A beyond-mean-field example with zero-range effective interactions in infinite nuclear matter

TL;DR

This paper investigates the ultraviolet divergence issues caused by zero-range effective interactions in beyond-mean-field nuclear matter models, analyzing divergences in Skyrme interactions and proposing a path for finite nuclei applications.

Contribution

It provides a detailed analysis of divergences in beyond-mean-field models with zero-range interactions and extends the framework to more complex Skyrme interactions.

Findings

Second-order energy correction diverges linearly with momentum cutoff in simplified models.

Velocity-dependent terms cause strong divergences in full Skyrme interactions.

A global fit can be performed for different nuclear matter compositions.

Abstract

Zero-range effective interactions are commonly used in nuclear physics to describe a many-body system in the mean-field framework. If they are employed in beyond- mean-field models, an artificial ultraviolet divergence is generated by the zero-range of the interaction. We analyze this problem in symmetric nuclear matter with the t0-t3 Skyrme model. In this case, the second-order energy correction diverges linearly with the momentum cutoff. After that, we extend the work to the case of nuclear matter with the full Skyrme interaction. A strong divergence related to the velocity-dependent terms of the interaction is obtained. Moreover, a global fit can be simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratios. These results pave the way for applications to finite nuclei in the framework of beyond mean-field theories.