Effective method for calculating the phase shifts for the scattering of slow particles with nonzero orbital angular momentum

Pais's functional equation for the phase shifts for scattering with nonzero angular momentum is solved for particles with low energies. It is shown that for shortrange potentials with screening (in particular, of Yukawa or Thomas–Fermi type), Pais's equation reduces to transcendent equations. For potentials $\sim 1/r^n$, $n>0$, simple algebraic equations are obtained for finding the phase shifts $\delta_l$, $l\not=0$. The possibility of using Pals's approximation to find resonance situations in the case of the scattering of slow particles with nonzero angular momentum is discussed.