Ab initio calculation of the potential bubble nucleus ${}^{34}\mathrm{Si}$
Abstract
Background: The possibility that an unconventional depletion (referred to as a “bubble”) happens in the middle 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 meanfield rationale, a correlation between the occurrence of such a semibubble and an anomalously weak splitting between low angularmomentum spinorbit partners has been further conjectured. Energy density functional and valencespace shell model calculations have been performed to identify and characterize the best candidates, among which ${}^{34}\mathrm{Si}$ appears as a particularly interesting case. While the experimental determination of the charge density distribution of the unstable ${}^{34}\mathrm{Si}$ 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 ${}^{35}\mathrm{Si}$as compared to ${}^{37}\mathrm{S}$. Purpose: We study the potential bubble structure of ${}^{34}\mathrm{Si}$ on the basis of the stateoftheart ab initio selfconsistent Green's function manybody method. Methods: We perform the first ab initio calculations of ${}^{34}\mathrm{Si}$ and ${}^{36}\mathrm{S}$. In addition to binding energies, the first observables of interest are the charge density distribution and the charge rootmeansquare radius for which experimental data exist in ${}^{36}\mathrm{S}$. The next observable of interest is the lowlying spectroscopy of ${}^{35}\mathrm{Si}$ and ${}^{37}\mathrm{S}$ obtained from ($d, p$) experiments along with the spectroscopy of ${}^{33}\mathrm{Al}$ and ${}^{35}\mathrm{P}$ obtained from knockout 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 manybody expansion, i.e., with respect to the manybody correlations included in the calculation, is studied in detail. We eventually compare our predictions to stateoftheart multireference energy density functional and shell model calculations. Results: The prediction regarding the (non)existence of the bubble structure in ${}^{34}\mathrm{Si}$ varies significantly with the nuclear Hamiltonian used. Yet, demanding that the experimental charge density distribution and the rootmeansquare radius of ${}^{36}\mathrm{S}$ be well reproduced, along with ${}^{34}\mathrm{Si}$ and ${}^{36}\mathrm{S}$ binding energies, only leaves the NNLO 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 ${}^{34}\mathrm{Si}$, 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 ${}^{35}\mathrm{Si}$ as compared to ${}^{37}\mathrm{S}$. Conclusions: The occurrence of a bubble structure in the charge distribution of ${}^{34}\mathrm{Si}$ is convincingly established on the basis of stateoftheart 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 ${}^{34}\mathrm{Si}$ in future electron scattering experiments on unstable nuclei. In the meantime, it is of interest to perform oneneutron removal on ${}^{34}\mathrm{Si}$ and ${}^{36}\mathrm{S}$ in order to further test our theoretical spectral strength distributions over a wide energy range.
 Authors:

 Univ. ParisSaclay, GifsurYvette (France); Katholieke Univ. Leuven, Heverlee (Belgium). Inst. voor Kern en Stralingsfysica; Michigan State Univ., East Lansing, MI (United States). Dept. of Physics and Astronomy
 Univ. ParisSaclay, GifsurYvette (France)
 Katholieke Univ. Leuven, Heverlee (Belgium). Inst. voor Kern en Stralingsfysica
 Univ. of Surrey, Guildford (United Kingdom). Dept. of Physics
 TRIUMF, Vancouver, BC (Canada)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1565610
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review C
 Additional Journal Information:
 Journal Volume: 95; Journal Issue: 3; Journal ID: ISSN 24699985
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Citation Formats
Duguet, Thomas, Somà, Vittorio, Lecluse, Simon, Barbieri, C., and Navrátil, P. Ab initio calculation of the potential bubble nucleus Si34. United States: N. p., 2017.
Web. doi:10.1103/physrevc.95.034319.
Duguet, Thomas, Somà, Vittorio, Lecluse, Simon, Barbieri, C., & Navrátil, P. Ab initio calculation of the potential bubble nucleus Si34. United States. doi:10.1103/physrevc.95.034319.
Duguet, Thomas, Somà, Vittorio, Lecluse, Simon, Barbieri, C., and Navrátil, P. Thu .
"Ab initio calculation of the potential bubble nucleus Si34". United States. doi:10.1103/physrevc.95.034319. https://www.osti.gov/servlets/purl/1565610.
@article{osti_1565610,
title = {Ab initio calculation of the potential bubble nucleus Si34},
author = {Duguet, Thomas and Somà, Vittorio and Lecluse, Simon and Barbieri, C. and Navrátil, P.},
abstractNote = {Background: The possibility that an unconventional depletion (referred to as a “bubble”) happens in the middle 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 meanfield rationale, a correlation between the occurrence of such a semibubble and an anomalously weak splitting between low angularmomentum spinorbit partners has been further conjectured. Energy density functional and valencespace shell model calculations have been performed to identify and characterize the best candidates, among which Si34 appears as a particularly interesting case. While the experimental determination of the charge density distribution of the unstable Si34 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 Si35as compared to S37. Purpose: We study the potential bubble structure of Si34 on the basis of the stateoftheart ab initio selfconsistent Green's function manybody method. Methods: We perform the first ab initio calculations of Si34 and S36. In addition to binding energies, the first observables of interest are the charge density distribution and the charge rootmeansquare radius for which experimental data exist in S36. The next observable of interest is the lowlying spectroscopy of Si35 and S37 obtained from ($d, p$) experiments along with the spectroscopy of Al33 and P35 obtained from knockout 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 manybody expansion, i.e., with respect to the manybody correlations included in the calculation, is studied in detail. We eventually compare our predictions to stateoftheart multireference energy density functional and shell model calculations. Results: The prediction regarding the (non)existence of the bubble structure in Si34 varies significantly with the nuclear Hamiltonian used. Yet, demanding that the experimental charge density distribution and the rootmeansquare radius of S36 be well reproduced, along with Si34 and S36 binding energies, only leaves the NNLO 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 Si34, 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 Si35 as compared toS37. Conclusions: The occurrence of a bubble structure in the charge distribution of Si34 is convincingly established on the basis of stateoftheart 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 Si34 in future electron scattering experiments on unstable nuclei. In the meantime, it is of interest to perform oneneutron removal on Si34 and S36 in order to further test our theoretical spectral strength distributions over a wide energy range.},
doi = {10.1103/physrevc.95.034319},
journal = {Physical Review C},
issn = {24699985},
number = 3,
volume = 95,
place = {United States},
year = {2017},
month = {3}
}
Web of Science
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