sp(4,R)-systematics of atomic nuclei. F-multiplets and nuclear structure

TL;DR

This paper develops a classification scheme for atomic nuclei using the non-compact algebra sp(4,R), analyzing nuclear properties within F-multiplets and revealing structural effects and mirror symmetry in energy levels.

Contribution

It introduces a novel classification framework based on sp(4,R) algebra for nuclear systematics, emphasizing F-multiplets and empirical analysis of nuclear properties.

Findings

Identification of structural effects in nuclear data

Clear indication of mirror symmetry in energy levels

Empirical relationships between nuclear properties and nucleon number

Abstract

A systematics of the atomic nuclei in the frame of the nucleon number $A = Z + N$ and the proton-neutron difference $F = Z - N$ is considered. The classification scheme is provided by means of the non-compact algebra $sp(4,R)$. In this scheme the nuclei are ordered into isobaric multiplets, for which $A={fix}$, as well as in F-multiplets, for which $F={fix}$. The dependence of the mass excess $\Delta$, the first exited states $E_{2^+}$ and the ratio $R_2=E_{4^+}/E_{2^+}$ on the nucleon number $A$ is empirically investigated within the $F$-multiplets. Appropriate filters are used to study the properties of the mass excess. Many structural effects are observed. The mirror symmetry is clearly indicated for the energy levels of the nuclei with the same value of $A$ and opposite $F$-values.