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CS[q0_,ϕq0_,Ee0_,θe0_,ϕe0_,ELab0_]:=Module{q=q0,ϕq=ϕq0,Ee=Ee0,θe=θe0,ϕe=ϕe0,ELab=ELab0},ELab=N[24*10^6];ZP=8;ZT=3.0;MP=16*1836.0;MT=7*1836.0;Ee=1.5;ϵI=5.4;ϵloss=(ϵI+Ee)27.2;v=Sqrt[ELab/(13.6MP)];μi=MP*(MT+3)(MP+MT+3);Ki=μi*v;ke=Sqrt[Ee/13.6];Kf=Sqrt[Ki^2+2μiϵloss];αT1=-(2.8683/ke);αPT=μi*(2.8683ZP)Kf;qz=ϵlossv;qx=Sqrt[q^2-qz^2];ZCS=2(2Pi)^4(1+(MP/MT))^2((MT+2)/(MT+3))((MP(MT+3))/(MP+MT+3))^2(Kfke)Ki;(*Intermediatecalculations*)β=1.8683;c=1+IαPT;cprime=1+IαT1;gamac=Gamma[c];gamacprime=Gamma[cprime];NCOFF=(ZP/(2Pi)^4.5)*gamac*gamacprime*Exp[-1/2Pi(αPT+αT1)]*Sqrt[(1.8683)^3/(32Pi)];Qdke=keqxSin[θe]Cos[ϕe-ϕq]+keqzCos[θe];Qmke2=(q^2+ke^2-2Qdke);KfdQ=Kiqz-q^2;KfDke=KikeCos[θe]-Qdke;(*Ai,Bi,Ci,Diexpressions*)Ai=(q^2+λ^2)(ke^2+ζ1^2)x^2+2(ζ1(q^2+λ^2)+λ(ke^2+ζ1^2))x+Qmke2+(λ+ζ1)^2;Bi=-2(IλKf-KfdQ)(ke^2+ζ1^2)x^2-2(2ζ1(IλKf-KfdQ)+I(ke^2+ζ1^2)Kf)x-2(Kfdke-KfdQ+I(λ+ζ1)Kf);Ci=-2(ke^2+Iζ1ke)(q^2+λ^2)x^2-2(2λ(ke^2+Iζ1ke)+I(q^2+λ^2)ke)x-2(ke^2+I(λ+ζ1)ke-Qdke);Di=4(IλKf-KfdQ)(ke^2+Iζ1ke)x^2+4(I(ke+Iζ1)keKf+I(IλKf-KfdQ)ke)x+2(KfDke-Kfke);(*TermsforFDCScalculation*)fβR=

∂

ζ1

αT1

2

(ke-ζ1)

αT1+1

(

2

ke

+

2

ζ1

)

/.{ζ1β/2,λ0};fβ2R=

∂

ζ1

∂

ζ1

αT1

2

(ke-ζ1)

αT1+1

(

2

ke

+

2

ζ1

)

/.{ζ1β/2,λ0};fβs1=

∂

λ

∂

ζ1

1

Ai

-αPT

Ai

Ai+Bi

-αT1

Ai

Ai+Ci

Hypergeometric2F1-αPT,-αT1,1,

BiCi-AiDi

(Ai+Bi)(Ci+Di)

/.{λ0,ζ1β/2};fβ2s1=

∂

λ

∂

ζ1

∂

ζ1

1

Ai

-αPT

Ai

Ai+Bi

-αT1

Ai

Ai+Ci

Hypergeometric2F1-αPT,-αT1,1,

BiCi-AiDi

(Ai+Bi)(Ci+Di)

/.{λ0,ζ1β/2};Tyek=-

64Pi^2*ZT

2

q

αPT

2Kiqz-

2

q

2

q

fβR;Tdo=

64Pi^2*ZT

2

q

αPT

2Kiqz-

2

q

2

q

fβ2R;Tse=NIntegrate[fβs1,{x,0,∞}]/.{ζ1->β/2,λ0};Tchar=NIntegrate[fβ2s1,{x,0,∞}]/.{ζ1->β/2,λ0};;TCDW=Tyek+Tdo+64Pi^2Tse+1.8683*64Pi^2Tchar;T2CDW=Abs[(NCOFF*TCDW)^2];FDCS=ZCS*T2CDWDo[Print[CS[1.0,0.0,1.5,θe,0.0,24000000.0]],{θe,0,2Pi,Pi/180}]

NIntegrate

:The integrand -

(2.+3.7366x)2Hypergeometric2F10.-2.96056,2,

-((-0.0434787+Times[2]+Times[2])(1))1((1)+1+1)11

((-0.242328-0.620473)-1-(19+18)1)(1)



2

(1.96119+1.8683x+0.98293

2

x

)

+

25

3

(1)

-

1

+21+

1

-

1

+

(339.685+72.5682)4Hypergeometric2F1[2.-19,3]

1.96119+1.8683x+0.98293

2

x

has evaluated to non-numerical values for all sampling points in the region with boundaries {{∞,0.}}.

NIntegrate

:The integrand -

(2.+3.7366x)2Hypergeometric2F10.-2.96056,2,

-((-0.0434787+Times[2]+Times[2])(1))1((1)+1+1)11

((-0.242328-0.620473)-1-(19+18)1)(1)



2

(1.96119+1.8683x+0.98293

2

x

)

+

25

3

(1)

-

1

+21+

1

-

1

+

(339.685+72.5682)4Hypergeometric2F1[2.-19,3]

1.96119+1.8683x+0.98293

2

x

has evaluated to non-numerical values for all sampling points in the region with boundaries {{∞,0.}}.

NIntegrate

:The integrand -

(2.+3.7366x)2Hypergeometric2F10.-2.96056,2,

-((-0.0434787+Times[2]+Times[2])(1))1((1)+1+1)11

((-0.242328-0.620473)-1-(19+18)1)(1)



2

(1.96119+1.8683x+0.98293

2

x

)

+

25

3

(1)

-

1

+21+

1

-

1

+

(339.685+72.5682)4Hypergeometric2F1[2.-19,3]

1.96119+1.8683x+0.98293

2

x

has evaluated to non-numerical values for all sampling points in the region with boundaries {{∞,0.}}.

General

:Further output of NIntegrate::inumr will be suppressed during this calculation.

Set

:Tag ReplaceAll in NIntegrate[fβ2s1,{x,0,∞}]/.{ζ10.93415,λ0};;TCDW is Protected.

$RecursionLimit

:Recursion depth of 1024 exceeded.

TerminatedEvaluation[RecursionLimit]

$RecursionLimit

:Recursion depth of 1024 exceeded.

TerminatedEvaluation[RecursionLimit]

$RecursionLimit

:Recursion depth of 1024 exceeded.

General

:Further output of $RecursionLimit::reclim will be suppressed during this calculation.

TerminatedEvaluation[RecursionLimit]