delta0=32.5*Pi/180.; delta1=8.6*Pi/180.; delta2=0.4*Pi/180.;
k=.491 (* k is in fm^-1 *)
f[t_]=(Exp[I delta0] Sin[delta0] LegendreP[0,Cos[t]]+3 Exp[I delta1] Sin[delta1] LegendreP[1,Cos[t]]+
5 Exp[I delta2] Sin[delta2] LegendreP[2,Cos[t]])/k
sigma=4 Pi/k^2 (Sin[delta0]^2+3 Sin[delta1]^2+5 Sin[delta2]^2)
Out[6]= 18.5574
N[Abs[f[Pi/2]^2]]
Out[7]= 1.13285
(* these are both in fm^2 *)

(* 1 barn= 100 fm^2 *)
Plot[Abs[f[t]^2]/100,{t,0,Pi}]

reversing all signs: if Exp[I t] Sin[t] = a + I b and you reverse the sign of t the result is
-a + I b
This change will not affect the magnitude, so sigma and d sigma/d Omega are unchanged

dOmega=Area/r^2=Pi .01^2/1^2
delta0=32.5*Pi/180.; delta1=-8.6*Pi/180.; delta2=0.4*Pi/180.;
