Source Function Integrals

S[x_,y_,z_,px_,py_,pz_]:=N Ep /(2 Pi Rs Po)^3  Exp[-(1/(2(1-s^2)))(((x^2+y^2+z^2)/Ro^2)-2s(px x +py y+ pz z)/(Ro Po) + ((px^2+py^2+pz^2)/Po^2))]
Rs = Ro Sqrt[1-s^2];

S(x,K) integral

P1 =Integrate[S[x,y,z,Kx,Ky,Kz],{x,-Infinity,Infinity},{y,-Infinity,Infinity},{z,-Infinity,Infinity},Assumptions->s>0 && s<1&&Ro>0&&Po>0]

S(x,K-q/2) integral and S(x,K+q/2)

P1qm =Integrate[S[x,y,z,Kx-qx/2,Ky-qy/2,Kz-qz/2],{x,-Infinity,Infinity},{y,-Infinity,Infinity},{z,-Infinity,Infinity},Assumptions->s>0 && s<1&&Ro>0&&Po>0]

P1qp =Integrate[S[x,y,z,Kx+qx/2,Ky+qy/2,Kz+qz/2],{x,-Infinity,Infinity},{y,-Infinity,Infinity},{z,-Infinity,Infinity},Assumptions->s>0 && s<1&&Ro>0&&Po>0]

S(x,K)e^(iqx)= integral

P12 =Integrate[S[x,y,z,Kx,Ky,Kz]Exp[I(qx x + qy y +qz z)],{x,-Infinity,Infinity},{y,-Infinity,Infinity},{z,-Infinity,Infinity},Assumptions->s>0 && s<1&&Ro>0&&Po>0 && {Kx,Ky,Kz,qx,qy,qz,s,Ro,Po,Ep,N} ∈ Reals ]

Correlation Function

Full Correlation

Cf = Simplify [1 + ComplexExpand[Abs[P12]]^2 /(P1qm P1qp),Assumptions-> s>0&& s<1]

Simplified Correlation

Cs = Simplify[1 + ComplexExpand[Abs[P12]]^2 /(P1 P1),Assumptions-> s>0&& s<1]

Rs=10 /197 (* To have it in MeV^-1 *);
Plot[1+Exp[-q^2 Rs^2],{q,0,50} ,AxesLabel->{"q (MeV)","C(q)"}]