Translation invariance and antisymmetry in the theory of the nucleon optical model

TL;DR

This paper critiques the traditional definition of the optical model wavefunction in nucleon-nucleus scattering, proposing a new, more consistent definition that respects antisymmetry and translational invariance, and suggests modifications to the Green's function formalism.

Contribution

It introduces a revised definition of the optical model wavefunction aligned with antisymmetry and translational invariance, and proposes modifications to the Green's function approach.

Findings

New definition of optical model wavefunction

Enhanced consistency with antisymmetry and invariance principles

Modified Green's function formalism

Abstract

The first step in any formalism that aims to connect a many-nucleon theory of nucleon-nucleus scattering and the concept of an optical model potential in the sense pioneered by Feshbach is to explain what is meant by the optical model wavefunction. By definition this is a function of a single space coordinate plus a set of single nucleon internal variables. This article gives a critique of the definitio as it is frequently expressed in 2nd Quantisation language and suggest a new definition which is more consistent with the requirements of antisymmetry and translational invariance. A modification of the time-dependent Green's function formalism is suggested.