Ab initio calculation of the potential bubble nucleus ³⁴Si

Background: The possibility that an unconventional depletion (referred to as a 'bubble') occurs in the center of the charge density distribution of certain nuclei due to a purely quantum mechanical effect has attracted theoretical and experimental attention in recent years. Based on a mean-field rationale, a correlation between the occurrence of such a semi-bubble and an anomalously weak splitting between low angular-momentum spin-orbit partners has been further conjectured. Energy density functional and valence-space shell model calculations have been performed to identify and characterize the best candidates, among which ³⁴Si appears as a particularly interesting case. While the experimental determination of the charge density distribution of the unstable ³⁴Si is currently out of reach (d, p) experiments on this nucleus have been performed recently to test the correlation between the presence of a bubble and an anomalously weak 1/2^- -3/2^- splitting in the spectrum of ³⁵Si as compared to ³⁷S. Purpose: We study the potential bubble structure of ³⁴Si on the basis of the state-of-the-art ab initio self-consistent Green's function many-body method. Methods: We perform the first ab initio calculations of ³⁴Si and ³⁶S. In addition to binding energies, the first observables of interest are the charge density distribution and the charge root-mean-square radius for which experimental data exist in ³⁶S. The next observable of interest is the low-lying spectroscopy of ³⁵Si and ³⁷S obtained from (d, p) experiments along with the spectroscopy of ³³Al and ³⁵P obtained from knock-out experiments. The interpretation 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 internucleon interactions. The convergence of the results with respect to the truncation of the many-body expansion, i.e., with respect to the many-body correlations included in the calculation, is studied in detail. We eventually compare our predictions to state-of-the-art multireference energy density functional and shell model calculations. Results: The prediction regarding the (non) existence of the bubble structure in ³⁴Si varies significantly with the nuclear Hamiltonian used. However, demanding that the experimental charge density distribution and the root-mean-square radius of ³⁶S be well reproduced, along with ³⁴Si and ³⁶S binding energies, only leaves the NNLOsat 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 ³⁴Si, 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 ³⁵Si as compared to ³⁷S. Conclusions: The occurrence of a bubble structure in the charge distribution of ³⁴Si is convincingly established on the basis of state-of-the-art ab initio calculations. This prediction will have to be reexamined in the future when improved chiral nuclear Hamiltonians are constructed. On the experimental side, present results act as a strong motivation to measure the charge density distribution of ³⁴Si in future electron scattering experiments on unstable nuclei. In the meantime, it is of interest to perform one-neutron removal on ³⁴Si and ³⁶S in order to further test our theoretical spectral strength distributions over a wide energy range. (authors)