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Description
Nuclei around doubly magic $^{208}$Pb have long served as a testing ground for the validity of the shell model. While the high-spin states of these nuclei have been studied extensively, data on electromagnetic transition rates between the low-spin states are scarce. Members of the $N = 125$ isotone chain – including $^{209}$Po, $^{211}$Rn and $^{213}$Ra – exhibit a ground state with spin-parity of $J^{\pi} = 1/2^-$, and a $5/2^-$ first-excited state at near-constant excitation energy. The ground state can be attributed to a p$_{1/2}$ neutron hole coupling to the $0^+$ ground-state of the neighbouring semi-magic, $N = 126$ core; likewise, coupling the ground state of the core to a $\nu f_{5/2}$ hole accounts for the excited $5/2^-$ state.
These nuclei have been studied using stable-beam experiments at the Australian National University Heavy Ion Accelerator Facility. Lifetimes of the $5/2-$ states in the $N = 125$ isotone chain were measured directly from γ- γ time differences using Compton-suppressed, ultrafast LaBr$_3$ scintillators installed in the CAESAR detector array. The near-constant excitation energy of the $5/2^-$ state across the chain suggests that the simple single-hole structure persists as pairs of protons are added. However, the measured $B(E2; 5/2^- \to 1/2^-$) values indicate enhanced collective contributions from valence protons that increase with Z. It appears that the near-constant $5/2^-$ excitation energies are a coincidental outcome of the interplay between the single-particle behaviour and emerging collectivity beyond the shell-model valence space. Shell-model calculations were performed to understand the microscopic origins of this behaviour.
This research was supported by the Australian Research Council through grant numbers No.~DP170101673 and No.~DP170101675, and by the International Technology Center Pacific (ITC-PAC) under Contract No.~FA520919PA138. A.~A., B.~J.~C., J.~T.~H.~D., T.~J.~G., and B.~P.~M. acknowledge the support of the Australian Government Research Training Program. Support for the ANU Heavy Ion Accelerator Facility operations through the Australian National Collaborative Research Infrastructure Strategy (NCRIS) program is also acknowledged.