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Gamow shell model predictions for six-proton unbound nucleus $^{20}$Si

J. L. Wang, M. R. Xie, K. H. Li, P. Y. Wang, N. Michel, Q. Yuan, J. G. Li

TL;DR

This work uses the Gamow shell model to study the six-proton unbound nucleus $^{20}$Si and related isotones, addressing how continuum coupling and isospin-breaking effects shape its structure and decay. Employing a Berggren basis with COSM, a core-plus-valence Hamiltonian, and EFT-based interactions, the paper provides quantitative predictions for ground- and excited-state energies and widths, including a ground-state $6p$ decay to $^{14}$O with $E_{6p}\,ig brace\approx 10.15$ MeV and $ ext{Γ}\,ig brace\approx 371$ keV, and a $2^+_1$ state near 1.7 MeV, suggesting the disappearance of the $Z=14$ subshell. Analyses of mirror partners $^{19}$Al/$^{19}$C and $^{20}$Si/$^{20}$C reveal strong dynamic Thomas-Ehrman shifts via altered $s_{1/2}$ and $d_{5/2}$ occupancies and non-negligible Coulomb and nuclear contributions to mirror-energy differences, highlighting the complex interplay of continuum effects and isospin symmetry breaking. The results provide robust predictions and a framework for guiding future experimental exploration of proton-rich nuclei near the drip line.

Abstract

Proton-rich nuclei beyond the proton drip line are of great interest in nuclear structure physics, due to exotic phenomena such as proton emissions and the Thomas-Ehrman shift (TES). In this work, we employ the Gamow shell model (GSM) to investigate the structure and decay of $^{20}$Si, a candidate for six-proton (6$p$) emission, which can be produced via two-neutron knockout from the drip line nucleus $^{22}$Si. We predict that its ground state decays via $6p$ emission to the ground state of $^{14}$O, with a decay energy $E_{6p} = 10.125$ MeV and a width of 371~keV. A $2^+$ state is predicted at 1.7 MeV, comparable with that in $^{18}$Mg, indicating the disappearance of the $Z=14$ magic number in $^{20}$Si. Instead, analyses of the many-body configurations and the average occupancies of the mirror states suggest the presence of $dynamic$ TES in low-lying states of $^{19}$Al/$^{19}$C and $^{20}$Si/$^{20}$C. Further evidence is provided by analyzing the contributions of different components of the GSM Hamiltonian. Moreover, this study offers the first theoretical description of $^{20}$Si and guidance for future experiments.

Gamow shell model predictions for six-proton unbound nucleus $^{20}$Si

TL;DR

This work uses the Gamow shell model to study the six-proton unbound nucleus Si and related isotones, addressing how continuum coupling and isospin-breaking effects shape its structure and decay. Employing a Berggren basis with COSM, a core-plus-valence Hamiltonian, and EFT-based interactions, the paper provides quantitative predictions for ground- and excited-state energies and widths, including a ground-state decay to O with MeV and keV, and a state near 1.7 MeV, suggesting the disappearance of the subshell. Analyses of mirror partners Al/C and Si/C reveal strong dynamic Thomas-Ehrman shifts via altered and occupancies and non-negligible Coulomb and nuclear contributions to mirror-energy differences, highlighting the complex interplay of continuum effects and isospin symmetry breaking. The results provide robust predictions and a framework for guiding future experimental exploration of proton-rich nuclei near the drip line.

Abstract

Proton-rich nuclei beyond the proton drip line are of great interest in nuclear structure physics, due to exotic phenomena such as proton emissions and the Thomas-Ehrman shift (TES). In this work, we employ the Gamow shell model (GSM) to investigate the structure and decay of Si, a candidate for six-proton (6) emission, which can be produced via two-neutron knockout from the drip line nucleus Si. We predict that its ground state decays via emission to the ground state of O, with a decay energy MeV and a width of 371~keV. A state is predicted at 1.7 MeV, comparable with that in Mg, indicating the disappearance of the magic number in Si. Instead, analyses of the many-body configurations and the average occupancies of the mirror states suggest the presence of TES in low-lying states of Al/C and Si/C. Further evidence is provided by analyzing the contributions of different components of the GSM Hamiltonian. Moreover, this study offers the first theoretical description of Si and guidance for future experiments.

Paper Structure

This paper contains 5 sections, 2 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Method
  3. Results
  4. Summary
  5. Acknowledgments

Figures (4)

  • Figure 1: The calculated energies ($E_{x}$, in MeV) and widths (in keV) for ground and excited states of carbon isotones with GSM relative to the $\rm{^{14}O}$ core, along with available experimental data. Green striped squares represent the widths, and the corresponding values are written nearby. Experimental data for $\rm{^{15}F}$, $\rm{^{16}Ne}$ and $\rm{^{18}Mg}$ are obtained from Ref. ensdfPhysRevLett.113.232501PhysRevLett.127.262502.
  • Figure 2: Comparison of the excitation energies and widths of mirroring nuclear states of $\rm{^{19}C/^{19}Al}$ and $\rm{^{20}C/^{20}Si}$. Experimental data of $\rm{^{19}C}$ and $\rm{^{20}C}$ are taken from Ref. ensdf.
  • Figure 3: The calculated average occupations of the $s_{1/2}$ and $d_{5/2}$ partial waves for the low-lying states of $\rm{^{19}Al/ ^{19}C}$ and $\rm{^{20}Si/^{20}C}$.
  • Figure 4: The contributions of different components of the Hamiltonian calculated by GSM to the low-lying excited states in $\rm{^{19}Al/^{19}C}$ (the left part) and $\rm{^{20}Si/^{20}C}$ (the right part). The upper panel shows the absolute energies relative to their inner core. GSM-Coulomb represent the calculated energies of $\rm{^{19}Al}$ or $\rm{^{20}Si}$ minus the Coulomb force contribution. The lower panel shows the value of each contribution, where $\Delta E$ is the difference between contributions of nuclear forces in $^{19}$Al/$^{19}$C or $^{20}$Si/$^{20}$C. Experimental data are taken from Ref. ensdf.