Large-scale shell-model calculations of nuclei around mass 210

Large-scale shell-model calculations are performed for even-even, odd-mass, and doubly odd nuclei of Pb, Bi, Po, At, Rn, and Fr isotopes in the neutron deficit region $\left(Z\ge 82,N\le 126\right)$ assuming ${}^{208}\mathrm{Pb}$ as a doubly magic core. All the six single-particle orbitals between the magic numbers 82 and 126, namely, $0h_{9/2},1f_{7/2},0i_{13/2},2p_{3/2},1f_{5/2}$, and $2p_{1/2}$, are considered. For a phenomenological effective two-body interaction, one set of the monopole pairing and quadrupole-quadrupole interactions including the multipole-pairing interactions is adopted for all the nuclei considered. The calculated energies and electromagnetic properties are compared with the experimental data. Furthermore, many isomeric states are analyzed in terms of the shell-model configurations.

Figure 1

Theoretical energy spectra for even-even Pb isotopes in comparison with the experimental data. The squares and diamonds represent experimental positive and negative parity states, respectively. The asterisks and crosses represent theoretical positive and negative parity states, respectively. The experimental data are taken from Refs. [39, 40, 41]. Ambiguous states are shown with parentheses.

Figure 2

Same as Fig. 1, but for odd-mass Pb isotopes. The experimental data are taken from Refs. [39, 42, 43].

Figure 3

Same as Fig. 1, but for odd-mass Bi isotopes. The experimental data are taken from Refs. [39, 43, 45].

Figure 4

Same as Fig. 1, but for doubly odd Bi isotopes. The experimental data are taken from Refs. [17, 23, 39, 40, 41].

Figure 5

Same as Fig. 1, but for even-even Po isotopes. The experimental data are taken from Refs. [17, 39, 41, 48].

Figure 6

Same as Fig. 1, but for odd-mass Po isotopes. The experimental data are taken from Refs. [39, 43, 45, 49].

Figure 7

Same as Fig. 1, but for odd-mass At isotopes. The experimental data are taken from Refs. [39, 45, 49, 50].

Figure 8

Same as Fig. 1, but for doubly odd At isotopes. The experimental data are taken from Refs. [17, 39, 41, 48].

Figure 9

Same as Fig. 1, but for even-even Rn isotopes. The experimental data are taken from Refs. [17, 19, 39, 48, 52].

Figure 10

Same as Fig. 1, but for odd-mass Rn isotopes. The experimental data are taken from Refs. [39, 45, 49, 50].

Figure 11

Same as Fig. 1, but for odd-mass Fr isotopes. The experimental data are taken from Refs. [39, 49, 50, 53].

Figure 12

Same as Fig. 1, but for doubly odd Fr isotopes. The experimental data are taken from Refs. [17, 22, 39, 48, 52].

Figure 13

Comparison between the experimental spectra (expt.) and the shell-model results with (calc. with) and without (calc. without) the $\mathrm{MP}$-8 interaction for positive parity states in ${}^{210}\mathrm{Po}$. The experimental data are taken from Refs. [39, 48]. The states with the energy difference of more than 0.1 MeV between those with and without the $\mathrm{MP}$-8 interaction are indicated by dotted lines.

Figure 14

Same as Fig. 13, but for negative parity states of ${}^{211}\mathrm{At}$. Spin is denoted by twice the original value. The experimental data are taken from Refs. [39, 50]. Only the first and second states for each spin are shown.

Figure 15

Same as Fig. 13, but for positive parity states of ${}^{212}\mathrm{Rn}$. The experimental data are taken from Refs. [39, 52]. Only the first and second states for each spin are shown. The ${14}_2^{+}$ state calculated without the $\mathrm{MP}$-8 interaction is not shown in the figure, but this state is predicted at 5.282 MeV.

Figure 16

Comparison between the experimental spectra (expt.) and the shell-model results with (calc. with) and without (calc. without) the particle number dependence of the $i_{13/2}$ orbitals for ${}^{205}\mathrm{Po}$. The experimental data are taken from Refs. [39, 43]. Only the first and second states for each spin and parity are shown. Spin is denoted by twice the original value.

Figure 17

Same as Fig. 16, but for ${}^{207}\mathrm{Rn}$. The experimental data are taken from Refs. [39, 45].

Figure 18

Theoretical energy levels for positive parity states in ${}^{208}\mathrm{Fr}$. The circles and triangles represent the theoretical results of the positive-positive configuration and negative-negative configurations, respectively. Up to four calculated states are shown for each spin and each configuration.