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

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.

Comments: 6 pages, 3 figures, 3 tables