Universal Expression for the Lowest Excitation Energy of Natural Parity Even Multipole States

TL;DR

This paper introduces a universal empirical formula for the lowest excitation energies of natural parity even multipole states in all even-even nuclei, depending only on mass and valence nucleons.

Contribution

It proposes a new, simple, and universal empirical expression for excitation energies across the entire periodic table, based on only six parameters.

Findings

Formula accurately reproduces experimental energies

Parameters are easily determined from data

Good agreement with previous studies

Abstract

We present a new expression for the energy of the lowest collective states in even-even nuclei throughout the entire periodic table. Our empirical formula is extremely valid and holds universally for all of the natural parity even multipole states. This formula depends only on the mass number and the valence nucleon numbers with six parameters. These parameters are determined easily and unambiguously from the data for each multipole state. We discuss the validity of our empirical formula by comparing our results with those of other studies and also by estimating the average and the dispersion of the logarithmic errors of the calculated excitation energies with respect to the measured ones.