Ab initio calculation of the potential bubble nucleus ${}^{34}$Si

Abstract

The possibility that an unconventional depletion in the center of the charge density distribution of certain nuclei occurs due to a purely quantum mechanical effect has attracted theoretical and experimental attention in recent years. We report on ab initio self-consistent Green's function calculations of one of such candidates, ${}^{34}$Si, together with its Z+2 neighbour ${}^{36}$S. Binding energies, rms radii and density distributions of the two nuclei as well as low-lying spectroscopy of ${}^{35}$Si, ${}^{37}$S, ${}^{33}$Al and ${}^{35}$P are discussed. The interpretation of one-nucleon removal and addition spectra in terms of the evolution of the underlying shell structure is also provided. The study is repeated using several chiral effective field theory Hamiltonians as a way to test the robustness of the results with respect to input inter-nucleon interactions. The prediction regarding the (non-)existence of the bubble structure in ${}^{34}$Si varies significantly with the nuclear Hamiltonian used. However, demanding that the experimental charge density distribution and the root mean square radius of ${}^{36}$S are well reproduced, along with ${}^{34}$Si and ${}^{36}$S binding energies, only leaves the NNLO${}_{\text{sat}}$ Hamiltonian as a serious candidate to perform this prediction. In this context, a bubble structure, whose fingerprint should be visible in an electron scattering experiment of ${}^{34}$Si, is predicted. Furthermore, a clear correlation is established between the occurrence of the bubble structure and the weakening of the 1/2${}^{-}$-3/2${}^{-}$ splitting in the spectrum of ${}^{35}$Si as compared to ${}^{37}$S.

19 pages, 21 figures

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