Figure 1: Stength of the <((((Subscript[R, 0])/R))^2)> effect

data=Table[{δ,A=1/ϵ;NIntegrate[-((8 (A^2) (1+δ Cos[θ]) Sin[θ] Sin[θ+δ Sin[θ]])/(π (4 A-δ) (-1+cd (δ^2)) (A+Cos[θ+δ Sin[θ]])))/.cd->0.1274,{θ,0,π}]},{δ,-0.8,0.8,0.05},{ϵ,{0.2,0.3,0.4,0.5,0.6}}];

endpoints={#1+0.07,#2}&@@@data[[-1]];

ListPlot[data\[Transpose],Joined->True,Epilog->{Text["ϵ",{0.87,1.50}],(Text[#1,#2]&@@@({{0.2,0.3,0.4,0.5,0.6},endpoints}\[Transpose]))},PlotRange->{{-0.8,1.0},{0.75,1.55}},Frame->True,GridLines->Automatic,FrameLabel->{"δ","⟨((Subscript[R, 0])/R)^2⟩_v = (Subscript[β, T]) / ⟨(Subscript[β, T])⟩"},ImageSize->Medium,PlotStyle->{{Thickness[0.0025],Darker[Gray]},{Thickness[0.0025], Gray},{Thickness[0.0025], Gray}, {Thickness[0.0025], Gray}, {Thickness[0.0025], Black}}]

exportdata=Table[A=1/ϵ;NIntegrate[-((8 (A^2) (1+δ Cos[θ]) Sin[θ] Sin[θ+δ Sin[θ]])/(π (4 A-δ) (-1+cd (δ^2)) (A+Cos[θ+δ Sin[θ]])))/.cd->0.1274,{θ,0,π}],{δ,-0.8,0.8,0.05},{ϵ,{0.2,0.3,0.4,0.5,0.6}}];
exportdatax=Table[δ,{δ,-0.8,0.8,0.05}];
exportdata=Prepend[exportdata\[Transpose],exportdatax]\[Transpose];
PrependTo[exportdata,{"delta", "epsilon = 0.2", "epsilon = 0.3", "epsilon = 0.4", "epsilon = 0.5", "epsilon = 0.6"}];

Export["Figure1.csv",SetPrecision[exportdata,5], "CSV"]