First proton-pair breaking in semi-magic nuclei beyond ${}^{\mathbf{132}}$Sn and ${}^{\mathbf{208}}$Pb: Configuration of the long-lived isomer of ${}^{\mathbf{217}}$Pa

The close similarity between the shell structures in the ${}^{132}$Sn and ${}^{208}$Pb regions is a well known phenomenon. Thus, using the correspondence between the high-$j$ orbits located above the $Z=50$ and $Z=82$ shell gaps, we discuss the evolutions of the fully aligned states with one broken proton pair in the $N=82$ and $N=126$ isotones. A long-lived isomeric state was discovered in ${}^{217}$Pa more than thirty years ago and, despite two other experiments giving new experimental results, the discussions on its main properties (spin, parity, configuration) remained inconclusive. Then, using the comparison with the $I^{\pi }=17/2^{+}$ isomeric state recently measured in ${}^{139}$La, the isomeric state of ${}^{217}$Pa is assigned as the fully aligned state of the ${\left(\pi h_{9/2}\right)}^2{\left(\pi f_{7/2}\right)}^1$ configuration.

Figure 1

Experimental excitation energies of the fully-aligned states with one broken proton pair in the $N=82$ isotones with $52\le Z\le 58$, involving the three high-$j$ orbits located just above the $Z=50$ gap, $\pi g_{7/2}$, $\pi d_{5/2}$, and $\pi h_{11/2}$ (a), and in the $N=126$ isotones with $84\le Z\le 92$, involving the three high-$j$ orbits located just above the $Z=82$ gap, $\pi h_{9/2}$, $\pi f_{7/2}$, and $\pi i_{13/2}$ (b). The isomeric states are drawn with filled symbols. The ellipse drawn at $Z=56\left(90\right)$ means that the two 6${}^{+}$(8${}^{+}$) states are strongly mixed. The low-lying isomeric states measured in ${}_{57}^{137}$La and ${}_{91}^{217}$Pa and discussed in this paper are marked.

Figure 2

Systematics of the first excited states of the $N=126$ isotones with $84\le Z\le 92$; the colored states are the fully aligned states with one broken proton pair shown in Fig. 1b. The $g$ factors of most of the 8${}_1^{+}$, 11${}^{-}$, 21/2${}^{-}$, and 29/2${}^{+}$ states have been measured, confirming their proton configurations (see for instance, Figs. 4(a) and 4(b) of Ref. [8]). The $\alpha$-decaying states of ${}^{216}$Th, ${}^{217}$Pa, and ${}^{218}$U are drawn with a thicker line. The experimental data come from Refs. [8, 9, 10] for $Z=89$, 91, and 92, respectively and from the “Evaluated Nuclear Structure Data File” [4] for the others.