Large-scale shell-model calculations on the spectroscopy of $N<126$ Pb isotopes

Large-scale shell-model calculations are carried out in the model space including neutron-hole orbitals $2p_{1/2},1f_{5/2},2p_{3/2},0i_{13/2},1f_{7/2}$, and $0h_{9/2}$ to study the structure and electromagnetic properties of neutron-deficient Pb isotopes. An optimized effective interaction is used. Good agreement between full shell-model calculations and experimental data is obtained for the spherical states in isotopes ${}^{194-206}\mathrm{Pb}$. The lighter isotopes are calculated with an importance-truncation approach constructed based on the monopole Hamiltonian. The full shell-model results also agree well with our generalized seniority and nucleon-pair-approximation truncation calculations. The deviations between theory and experiment concerning the excitation energies and electromagnetic properties of low-lying $0^{+}$ and $2^{+}$ excited states and isomeric states may provide a constraint on our understanding of nuclear deformation and intruder configuration in this region.

Figure 1

Dimensions of the $M^{\pi }=0^{+}$ (circle) and the corresponding $J^{\pi }=0^{+}$ (square) states in even-even Pb isotopes with $N<126$ as a function of valence neutron (hole) numbers. $M,J$, and $N$ denote the total magnetic quantum number, total spin, and the number of valence neutrons, respectively. The green diamonds correspond to the total number of partitions (particle distributions). The dashed lines correspond to the limit of present shell-model calculations.

Figure 2

Convergence of the shell-model energies for the lowest three states in nucleus ${}^{194}\mathrm{Pb}$ as a function of the fraction of the $M$-scheme bases consider. $D$ is the total number of bases while $d$ denotes the number of bases considered in the truncated shell-model calculations.

Figure 3

Experimental data and shell-model calculations on the low-lying spectrum of ${}^{206}\mathrm{Pb}$.

Figure 4

Experimental and shell-model calculated low-lying spectra of ${}^{204}\mathrm{Pb}$.

Figure 5

Experimental and shell-model calculated low-lying spectra of ${}^{202}\mathrm{Pb}$.

Figure 6

Experimental and shell-model calculated low-lying spectra of ${}^{200}\mathrm{Pb}$.

Figure 7

Experimental and shell-model calculated low-lying spectra of ${}^{198}\mathrm{Pb}$.

Figure 8

Experimental and shell-model calculated low-lying spectra of ${}^{196}\mathrm{Pb}$.

Figure 9

Experimental and NPA calculated low-lying spectra of ${}^{204}\mathrm{Pb}$.

Figure 10

Experimental and NPA calculated low-lying spectra of ${}^{202}\mathrm{Pb}$.

Figure 11

Experimental and NPA calculated low-lying spectra of ${}^{200}\mathrm{Pb}$.

Figure 12

Experimental and shell-model calculated low-lying spectra of ${}^{194}\mathrm{Pb}$.

Figure 13

Left: Experimental [84] (solid symbols) and shell-model calculated (open symbols) excitation energies for the first-excited (circle) and second-excited (square) $0^{+}$ states in Pb isotopes as a function of neutron number. The dashed lines correspond to calculations with the generalized seniority model with the truncation $v=6$.

Figure 14

(a) Experimental [91] and shell-model calculated shell-model correlation energies [Eq. (2)] as a function of neutron number. (b) The empirical pairing gaps as extracted according to Eq. (4).

Figure 15

Experimental (circle) [92] and shell-model calculated (square) quadrupole moments for the ${12}^{+}$ (a), $13/2+$ (b), and $33/2^{+}$ (c) states in even and odd Pb isotopes. The dashed lines correspond to the average number of neutron holes in the $i_{13/2}$ orbital. The blue long dashed line in the upper panel is the predictions by the generalized seniority calculations with $v=6$.

Figure 16

Experimental [96] (circle) and shell-model calculated (diamond) $B$($E2$; $0_1{}^{+}\to 2_1{}^{+}$) values for even-even Pb isotopes. The blue line corresponds to predictions by the generalized seniority model. The open symbols are preliminary results from Ref. [97].