Thomas-Ehrman effect in a three-body model: $^{16}$Ne case

TL;DR

This paper investigates the Thomas-Ehrman shift in three-body nuclear systems, specifically in $^{16}$Ne and its mirror $^{16}$C, revealing significant isospin symmetry breaking and the importance of parameter consistency for accurate Coulomb energy descriptions.

Contribution

It introduces a three-body model analysis of the Thomas-Ehrman effect, highlighting configuration mixing and isospin symmetry breaking in $^{16}$Ne and $^{16}$C, and infers the $^{15}$F ground state energy.

Findings

Large isospin symmetry breaking in wave function components.

Configuration mixing is crucial for describing Coulomb displacement energies.

Inferred $^{15}$F ground state energy as 1.39-1.42 MeV.

Abstract

The dynamic mechanism of the Thomas-Ehrman shift is studied in three-cluster systems by example of $^{16}$Ne and $^{16}$C isobaric mirror partners. We predict configuration mixings for $0^+$ and $2^+$ states in $^{16}$Ne and $^{16}$C. Large isospin symmetry breaking on the level of wave function component weights is demonstrated for these states and discussed as three-body mechanism of Thomas-Ehrman shift. It is shown that the description of the Coulomb displacement energies requires a consistency among three parameters: the $^{16}$Ne decay energy $E_T$, the $^{15}$F ground state energy $E_r$, and the configuration mixing parameters for the $^{16}$Ne/$^{16}$C $0^+$ and $2^+$ states. Basing on this analysis we infer the $^{15}$F $1/2^+$ ground state energy to be $E_r=1.39-1.42$ MeV.