(* Input *)
(*kin = 20.;*)
m= 939.;
r0 = 3;
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]}};

j1[r_]:=((Sin[r])/r)-Cos[r];

y1[r_]:=Sin[r]+((Cos[r])/r);

Plot[{j1[r],Sin[r-(Pi/2)]},{r,0,50},PlotStyle->sps]

Plot[{y1[r],Cos[r-(Pi/2)]},{r,0,50},PlotStyle->sps]

myJout[r_,e_,U_]:=j1[(Sqrt[2 m (e-U)]) (r/197.327)];

myJin[r_,e_]:=j1[(Sqrt[2 m e]) (r/197.327)];

myYout[r_,e_,U_]:=y1[(Sqrt[2 m (e-U)]) (r/197.327)];

myDJout[r_,e_,U_]:=D[myJout[r,e,U],r];

myDJin[r_,e_]:=D[myJin[r,e],r];

myDYout[r_,e_,U_]:=D[myYout[r,e,U],r];

δ[e_,U_]:=ArcTan[(((Sqrt[2 m (e-U)])myJin[r,e]myDJout[r,e,U] - (Sqrt[2 m e])myDJin[r,e]myJin[r,e] )/((Sqrt[2 m e])myDJin[r,e]myYout[r,e,U] - (Sqrt[2 m (e-U)])myJin[r,e]myDYout[r,e,U]))]/.r->3

TotalSec[e_,U_]:=((3 π)/( m e))  (((Sin[δ[e,U]]))^2);

Plot[{TotalSec[ee,-15.],TotalSec[ee,-16],TotalSec[ee,-17],TotalSec[ee,-18]},{ee,0,10},PlotStyle->sps]