtot2*gam**2
sig=sig/((cmtot2-effmass**2)**2+cmtot2*gam**2)
sig=sig*(gamr/gam)*sigcon
sig2n=sig
wthresh=qms/4.d0/pm
if(w.gt.wthresh)then
thresh=1.d0-exp(-(w-wthresh)/gam2n)
else
thresh=0.d0
endif
sig2n=sig2n*thresh
return
end
*radiate
subroutine radiate(e,th,w,z,a,signr,sigrad)
implicit real*8 (a-h,o-z)
common /par/ eps,epsd,pf,spence
alph=1./137.03604
emass=0.511
del=10.
pi=acos(-1.d0)
prec=.0005
thr=th*pi/180.
arg=cos(thr/2.)**2
spence=pi**2/6.-log(arg)*log(1.-arg)
do 10 nsp=1,50
10 spence=spence-arg**nsp/float(nsp)**2
c print 15,spence
15 format(' spence function = ',1f14.9)
qms=4.*e*(e-w)*sin(thr/2.)**2
d1=(2.*alph/pi)*(log(qms/emass**2)-1.)
d2=13.*(log(qms/emass**2)-1.)/12.-17./36.-0.5*(pi**2/6.-spence)
d2=d2*(2.*alph/pi)
ebar=sqrt(e*(e-w))
sigrad=signr*(1.+d2)*exp(-d1*log(ebar/del))
c print 20,d1,d2
20 format(' delta1 and delta2 = ',2e14.6)
x1=0.
x2=w-del
call rom(e,th,w,z,a,x1,x2,prec,ans,kf)
ans=ans*1.d-26
iflag=0
err=0.
c print 25,x1,x2,prec,ans,err
25 format(' x1,x2,prec,ans,err = ',5e10.3)
c print 30,kf,iflag
30 format(' kf,iflag = ',2i5)
sigrad=sigrad+ans
return
end
*rom
subroutine rom(e0,th0,w0,z0,a0,a,b,eps,ans,k)
implicit real*8 (a-h,o-z)
c romberg method of integration
dimension w(50,50)
h=b-a
k=0
call value(e0,th0,w0,z0,a0,a,fa)
call value(e0,th0,w0,z0,a0,b,fb)
w(1,1)=(fa+fb)*h/2.
4 k=k+1
if(k.ge.49)go to 5
h=h/2.
sig=0.
m=2**(k-1)
do 1 j=1,m
j1=2*j-1
x=a+float(j1)*h
call value(e0,th0,w0,z0,a0,x,f)
1 sig=sig+f
w(k+1,1)=w(k,1)/2.+h*sig
do 2 l=1,k
iu=k+1-l
iv=l+1
2 w(iu,iv)=(4.**(iv-1)*w(iu+1,iv-1)-w(iu,iv-1))/(4.**(iv-1)-1.)
e=(w(iu,iv)-w(iu,iv-1))/w(iu,iv)
if(abs(e)-eps) 3,3,4
3 ans=w(1,iv)
return
5 print 100
100 format(' k overflow')
stop
! call exit
end
*value
subroutine value(e,th,w,z,a,x,f)
implicit real*8 (a-h,o-z)
common /par/ eps,epsd,pf,spence
alph=1./137.03604
emass=.511
pi=acos(-1.d0)
thr=th*pi/180.
sig1=sigqfs(e,th,x,z,a,eps,pf,delnu)
sig1=sig1+sigdel(e,th,x,a,epsd,pf,z)
sig1=sig1+sigx(e,th,x,a)
sig1=sig1+sigr1(e,th,x,a,pf,z)
sig1=sig1+sigr2(e,th,x,a,pf,z)
sig1=sig1+sig2n(e,th,x,z,a,pf)
sig2=sigqfs(e-w+x,th,x,z,a,eps,pf,delnu)
sig2=sig2+sigdel(e-w+x,th,x,a,epsd,pf,z)
sig2=sig2+sigx(e-w+x,th,x,a)
sig2=sig2+sigr1(e-w+x,th,x,a,pf,z)
sig2=sig2+sigr2(e-w+x,th,x,a,pf,z)
sig2=sig2+sig2n(e-w+x,th,x,z,a,pf)
qms1=4.*e*(e-x)*sin(thr/2.)**2
qms2=4.*(e-w+x)*(e-w)*sin(thr/2.)**2
qmsbar=sqrt(qms1*qms2)
f1=(log(qms1/emass**2)-1.)/2./(e-x)**2
f1=f1*sig1
f1=f1*alph*((e-x)**2+(e-w)**2)/(w-x)/pi
f2=sig2*(log(qms2/emass**2)-1.)/2./e**2
f2=f2*alph*(e**2+(e-w+x)**2)/(w-x)/pi
d1=(2.*alph/pi)*(log(qmsbar/emass**2)-1.)
d2=13.*(log(qmsbar/emass**2)-1.)/12.-17./36.
d2=(2.*alph/pi)*(d2-0.5*(pi**2/6.-spence))
ebar=sqrt((e-x)*(e-w))
f=(f1+f2)*(1.+d2)*((w-x)/ebar)**d1
return
end