The cranking formula and the spurious behaviour of the mass parameters

TL;DR

This paper examines issues with the cranking formula for mass parameters, identifies the cause of ambiguities, proposes a simplification by removing derivatives, and analyzes the impact of shell effects through numerical tests.

Contribution

It introduces an ansatz to eliminate problematic derivatives in the cranking formula, simplifying the calculation of mass parameters and clarifying shell effects.

Findings

Removing derivatives resolves ambiguities in the formula.

Simplified formula is easier to interpret and apply.

Shell effects significantly influence mass parameters.

Abstract

We discuss some aspects of the approach of the mass parameters by means of the simple cranking model. In particular, it is well known that the numerical application of this formula is often subject to ambiguities or contradictions. It is found that these problems are induced by the presence of two derivatives in the formula. To overcome these problems, we state a useful ansatz and we develop a number of simple arguments which tend to justify the removal of these terms. As soon as this is done, the formula becomes simpler and easier to interpret. In this respect, it is shown how the shell effects affect the mass parameters. A number of numerical tests help us in our conclusions.