Description of collective and quasiparticle excitations in deformed actinide nuclei: The first application of the multishell shell model for heavy nuclei

The heavy shell model (HSM) [Y. Sun and C.-L. Wu, Phys. Rev. C 68, 024315 (2003)] was proposed to take the advantages of two existing models, the projected shell model (PSM) and the fermion dynamical symmetry model (FDSM). To construct the HSM, one extends the PSM by adding collective $D$ pairs into the intrinsic basis. The HSM is expected to describe simultaneously low-lying collective and quasiparticle excitations in deformed nuclei, and still keeps the model space tractable even for the heaviest systems. As the first numerical realization of the HSM, we study systematically the band structures for some deformed actinide nuclei, with a model space including up to 4-quasiparticle and 1-$D$-pair configurations. The calculated energy levels for the ground-state bands, the collective bands such as $\beta$ and $\gamma$ bands, and some quasiparticle bands agree well with known experimental data. Some low-lying quasiparticle bands are predicted, awaiting experimental confirmation.

Figure 1

Comparison of the angular momentum projected energies and the bandhead energies for $(I^{\pi },K^{\pi })=(0^{+},0^{+})$ and $(I^{\pi },K^{\pi })=(2^{+},2^{+})$ states of ${}^{232}\mathrm{U}$, respectively. The projected energies represent the values of $H_{0\kappa ,0\kappa }^{I=0}/N_{0\kappa ,0\kappa }^{I=0}$ and $H_{2\kappa ,2\kappa }^{I=2}/N_{2\kappa ,2\kappa }^{I=2}$, respectively. The bandhead energies indicate the energies after the diagonalization of Hamiltonian matrix [see Eq. (8)].

Figure 2

Comparison of the calculated and experimental g.s. bands, and $\beta$ and $\gamma$ bands of ${}^{230}\mathrm{Th}$. Some 2-qp and 4-qp rotational bands are also given as a theoretical prediction. The experimental energies are from the National Nuclear Data Center, Ref. [32] and references therein.

Figure 3

Same as Fig. 2, but for ${}^{232}\mathrm{Th}$.

Figure 4

Same as Fig. 2, but for ${}^{232}\mathrm{U}$.

Figure 5

Same as Fig. 2, but for ${}^{234}\mathrm{U}$.

Figure 6

Same as Fig. 2, but for ${}^{236}\mathrm{U}$.

Figure 7

Same as Fig. 2, but for ${}^{240}\mathrm{Pu}$.

Figure 8

Comparison of the calculated $S\left(J\right)$ values of $\gamma$-vibrational bands with experimental data for ${}^{230,232}$Th, ${}^{232,234,236}$U, and ${}^{240}\mathrm{Pu}$, respectively.