sps={{Dashing[None],RGBColor[0,0,0]}, {Dashing[Large],RGBColor[1,0,0]},{Dashing[Medium],RGBColor[0,0,1]},{Dashing[Small],RGBColor[0,1,0]},{Dashing[Tiny],RGBColor[0,1,1]}}

INPUTS

{mass = 939,
radius = 3.}

momenta[energy_]:= ((Sqrt[ energy*energy + 2*mass*energy])/197.327)

phase[angMomenta_,energy_] := ArcTan[((SphericalBesselJ[angMomenta,momenta[energy]*radius])/(SphericalBesselY[angMomenta,momenta[energy]*radius]))]

Plot[{phase[0,k],phase[1,k],phase[2,k],phase[3,k],phase[4,k]},{k,0,0.5},PlotStyle->sps]

Plot[{phase[0,k],phase[1,k],phase[2,k],phase[3,k],phase[4,k]},{k,0,25},PlotStyle->sps]

LogPlot[{-((phase[0,k])/(k^(1/2))),-((phase[1,k])/(k^(3/2))),-((phase[2,k])/(k^(5/2))),-((phase[3,k])/(k^(7/2)))},{k,0,3},PlotStyle->sps]

sMatrix[angMomenta_,energy_] := Exp[2*I*phase[angMomenta,energy]]

crossSection[energy_,lmax_,thetaCos_]:=0.01* (Pi/((momenta[energy])^2))(((Abs[Sum[((2 l+1)/(Sqrt[2]))*(sMatrix[l,energy]-1)*LegendreP[l,thetaCos],{l,0,lmax}]]))^2)

ee=0.1;

Plot[{crossSection[ee,0,Cos[x]]},{x,0,Pi},PlotRange->{0,1},PlotStyle->sps]

ee=1;Plot[{crossSection[ee,2,Cos[x]],crossSection[ee,3,Cos[x]],crossSection[ee,4,Cos[x]]},{x,0,Pi},PlotRange->{0,1},PlotStyle->sps]

ee=10;LogPlot[{crossSection[ee,2,Cos[x]],crossSection[ee,3,Cos[x]],crossSection[ee,4,Cos[x]],crossSection[ee,5,Cos[x]]},{x,0,Pi},PlotRange->{0,3},PlotStyle->sps]

ee=100;LogPlot[{crossSection[ee,10,Cos[x]],crossSection[ee,15,Cos[x]],crossSection[ee,20,Cos[x]],crossSection[ee,25,Cos[x]]},{x,0,Pi},PlotRange->All,PlotStyle->sps]

ee=1000;LogPlot[{crossSection[ee,50,Cos[x]],crossSection[ee,60,Cos[x]],crossSection[ee,70,Cos[x]],crossSection[ee,80,Cos[x]]},{x,0,Pi},PlotRange->All,PlotStyle->sps]

csPartial[energy_,lPart_,thetaCos_]:=0.01* (Pi/((momenta[energy])^2))(((Abs[((2 *lPart+1)/(Sqrt[2]))*(sMatrix[lPart,energy]-1)*LegendreP[lPart,thetaCos]]))^2)

ee=5;LogPlot[{csPartial[ee,0,Cos[x]]},{x,0,Pi},PlotRange->All,PlotStyle->sps]

totalCS[energy_,lmax_]:=0.01*(Pi/((momenta[energy])^2))Sum[(2l+1)((Sin[phase[l,energy]])^2),{l,0,lmax}]

Plot[totalCS[e,5],{e,0,50}]