Unitarizing non-relativistic Coulomb scattering

TL;DR

This paper compares two unitarization methods for nonrelativistic Coulomb scattering, showing that one accurately reproduces the exact solution while the other does not, based on perturbative calculations up to one-loop order.

Contribution

It provides a detailed comparison of two unitarization techniques applied to Coulomb scattering, highlighting the accuracy of one method over the other in reproducing known solutions.

Findings

One method accurately reproduces the exact Coulomb solution.

The other method fails to match the known solution and predicts zero binding energy.

Accuracy improves with higher-order perturbative input.

Abstract

We compare the exactly solvable nonrelativistic Coulomb scattering with two recent unitarization methods for infinite-range forces. These methods require to calculate perturbatively the corresponding partial-wave amplitudes, which are then unitarized. We calculate the Coulomb partial-wave amplitudes up to the one-loop order. On the one hand, the unitarization method developed by Refs. [1, 2] reproduces properly the exact solution, with an accuracy improving as the order in the perturbative calculation of the input perturbative partial-wave amplitudes increases. This is also shown to be the case for the pole position of the ground state. On the other hand, the method developed by the more recent Ref. [3] gives rise to partial-wave amplitudes that do not reproduce the known solvable solution, and gives rise to a pole position with zero binding energy.