Intruder-driven mirror energy differences between $^{29}$Cl and $^{29}$Mg studied with antisymmetrized molecular dynamics

Abstract

To clarify the mirror energy differences (MEDs) of the proton-unbound nucleus $^{29}$Cl and their microscopic origins, we investigate the low-lying states of the $^{29}$Cl-$^{29}$Mg mirror pair using antisymmetrized molecular dynamics. The calculation reasonably reproduces the normal and intruder states of $^{29}$Mg, while suggesting alternative spin-parity assignments for $^{29}$Cl. The $1/2^+$ and $3/2^+$ states are predicted to form a nearly degenerate ground-state doublet with a small MED because of their similar intrinsic structures. In contrast, the $3/2^-$ and $7/2^-$ intruder states exhibit large negative MEDs and are assigned to the observed resonances at approximately 500~keV and 1.1~MeV, respectively. Their large MEDs originate from the reduced Coulomb energies associated with the stronger deformation and spatially extended proton distributions in the intruder configurations.