# Existence problem of proton semi-bubble structure in the $2_1^+$ state of $^{34}$Si

## TL;DR

This study uses self-consistent HF+RPA calculations to investigate the proton semi-bubble structure in the $2_1^+$ state of $^{34}$Si, finding it unlikely due to the dominant proton transition and minimal density distribution effects.

## Contribution

It provides a detailed analysis of the $2_1^+$ state in $^{34}$Si using Skyrme interactions, highlighting the impact of tensor effects and the unlikelihood of a proton semi-bubble structure.

## Key findings

- Reproduces experimental excitation energy and B(E2) strength accurately.
- Tensor interaction affects excitation energy but not density distributions.
- Proton transition from $ ext{1d}_{5/2}$ to $ ext{2s}_{1/2}$ dominates the state.

## Abstract

The fully self-consistent Hartree-Fock (HF) plus random phase approximation (RPA) based on Skyrme-type interaction is used to study the existence problem of proton semi-bubble structure in the $2_1^+$ state of $^{34}$Si. The experimental excitation energy and the B(E2) strength of the $2_1^+$ state in $^{34}$Si can be reproduced quite well. The tensor effect is also studied. It is shown that the tensor interaction has a notable impact on the excitation energy of the $2_1^+$ state and a small effect on the B(E2) value. Besides, its effect on the density distributions in the ground and $2_1^+$ state of $^{34}$Si is negligible. Our present results with T36 and T44 show that the $2_1^+$ state of $^{34}$Si is mainly caused by proton transiton from $\pi 1d_{5/2}$ orbit to $\pi 2s_{1/2}$ orbit, and the existence of a proton semi-bubble structure in this state is very unlikely.