Operator overlaps in harmonic oscillator bases with different oscillator lengths

TL;DR

This paper develops a formalism for calculating operator overlaps when using harmonic oscillator bases with different oscillator lengths, facilitating advanced generator coordinate method calculations in nuclear physics.

Contribution

It introduces a general formalism for operator overlaps in HO bases with varying lengths, enabling more flexible and accurate GCM calculations.

Findings

Derived explicit expressions for matrix elements in HO bases with different lengths

Applied the formalism to a fission example demonstrating its practical utility

Enhanced the computational framework for nuclear structure calculations

Abstract

We apply a formalism recently developed to carry out Generator Coordinate Method calculations using a set of Hartree- Fock- Bogoliubov wave functions, where each of the members of the set can be expanded in an arbitrary basis. In this paper it is assumed that the HFB wave functions are expanded in Harmonic Oscillator (HO) bases with different oscillator lengths. General expressions to compute the required matrix elements of arbitrary operators are given. The application of the present formalism to the case of fission is illustrated with an example.