Nuclear giant quadruple resonance within transport approach and its constraint on nucleon effective mass

TL;DR

This study uses a transport approach based on the BUU equation to analyze the nuclear giant quadruple resonance, providing constraints on the nucleon effective mass and highlighting the role of collisional damping.

Contribution

It introduces a BUU transport model with stochastic collision term to accurately reproduce ISGQR width and extract the nucleon effective mass from experimental data.

Findings

Collisional damping dominates ISGQR width in heavy nuclei.

The nucleon effective mass at saturation density is approximately 0.82-0.83 times the nucleon mass.

Negligible impact of 2p-2h correlations on constraining the effective mass.

Abstract

We study the nuclear iso-scalar giant quadruple resonance~(ISGQR) based on the Boltzmann-Uehling-Uhlenbeck~(BUU) transport equation. The mean-field part of the BUU equation is described by the Skyrme nucleon-nucleon effective interaction, and its collision term, which embodies the two-particle-two-hole ($2$p-$2$h) correlation, is implemented through the stochastic approach. We find that the width of ISGQR for heavy nuclei is exhausted dominated by collisional damping, which is incorporated into the BUU equation through its collision term, and it can be well reproduced through employing a proper in-medium nucleon-nucleon cross section. Based on further Vlasov and BUU calculations with a number of representative Skyrme interactions, the iso-scalar nucleon effective mass at saturation density is extracted respectively as $m^{*}_{s,0}/m$ $=$ $0.83\pm0.04$ and $m^{*}_{s,0}/m$ $=$ $0.82\pm0.03$ from the measured excitation energy $E_x$ of the ISGQR of $\isotope[208]{Pb}$. The small discrepancy between the two constraints indicates the negligible role of $2$p-$2$h correlation in constraining $m_{s,0}^*$ with the ISGQR excitation energy.