Nuclear level densities away from line of $\beta$-stability

TL;DR

This study investigates how nuclear level densities vary with proton number around the beta-stable isotope, revealing that microscopic effects significantly influence the expected parabolic trend and its sensitivity to shell effects.

Contribution

It provides a detailed analysis of nuclear level densities across a wide mass range using different microscopic models, challenging previous predictions of a strong parabolic trend.

Findings

NLDs do not show a strong inverted parabolic trend with a peak at $Z_0$.

The inverted parabolic trend becomes visible only when collective and pairing effects are ignored.

Shell effects significantly influence the $Z-Z_0$ dependence of NLDs.

Abstract

The variation of total nuclear level densities (NLDs) and level density parameters with proton number $(Z)$ are studied around the $\beta$-stable isotope, $Z_{0}$, for a given mass number. We perform our analysis for a mass range $A=40$ to 180 using the NLDs from popularly used databases obtained with the single-particle energies from two different microsopic mass-models. These NLDs which include microscopic structural effects such as collective enhancement, pairing and shell corrections, do not exhibit inverted parabolic trend with a strong peak at $Z_{0}$ as predicted earlier. We also compute the NLDs using the single-particle energies from macroscopic-microscopic mass-model. Once the collective and pairing effects are ignored, the inverted parabolic trends of NLDs and the corresponding level density parameters become somewhat visible. Nevertheless, the factor that governs the $(Z-Z_{0})$ dependence of the level density parameter, leading to the inverted parabolic trend, is found to be smaller by an order of magnitude. We further find that the $(Z-Z_{0})$ dependence of NLDs is quite sensitive to the shell effects.