Configuration-constrained calculations of high-<italic>K </italic>rotational bands in even-even isotones around <italic>N</italic>=100

Abstract

Nuclear rotational spectroscopy has been extensively investigated in experimental and theoretical studies. In the collective model, a nucleus can be excited in two ways. One is by breaking pairs of nucleons and exciting nucleons to a higher level. An excited state with a higher K -value sometimes has a long lifetime. Usually those states with lifetimes longer than 1 ns are called isomeric state because of forbidden transitions from high K to low K state. The other way is by collective motions, like rotation and vibration. A rotational band built on the multi-particle state is called a sideband. In general, a nucleus can have more than one sideband. Investigations of sidebands can provide rich information about the nucleus structure, like single-particle level, nuclear shape, and electromagnetic transitions and so on. The traditional total Routhian surface method, which is a powerful tool for investigating nuclear rotation, has been successfully used to describe yrast bands. However, it often encounters non-convergence problems when calculating sidebands. To overcome this problem, we recently developed a configuration-constrained cranking Skyrme Hartree-Fock mean-field calculation with pairing treated by the particle-number-conserving (PNC) method for sidebands. The PNC pairing method follows the technique of a “standard” shell model, which diagonalizes the Hamiltonian in a truncated model space and guarantees the conservation of the particle number. The rare-earth ( Z =57−71) neutron-rich nuclides are good candidates for investigating the high- K rotational bands. In this mass region, nuclei with N ≥90 are known to be well deformed and many high- j orbitals exist near the neutron and proton Fermi surfaces. These orbitals can form various multi-particle configurations and lead to high- K rotational sidebands. We perform configuration-constrained cranking Skyrme Hartree-Fock mean-field calculations with pairing treated using the PNC method for the high- K rotational bands in even-even isotones near N =100. The K π=6− rotational bands in 160Sm, 164Dy, 166Er, 168Yb, 170Er, and 172Yb and the K π=4− rotational bands in 168Er and 170Yb have been observed during experiments. K π=6− isomers were first observed in very neutron-rich nuclei, i.e., 158Nd, 164Sm, and 166Gd. Further, K π=4− isomers were first observed in neutron-rich N =100 isotones, i.e., 160Nd, 162Sm, and 164Gd. Theoretically, several models have been used to study these neutron-rich nuclei, including the cranked shell model, projected shell model, deformed Hartree-Fock method, cranking PNC method, and quasiparticle random phase approximation. We systematically investigated these high- K rotational bands and the ground state bands in N =98, 100, and 102 isotones using the configuration-constrained cranking Skyrme Hartree-Fock mean-field calculation with PNC pairing. The Skyrme force of SKM* is adopted. The pairing strength is determined using the odd-even mass difference and a three-point formula, which includes the mean-field and blocking effects. The calculations reproduce the experimental moments of inertia of both the ground state and sidebands well. Configurations are assigned to the observed high- K rotational bands. Further, we predict possible high- K rotational bands in 158Nd, 162Gd, 160Nd, 162Sm, 164Gd, and 166Dy. This study on high- K rotational bands can provide new insights into the structure of the states, and the predictions may provide useful information for future experiments.