A puzzle on isomeric configurations in and around $N=126$ closed shell

TL;DR

This paper investigates the isomeric configurations near the N=126 closed shell using the generalized seniority scheme, emphasizing the importance of configuration mixing and confirming results with shell model calculations.

Contribution

It introduces a comprehensive analysis of isomeric properties near N=126, highlighting the role of configuration mixing and validating findings with microscopic shell model calculations.

Findings

Configuration mixing from f7/2 and i13/2 orbitals is crucial.

Structural behavior of N=126 isomers resembles N=124 and N=128 cases.

Shell model occupancies support generalized seniority results.

Abstract

The puzzle of finding consistent nuclear configurations for explaining both the decay probabilities and moments of the ${9/2}^-$, ${8}^+$ and ${21/2}^-$ isomers in and around $N=126$ closed shell has been approached in the generalized seniority scheme. Though $h_{9/2}$ is the dominant orbital near Fermi energy, the role of configuration mixing from the surrounding $f_{7/2}$ and $i_{13/2}$ orbitals is found to be very important for the consistent explanation of all the isomeric properties such as the $B(E2)$ rates, $Q-$moments and $g-$factors. The structural behavior of the closed shell $N=126$ isotonic isomers turns out to be very similar to the $N=124$ and $N=128$ isotonic isomers which have two neutron-holes and two neutron-particles, respectively. This is due to the pairing symmetries of nuclear many-body Hamiltonian. As a confirmation, the microscopic shell model occupancies are also calculated for these isomers in $N=126$ chain which support the generalized seniority results. Additional arguments using the systematics of odd-proton ${9/2}^-$ states in Tl ($Z=81$), Bi ($Z=83$), At ($Z=85$) and Fr ($Z=87$) isotopes are also presented.