Empirical formula extended to the yrast excitation energies of the unnatural parity states in even-even nuclei

TL;DR

This paper extends a simple empirical formula, originally used for natural parity states, to describe the yrast excitation energies of unnatural parity states in even-even nuclei across the periodic table, showing it remains effective despite different residual interactions.

Contribution

The study demonstrates that the same empirical formula can effectively describe unnatural parity yrast excitation energies, broadening its applicability beyond natural parity states.

Findings

Empirical formula fits unnatural parity states well

Effective across entire periodic table

Works despite different residual interactions

Abstract

Recently, it was shown that a simple empirical formula, in terms of the mass and valence nucleon numbers, can describe the main trends of the yrast excitation energies of the natural parity states up to $10^+$ in even-even nuclei throughout the entire periodic table. The same empirical formula was applied to the yrast excitation energies of unnatural parity states including $1^+$, $2^-$, $3^+$, $4^-$, $5^+$, $6^-$, $7^+$, $8^-$, $9^+$, $10^-$, and $11^+$ in even-even nuclei. Although the overall character of the effective residual interaction for the unnatural parity states was quite different to that of the natural parity states, the same form of the empirical formula was found to hold reasonably well for the yrast excitation energies of the unnatural parity states.