Does a proton "bubble" structure exist in the low-lying states of 34Si?

TL;DR

This study uses advanced relativistic configuration mixing methods to investigate the proton density distribution in $^{34}$Si, finding that a proton "bubble" structure in low-lying states is unlikely due to shape fluctuations.

Contribution

It introduces a relativistic beyond mean-field approach with configuration mixing to analyze proton density distributions in $^{34}$Si, providing new insights into the proton bubble structure.

Findings

Proton density central depression is reduced by shape fluctuations.

Proton "bubble" structure in low-lying states is unlikely.

Results agree well with experimental data without parameters.

Abstract

The possible existence of a "bubble" structure in the proton density of $^{34}$Si has recently attracted a lot of research interest. To examine the existence of the "bubble" structure in low-lying states, we establish a relativistic version of configuration mixing of both particle number and angular momentum projected quadrupole deformed mean-field states and apply this state-of-the-art beyond relativistic mean-field method to study the density distribution of the low-lying states in $^{34}$Si. An excellent agreement with the data of low-spin spectrum and electric multipole transition strengths is achieved without introducing any parameters. We find that the central depression in the proton density is quenched by dynamic quadrupole shape fluctuation, but not as significantly as what has been found in a beyond non-relativistic mean-field study. Our results suggest that the existence of proton "bubble" structure in the low-lying excited $0^+_2$ and $2^+_1$ states is very unlikely.