Theoretical study of the two-proton halo candidate $^{17}$Ne including contributions from resonant continuum and pairing correlations

TL;DR

This paper presents a theoretical analysis of the two-proton halo candidate $^{17}$Ne, incorporating resonant continuum and pairing correlations using advanced relativistic mean field methods, aligning well with experimental data.

Contribution

It introduces a comprehensive relativistic framework that includes resonant continuum and pairing effects to study $^{17}$Ne, providing insights consistent with experimental observations.

Findings

Energies and wave functions of resonant orbitals calculated with ACCC approach.

Results agree with experimental measurements of binding energies and radii.

Occupation probability of specific orbitals aligns with shell model predictions.

Abstract

With the relativistic Coulomb wave function boundary condition, the energies, widths and wave functions of the single proton resonant orbitals for $^{17}$Ne are studied by the analytical continuation of the coupling constant (ACCC) approach within the framework of the relativistic mean field (RMF) theory. Pairing correlations and contributions from the single-particle resonant orbitals in the continuum are taken into consideration by the resonant Bardeen-Cooper-Schrieffer (BCS) approach, in which constant pairing strength is used. It can be seen that the fully self-consistent calculations with NL3 and NLSH effective interactions mostly agree with the latest experimental measurements, such as binding energies, matter radii, charge radii and densities. The energy of $\pi$2s$_{1/2}$ orbital is slightly higher than that of $\pi1d_{5/2}$ orbital, and the occupation probability of the $(\pi$2s$_{1/2})^2$ orbital is about 20%, which are in accordance with the shell model calculation and three-body model estimation.