f[theta_]:=1/(2 k I) (Sum[(Exp[2 I d2[[l+1]] ]-1) (2l+1) LegendreP[l, Cos[theta]],{l,0,2}])
d2={32.5,8.6,.4} Pi/180

sqrt(5e6*e*2*mp)/hbar

k=4.9088  10^14  

Plot[Abs[f[theta]]^2*10^28,{theta,0,Pi}] 
d2=-{32.5,8.6,.4} Pi/180
Plot[Abs[f[theta]]^2*10^28,{theta,0,Pi}] 
d2={32.5,-8.6,.4} Pi/180
Plot[Abs[f[theta]]^2*10^28,{theta,0,Pi}] 

d2={32.5,8.6,.4} Pi/180
sigma=Sum[(2 l +1) Sin[d2[[l+1]] ]^2,{l,0,2}] 4 Pi/k^2

                   -29
Out[10]= 1.85665 10

1.85665e-29*1e21*1e4*2e10
f( 0 )= 3.7133 × 106


N[Abs[f[Pi/2]]^2 ]

                  -30
Out[12]= 1.1334 10

1.1334e-30*1e21*1e4*2e10*pi*(.01)^2

f( 0 )= 71.214 

GraphicsGrid[{{%4},{%6},{%8}}]
Export["partial_waves_PLOTS.pdf",%]


----
np scatter
f[k_]:=ArcCot[-1/(k a)+ .5 r0 k]                                         

singlet:
 a = -23.3  
 r0=2.26 
 ParametricPlot[{20.75*k^2,f[k]},{k,.005,.5},PlotRange->{{0,5},{0,1.5}},AspectRatio->1] 

 triplet:
 a=5.38 
 r0=1.7 
 ParametricPlot[{20.75*k^2,f[k]+Pi},{k,.005,.5},PlotRange->{{0,5},{0,3.2}},AspectRatio->1]   
 
 