Scattering phases for particles with nonzero orbital momenta and resonance regimes in the Pais approximation

The functional Pais equation for scattering phases with nonzero orbital momenta is solved in the case of low-energy particles. For short-range screened potentials, in particular, Yukawa or Thomas–Fermi potentials, the Pais equation is shown to reduce to transcendental equations. For the potentials varying $\sim r^{- n}$, $n > 0$, simple algebraic equations are obtained for determining the phases $\delta_l$, $l\ne 0$. Possible applications of the Pais approximation to the problem of finding resonance regimes in the scattering of low-energy particles with nonzero orbital momenta are discussed.