Gamow shell model calculations for the Thomas-Ehrman shift in new isotopes 21Al

TL;DR

This work addresses TES in a proton-rich unbound system by applying the Gamow Shell Model (GSM) to the mirror pair $^{21}$Al/$^{21}$O and by extending GSM to reaction dynamics with GSM-CC for $^{20}$Mg$(p,p)$. The approach uses a Berggren basis to treat bound, resonant, and continuum states within a core+$n$ valence framework, with Woods-Saxon core potentials and EFT-based two-body forces, including Coulomb effects for protons. Key findings include accurate reproduction of ground-state energies for $A=18$–$22$ isotones, large TES in the $1/2^+$ and $3/2^+$ states driven by $s_{1/2}$ occupancy and extended densities, and a Hamiltonian decomposition showing Coulomb energy as the main MED contributor with variable NN contributions. GSM-CC yields an $S_p = -1.19$ MeV for $^{21}$Al, predicts a $1/2^+$ excitation at about 0.30 MeV relative to the ground, and forecasts a two-resonance structure in $^{20}$Mg$(p,p)$ at $E_r \approx 1.20$ MeV and $1.64$ MeV with widths of about $0.38$ keV and $225$ keV, respectively, offering testable benchmarks for future experiments.

Abstract

Proton-rich nuclei beyond the proton drip line exhibit unique phenomena, such as the Thomas-Ehrman shift (TES), providing valuable insights into nuclear stability and isospin symmetry breaking. The discovery of the lightest new isotope, 21Al, situated beyond the proton drip line, was recently reported in the experiment. In this study, we employ the Gamow shell model (GSM) to explore the TES in mirror pairs 21Al/21O, focusing on how this phenomenon affects the energy levels of these nuclei. Our calculations describe the ground state energies and reveal significant TES with large mirror energy differences in the excited mirror 1/2+ states in 21Al/21O. The large mirror energy difference is primarily due to the significant occupation of weakly bound or unbound s1/2 orbitals, resulting in the extended radial density distributions, and variations in Coulomb energy and nuclear interaction contributions between the mirror states. Additionally, the low-lying states of 21Al are also calculated with the GSM in coupled-channel (GSM-CC) representation, Furthermore, we also predict the cross-section of 20Mg(p, p) scattering, which serves as another candidate approach to study the unbound structure of 21Al in the experiment, offering a theoretical framework for studying the structure and reaction dynamics of 21Al in future experiments.

Figures (4)

• Figure 1: The ground state energy of A$= 18-22$ isotones and their mirror partners with $^{16}$O core. Experimental data for $^{21}$Al have been available PhysRevC.110.L031301, while other data are taken from ensdf.
• Figure 2: The radial density distributions of the ground and first excited states in $^{21}$Al/$^{21}$O are shown, with the solid line representing $^{21}$Al and the dotted line representing $^{21}$O.
• Figure 3: The calculated contribution of different components of the Hamiltonian for low-lying states in $^{21}$Al/$^{21}$O with GSM. The left panel shows the absolute energies relative to their inner core. GSM-2BC and GSM-1BC-2BC represent the calculated energies of $^{21}$Al minus two-body Coulomb force contribution and both one- and two-body Coulomb force contributions, respectively. The right panel shows the value of each contribution, where $\Delta E$ is the difference between contribution of $NN$ interactions in $^{21}$Al/$^{21}$O. In the right panel, the red arrows indicate the energy differences between the ground and excited states of mirror nuclei, corresponding to the MED. Experimental data are taken from PhysRevC.110.L031301ensdf.
• Figure 4: Excitation function of the $^{20}$Mg(p, p) scattering reaction calculated with GSM-CC. The energy and cross section are defined in the center of mass frame, with the cross section angle set at 180 degrees. The low-lying resonant states of $^{21}$Al are labeled next to their respective resonant peaks in the figure.