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physics_proton.f
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real*8 function sigep(vertex)
! elastic cross section, units are set by sigMott.f (microbarn/sr)
USE structureModule
implicit none
include 'simulate.inc'
real*8 q4sq,qmu4mp,W1p,W2p,Wp,GE,GM,sigMott
type(event):: vertex
q4sq = vertex%Q2
call fofa_best_fit(-q4sq/hbarc**2,GE,GM)
qmu4mp = q4sq/4./Mp2
W1p = GM**2*qmu4mp
W2p = (GE**2+GM**2*qmu4mp)/(1.0+qmu4mp)
Wp = W2p + 2.*W1p*tan(vertex%e%theta/2.)**2
sigep = sigMott(vertex%e%E,vertex%e%theta,vertex%q2) *
> vertex%e%E/vertex%Ein * Wp
if (debug(5)) write(6,*) 'sigMott',GE,GM
return
end
!-------------------------------------------------------------------------
real*8 function deForest(ev)
USE structureModule
implicit none
include 'simulate.inc'
type(event):: ev
real*8 q4sq,ebar,qbsq,GE,GM,f1,kf2,qmu4mp,sigMott,sin_gamma,cos_phi
real*8 pbarp,pbarq,pq,qbarq,q2,f1sq,kf2_over_2m_allsq
real*8 sumFF1,sumFF2,termC,termT,termS,termI,WC,WT,WS,WI,allsum
! Compute deForest sigcc cross-section, according to value of DEFOREST_FLAG:
! Flag = 0 -- use sigcc1
! Flag = 1 -- use sigcc2
! Flag = -1 -- use sigcc1 ONSHELL, replacing Ebar with E = E'-nu
! and qbar with q (4-vector)
! N.B. Beware of deForest's metric when taking all those 4-vector inner
! products in sigcc2 ... it is (-1,1,1,1)!
! Here, I've defined all the inner products with the regular signs,
! and then put them in the structure function
! formulas with reversed signs compared to deForest.
!
! Note that this can be called with either the vertex or recon event records,
! but like a good function, it does not modify anything in those records.
!
! JRA: Note, let me make a comment about the following, because I was badly
! confused about it the first time through. The 6-fold cross section is:
! d6sigma = K * S(E,p) * sigma_eN. This routine returns a quantity 'deForest'
! which is d6sigma/S(E,p) = K*sigma_eN
! = (E'*p')*sigma_mott*[sum of terms like a_i*W_i].
! Each W_i term has E'/Ebar in it. In the following code, the E'/Ebar appears
! to have been removed from the W_i terms, and combined with the K=E'*p' term
! to give an overall p'/Ebar in the final expression.
! More importantly, since the Spectral Function has been divided out, the
! units are MeV^4 * the 6-fold cross section units, and so for sigma_mott
! in microbarn/sr, 'deForest' is in microbarn*MeV^2/sr^2, giving the correct
! cross seciton units once we multiply by S(E,p) which is in MeV^-4
q4sq = -ev%Q2
q2 = ev%q**2
if (deForest_flag.ge.0) then
ebar = sqrt(ev%Pm**2 + Mh2)
qbsq = (ev%p%E-ebar)**2 - q2
else
ebar = ev%p%E - ev%nu
qbsq = q4sq
endif
sin_gamma = 1. - (ev%uq%x*ev%up%x+ev%uq%y*ev%up%y+ev%uq%z*ev%up%z)**2
if (sin_gamma.lt.0) then
write(6,'(1x,''WARNING: deForest came up with sin_gamma = '',f10.3,'' at event '',i10)') sin_gamma, nevent
sin_gamma = 0.0
endif
sin_gamma = sqrt(sin_gamma)
cos_phi = 0.0
if (sin_gamma.ne.0) cos_phi=(ev%uq%y*(ev%uq%y*ev%up%z-ev%uq%z*ev%up%y)
