Particle-hole symmetry parameters for nuclei

TL;DR

This paper introduces two new parameters based on particle-hole symmetry, which effectively model nuclear properties and binding energies, revealing shell and sub-shell closure features across a wide range of nuclei.

Contribution

The paper proposes novel particle-hole symmetry parameters, ν and ζ, and demonstrates their effectiveness in modeling nuclear energies and shell effects with a simple fit.

Findings

Accurately reproduces binding energies of 2353 nuclei with 1.55 MeV RMS deviation.

Identifies shell closure and sub-shell features through deviations in model predictions.

Provides a new framework for understanding nuclear structure using symmetry-inspired parameters.

Abstract

Two new numbers, $\nu$ and $\zeta$, inspired by particle-hole symmetry are introduced. These numbers have extreme values at a closed shell and vanish mid-shell. A combination of even powers of these numbers has been used to model experimentally measured quantities such as $R4/2=E(4^+_1)/E(2^+_1)$ and the "microscopic" contribution to binding energies. A binding energy fit consisting of a total of six fit coefficients, including one new shell term, reproduces the experimental binding energies of 2353 nuclei with an r.m.s. standard deviation of 1.55 MeV. The difference between the experimental and fit values of observables, specifically the $R4/2$, provides an indication of where shell closure features are less pronounced and where sub-shells closures occur.