Analytic continuation in coupling constant applied to two-proton emitters

TL;DR

This paper demonstrates the effectiveness of the analytic continuation in coupling constant (ACCC) method for solving three-body resonance problems in two-proton emitters, aligning well with experimental data and time-dependent results.

Contribution

The study applies ACCC to complex three-body nuclear systems, showing it as a low-cost, reliable method for calculating energies and widths of two-proton emitters.

Findings

ACCC results agree with experimental data and time-dependent calculations.

$^{6}$Be and $^{16}$Ne show smooth energy shifts with interaction changes.

Avoid-crossing behavior observed in certain $^{16}$Ne resonances.

Abstract

For quantum meta-stable problems with three particles, the $^{6}$Be and $^{16}$Ne nuclei as two-proton ($2p$) emitters provide a testing field. Considering the complexity of many-body meta-stable systems, a tractable solver has been on demand. We apply the analytic continuation in coupling constant (ACCC) to these nuclei, and confirm that this method can solve such problems consistently to the time-dependent results as well as to the experimental data. The sensitivity of the $2p$ energies and widths to the proton-proton interaction is also investigated. The $^{6}$Be shows a smooth shift from short-life to long-life systems according to the proton-proton interaction. Same is concluded for the $2^+$ resonance of $^{16}$Ne. In contrast, for the first and second $0^+$ resonances of $^{16}$Ne, their energies and widths show the avoid-crossing behaviour, due to the coupling of two configurations in the core-proton subsystem, $^{15}$F. Since it requires only the bound-state solvers, the ACCC can be a low-cost option to solve three or more-body resonances.