> - ev%uq%x*(ev%uq%z*ev%up%x-ev%uq%x*ev%up%z))
> / sin_gamma / sqrt(1.-ev%uq%z**2)
if (abs(cos_phi).gt.1.) then !set to +/-1, warn if >1.e-10
cos_phi = sign(1.0,cos_phi)
if ( (abs(cos_phi)-1.) .gt. 1.e-10) write(6,*)
> 'WARNING: deForest give cos_phi = ',cos_phi,' at event',nevent
endif
call fofa_best_fit(q4sq/hbarc**2,GE,GM)
qmu4mp = q4sq/4./Mp2
f1 = (GE-GM*qmu4mp)/(1.0-qmu4mp)
kf2 = (GM-GE)/(1.0-qmu4mp)
f1sq = f1**2
kf2_over_2m_allsq = kF2**2/4./Mh2
termC = (q4sq/q2)**2
termT = (tan(ev%e%theta/2.))**2 - q4sq/2./q2
termS = tan(ev%e%theta/2.)**2 - (q4sq/q2)*cos_phi**2
termI = (-q4sq/q2)*sqrt(tan(ev%e%theta/2.)**2-q4sq/q2)*cos_phi
if (deForest_flag.le.0) then
sumFF1 = (f1 + kf2)**2
sumFF2 = f1sq - qbsq*kf2*kf2/4./Mh2
WC = ((ebar+ev%p%E)**2)*sumFF2 - q2*sumFF1
WT = -2*qbsq*sumFF1
WS = 4*(ev%p%P**2)*(sin_gamma**2)*sumFF2
WI = -4*(ebar+ev%p%E)*ev%p%P*sin_gamma*sumFF2
else
pbarp=ebar*ev%p%E-ev%p%p*(ev%up%x*ev%Pmx+ev%up%y*ev%Pmy+ev%up%z*ev%Pmz)
pbarq=ebar*ev%nu-ev%q*(ev%uq%x*ev%Pmx+ev%uq%y*ev%Pmy+ev%uq%z*ev%Pmz)
pq = ev%p%E*ev%nu - ev%p%p * ev%q * (ev%up%x*ev%uq%x +
> ev%up%y*ev%uq%y + ev%up%z*ev%uq%z)
qbarq = (ev%p%E-ebar)*ev%nu - q2
WC = (ebar*ev%p%E+(-pbarp+Mh2)/2.) * f1sq - q2*f1*kf2/2.
> - ( (-pbarq*ev%p%E-pq*ebar)*ev%nu + ebar*ev%p%E*q4sq +
> pbarq*pq - (-pbarp-Mh2)/2.*q2 ) * kf2_over_2m_allsq
WT = - (-pbarp+Mh2)*f1sq - qbarq*f1*kF2
> + (2.*pbarq*pq + (-pbarp-Mh2)*q4sq) * kf2_over_2m_allsq
WS = (ev%p%p*sin_gamma)**2 * (f1sq - q4sq*kf2_over_2m_allsq)
WI = ev%p%p*sin_gamma * ( -(ebar+ev%p%E)*f1sq + ((-pbarq-pq)*
> ev%nu+(ebar+ev%p%E)*q4sq)*kf2_over_2m_allsq )
endif
allsum = termC*WC + termT*WT + termS*WS + termI*WI
if (deForest_flag.le.0) allsum = allsum/4.0
deForest = sigMott(ev%e%E,ev%e%theta,ev%Q2)*ev%p%P*allsum/ebar !microbarn*(MeV/sr)**2
if (debug(5)) write(6,*) 'deForest',GE,GM
return
end
!-------------------------------------------------------------------------
subroutine fofa_best_fit(qsquar,GE,GM)
* csa 9/14/98 -- This calculates the form factors Gep and Gmp using
* Peter Bosted's fit to world data (Phys. Rev. C 51, 409, Eqs. 4
* and 5 or, alternatively, Eqs. 6)
USE structureModule
implicit none
include 'simulate.inc'
real*8 qsquar,GE,GM,mu_p
real*8 Q,Q2,Q3,Q4,Q5,denom
mu_p = 2.793
Q2 = -qsquar*(hbarc**2.)*1.e-6
Q = sqrt(max(Q2,0.e0))
Q3 = Q**3.
Q4 = Q**4.
Q5 = Q**5.
* Use Eqs 4, 5:
denom = 1. + 0.62*Q + 0.68*Q2 + 2.8*Q3 + 0.83*Q4
GE = 1./denom
denom = 1. + 0.35*Q + 2.44*Q2 + 0.5*Q3 + 1.04*Q4 + 0.34*Q5
GM = mu_p/denom
* OR Eqs 6:
* denom = 1. + 0.14*Q + 3.01*Q2 + 0.02*Q3 + 1.20*Q4 + 0.32*Q5
* GE = 1./denom
* GM = mu_p/denom
return
end
!-------------------------------------------------------------------------
real*8 function sigMott(e0,theta,Q2)
implicit none
include 'constants.inc'
real*8 e0,theta,Q2
real*8 sig
! The Mott cross section (for a point nucleus) in microbarns/sr.
sig = (2.*alpha*hbarc*e0*cos(theta/2.)/Q2 )**2
sigMott = sig*1.d4 !fm**2 --> microbarns
return
end