Composite-particle decay widths by the generator coordinate method

TL;DR

This paper explores the application of the Generator Coordinate Method (GCM) to compute decay widths of composite particles, assessing its accuracy in approximating continuum states and comparing two computational approaches.

Contribution

It demonstrates the feasibility of using GCM for decay width calculations and compares two methods for determining these widths within the framework.

Findings

Both methods yield consistent decay widths within uncertainties.

GCM can approximate continuum wave functions for decay processes.

The study provides a numerical validation of GCM-based decay width calculations.

Abstract

We study the feasibility of applying the Generator Coordinate Method (GCM) of self-consistent mean-field theory to calculate decay widths of composite particles to composite-particle final states. The main question is how well the GCM can approximate continuum wave functions in the decay channels. The analysis is straightforward under the assumption that the GCM wave functions are separable into internal and Gaussian center-of-mass wave functions. Two methods are examined for calculating decays widths. In one method, the density of final states is computed entirely in the GCM framework. In the other method, it is determined by matching the GCM wave function to an asymptotic scattering wave function. Both methods are applied to a numerical example and are found to agree within their determined uncertainties.