Correlating charge radius with quadrupole deformation and $B(E2)$ in atomic nuclei

TL;DR

This paper discovers a strong linear correlation between charge radius differences, quadrupole deformation, and $B(E2)$ values in even-even nuclei, leading to improved predictive relations with high precision.

Contribution

It introduces a new, highly precise relation linking charge radii, quadrupole deformation, and $B(E2)$ values in atomic nuclei, enhancing understanding of nuclear structure.

Findings

Linear correlation between charge radius differences and quadrupole deformation.

Improved charge radius relation with 0.005 fm precision.

Correlation extends to $B(E2)$ transition probabilities and lifetimes.

Abstract

A very good linear correlation is found between the four-point charge radius relation $\delta R_{2p-2n}(Z,N)$ with that of quadrupole deformation data in even-even nuclei. This results in a further improved charge radius relation that holds in a precision of about 5$\times 10^{-3}$ fm. Such correlations are also seen in global nuclear models, their precisions, however, are not enough to be consistent with the experimental data. The new relation between charge radii and deformation of even-even nuclei can be generalized to the reduced electric quadrupole transition probability $B(E2)$ between the first $2^+$ state and the $0^+$ ground state, and the mean lifetime $\tau$ of the first 2$^+$ state.