let be a potential in 3d invariant under rotations so $ V(r) $
in the WKB approximation the phase shifts are given by
$$ \delta _{l} (k)= \int_{a}^{\infty}dr \sqrt{k^{2}-2mV(r)-l(l+1)r^{-2}}-\int_{b}^{\infty}dr \sqrt{k^{2}-l(l+1)r^{-2}}$$
here 'a' and 'b' are the zeros of the integrands
my question is from this formula and for fixed l could we obtain the value of the potential $ V(r) $ if we know for every l (fixed) the values of the shifts ?? $ \delta_{l} (k) $
