Revised Huang-Yang multipolar pseudopotential

TL;DR

This paper identifies and corrects an algebraic mistake in the original derivation of the Huang-Yang multipolar pseudopotential, resolving previous inconsistencies and providing a revised, more accurate version for low-energy scattering calculations.

Contribution

The paper provides a corrected derivation of the Huang-Yang multipolar pseudopotential, addressing prior conceptual issues and improving its validity for low-energy scattering.

Findings

Identified an algebraic mistake in the original derivation.

Provided a revised, consistent form of the pseudopotential.

Resolved previous inconsistencies in low-energy scattering results.

Abstract

A number of authors have recently pointed out inconsistencies of results obtained with the Huang-Yang multipolar pseudo-potential for low-energy scattering [K. Huang and K. C. Yang, Phys. Rev. A, v 105, 767 (1957); later revised in K. Huang, ``Statistical Mechanics'', (Wiley, New York, 1963)]. The conceptual validity of their original derivation has been questioned. Here I show that these inconsistencies are rather due to an {\em algebraic} mistake made by Huang and Yang. With the corrected error, I present the revised version of the multipolar pseudo-potential.