Deuteron-Deuteron Interaction and Correlation Function

TL;DR

This paper develops a new deuteron-deuteron interaction model using phase shift fitting, and demonstrates how correlation functions can validate these interactions and reveal details about nuclear states and source sizes.

Contribution

It introduces a new set of $d$-$d$ interaction potentials fitted to phase shifts and shows their consistency with experimental correlation functions, emphasizing the importance of P-wave contributions.

Findings

Phase shifts and correlation functions are consistent.

Both bound states and repulsive interactions affect correlation functions.

P-wave contributions are significant in source size determination.

Abstract

The interaction between deuterons ($d$-$d$) is pivotal for understanding the characteristics of certain light nuclei from the perspective of the deuteron cluster and achieving a precise reproduction of $d$-$d$ fusion cross sections. In this work, we construct a new set of elastic $d$-$d$ interactions by fitting the phase shifts using potentials parameterized in a Woods-Saxon shape. Then, the correlation functions are calculated with the obtained potential and compared with the recent measurements by the STAR collaboration. We find that the $d$-$d$ phase shifts and the correlation functions are internally consistent, confirming that correlation functions can provide cross-check for the $d$-$d$ interaction. In addition, both the $^1S_0$ bound state and the repulsive $^5S_2$ interaction contribute to the observed suppression in the measured correlation function. Moreover, we demonstrate that the $P$-wave contribution of the correlation functions cannot be neglected, especially in determining the source size.