Jastrow functions in double-beta decay

TL;DR

This paper critically examines the use of Jastrow functions in double-beta decay calculations, highlighting potential errors in common approximations and comparing different correlation methods.

Contribution

It demonstrates that the two-body-cluster approximation with Jastrow functions can lead to significant errors, but including many-body clusters improves accuracy, and compares correlation methods.

Findings

Two-body-cluster approximation with Jastrow functions causes errors.

Including many-body clusters aligns Jastrow results with other methods.

Differences between Unitary Correlator and Brueckner methods are less significant.

Abstract

We use simple analytic considerations and a Monte Carlo calculation of nucleons in a box to argue that the use of Jastrow functions as short-range correlators in the commonly employed two-body-cluster approximation causes significant errors in the matrix elements for double-beta decay. The Jastrow approach appears to agree with others, however, if many-body clusters are included. A careful treatment of the charge-changing analog of the nuclear pair density shows, in addition, that differences between Unitary Correlator Operator Method and Brueckner methods for treating short-range correlations in double-beta are less significant than suggested by previous work.