Probe the 2$s_{1/2}$ and 1$d_{3/2}$ state level inversion with electron-nucleus scattering

TL;DR

This study investigates the potential inversion of 2s1/2 and 1d3/2 proton energy levels in neutron-rich nuclei using RMF and electron scattering methods, revealing measurable effects on charge density distributions.

Contribution

It provides the first detailed analysis of how proton level inversion affects charge densities and suggests experimental methods to observe this phenomenon in neutron-rich isotopes.

Findings

Level inversion may occur in neutron-rich magnesium, silicon, sulfur, and argon isotopes.

Charge density variations are highly sensitive to the level inversion.

Charge density differences can reveal both level inversion and proton wave function behavior.

Abstract

The neutron-rich even-even nuclei $^{26-40}$Mg, $^{28-46}$Si, $^{30-48}$S, and $^{32-56}$Ar are calculated with the RMF model and the phase-shift electron scattering method. Results show that level inversion of the 2$s_{1/2}$ and 1$d_{3/2}$ proton states may occur for the magnesium, silicon, sulphur, and argon isotopes with more neutrons away from the stability line. Calculations show that the variation of the central charge densities for $^{30-48}$S, and $^{32-56}$Ar are very sensitive to the 2$s_{1/2}$ and 1$d_{3/2}$ proton state level inversion, and the level inversion can lead to a large measurable central charge depletion to the charge density distributions for the neutron-rich isotopes. Calculations also show that the charge density differences between the isotopes with and without central charge depletion can reveal not only the level inversion of the 2$s_{1/2}$ and 1$d_{3/2}$ proton states but also the behavior of the proton wave functions of both states. The results can provide references for the possible study of the nuclear level inversion and nuclear bubble phenomenon with electron scattering off short-lived nuclei at RIKEN or/and GSI in the future. In addition, direct nuclear reaction $^{44}$S(n, d)$^{43}$P or $^{44}$S($^{3}$H, $\alpha$)$^{43}$P might also be a possible way to study the 2$s_{1/2}$ and 1$d_{3/2}$ proton state level inversion.