A note on bounds to central potential scattering parameters

Abstract

We derive a bound to the absolute value of the difference between the exact and approximate values of central potential scattering phase shifts. This bound, which is first order in the difference between the exact and approximate radial wave functions, is applicable to a wide class of potentials and/or partial waves, namely those for which dU/dr < 2l(l + 1)/r3 It is illustrated by using it to obtain simple, analytic bounds to the scattering length and total cross section for a screened Coulomb potential.