Octupole states in $^{207}$Tl studied through $β$ decay

The $β$ decay of $^{207}$Hg into the single-proton-hole nucleus $^{207}$Tl has been studied through $γ$-ray spectroscopy at the ISOLDE Decay Station (IDS) with the aim of identifying states resulting from coupling of the $πs^{−1}_{1/2}, πd^{−1}_{3/2},$ and $πh^{−1}_{11/2}$ shell model orbitals to the collective octupole vibration. Twenty-two states were observed lying between 2.6 and 4.0 MeV, eleven of which were observed for the first time, and 78 new transitions were placed. Two octupole states (s1/2-coupled) are identified and three more states ($d_{3/2}$-coupled) are tentatively assigned using spin-parity inferences, while further $h_{11/2}$-coupled states may also have been observed for the first time. Comparisons are made with state-of-the-art large-scale shell model calculations and previous observations made in this region, and systematic underestimation of the energy of the octupole vibrational states is noted. We suggest that in order to resolve the difference in predicted energies for collective and noncollective $t=1$ states ($t$ is the number of nucleons breaking the $^{208}$Pb core), the effect of $t=2$ mixing may be reduced for octupole-coupled states. The inclusion of mixing with $t=0,2,3$ excitations is necessary to replicate all $t=1$ state energies accurately.