A critical assessment of the current implementations of the Generator Coordinate Method

TL;DR

This paper critically evaluates current implementations of the Generator Coordinate Method (GCM) in nuclear physics, introduces an improved version called eGCM that overcomes previous flaws, and discusses its potential for describing nuclear reactions and fission.

Contribution

The paper proposes the enhanced GCM (eGCM), a new formulation that addresses flaws in previous GCM implementations, enabling better microscopic descriptions of nuclear reactions and fission.

Findings

eGCM overcomes limitations of earlier GCM versions.

eGCM's wave functions have a more complex structure.

eGCM is equivalent to a configuration interaction approach in the continuum.

Abstract

The generator coordinate method (GCM) was introduced in nuclear physics by Wheeler and independently by Peierls and their collaborators in 1950's and it is still one of the mostly used approximations for treating nuclear large amplitude collective motion (LACM). GCM was inspired by similar methods introduced in molecular and condensed matter physics in the late 1920's, after the Schr\"odinger equation became the tool of choice to describe quantum phenomena. The interest in the 1983 extension of GCM suggested by Reinhard, Cusson and Goeke, which includes the internal excitations (absent in the initial GCM formulation), was revived in recent years. Unfortunately this newer version of time-dependent GCM (TDGCM) framework has flaws, which prevents it from describing correctly many anticipated features, in particular interference and entanglement, which can play an important role in fission and many-nucleon transfer reactions. I present here an alternative formulation, the enhanced GCM (eGCM), which is free of difficulties encountered in previous GCM implementations and which is relevant for fission and many-nucleon transfer in heavy-ion reactions, and which can be used in either static or time-dependent eGCM formulations. In the eGCM framework the corresponding many-body waves functions have a much more complex structure and this framework is equivalent to a configuration interaction (CI) approach in the continuum for nuclear reactions. eGCM is aimed to be used in the microscopic description of heavy-ion reactions and fission in particular.