Compute the average energy lost per collision for a neutron that scatters isotropically off

a target given that:

$E_f=E_i\frac{(1+)+(1-)cos}{2},$ and $,P(E_i{E}_f)=\frac{4{}_s((widehat())*hat({)}^{\text{'}})}{(1-)E_i{}_s}$