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Register a new userRotational motion of triaxially deformed nuclei studied by microscopic angular-momentum-projection method II: Chiral doublet band
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In the sequel of the present study, we have investigated the rotational motion of triaxially deformed nucleus by using the microscopic framework of angular-momentum projection. The Woods-Saxon potential and the schematic separable-type interaction are employed as a microscopic Hamiltonian. As the first example nuclear wobbling motion was studied in detail in the part~I of the series. This second part reports on another interesting rotational mode, chiral doublet bands: two prototype examples, $^{128}$Cs and $^{104}$Rh, are investigated. It is demonstrated that the doublet bands naturally appear as a result of the calculation in this fully microscopic framework without any kind of core, and they have the characteristic properties of the $B(E2)$ and $B(M1)$ transition probabilities, which are expected from the phenomenological triaxial particle-rotor coupling model.
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Rotation of triaxially deformed nucleus has been an interesting subject in the study of nuclear structure. In the present series of work, we investigate wobbling motion and chiral rotation by employing the microscopic framework of angular-momentum projection from cranked triaxially deformed mean-field states. In this first part the wobbling motion is studied in detail. The consequences of the three dimensional cranking are investigated. It is demonstrated that the multiple wobbling rotational bands naturally appear as a result of fully microscopic calculation. They have the characteristic properties, that are expected from the macroscopic triaxial-rotor model or the phenomenological particle-triaxial-rotor model, although quantitative agreement with the existing data is not achieved. It is also found that the excitation spectrum reflects dynamics of the angular-momentum vector in the intrinsic frame of the mean-field (transverse vs. longitudinal wobbling). The results obtained by using the Woods-Saxon potential and the schematic separable interaction are mainly discussed, while some results with the Gogny D1S interaction are also presented.
We implemented a variation after projection (VAP) algorithm based on a triaxially deformed Hartree-Fock-Bogoliubov vacuum state. This is the first projected mean field study that includes all the quantum numbers (except parity), i.e., spin ($J$), isospin ($T$) and mass number ($A$). Systematic VAP calculations with $JTA$-projection have been performed for the even-even $sd$-shell nuclei with the USDB Hamiltonian. All the VAP ground state energies are within 500 keV above the exact shell model values. Our VAP calculations show that the spin projection has two important effects: (1) the spin projection is crucial in achieving good approximation of the full shell model calculation. (2) the intrinsic shapes of the VAP wavefunctions with spin projection are always triaxial, while the Hartree-Fock-Bogoliubov methods likely provide axial intrinsic shapes. Finally, our analysis suggests that one may not be possible to associate an intrinsic shape to an exact shell model wave function.
The effective field theory for collective rotations of triaxially deformed nuclei is generalized to odd-mass nuclei by including the angular momentum of the valence nucleon as an additional degree of freedom. The Hamiltonian is constructed up to next-to-leading order within the effective field theory formalism. The applicability of this Hamiltonian is examined by describing the wobbling bands observed in the lutetium isotopes $^{161,163,165,167}$Lu. It is found that by taking into account the next-to-leading order corrections, quartic in the rotor angular momentum, the wobbling energies $E_{textrm{wob}}$ and spin-rotational frequency relations $omega(I)$ are better described than with the leading order Hamiltonian.
Recently we have proposed a reliable method to describe the rotational band in a fully microscopic manner. The method has recourse to the configuration-mixing of several cranked mean-field wave functions after the angular-momentum-projection. By applying the method with the Gogny D1S force as an effective interaction, we investigate the moments of inertia of the ground state rotational bands in a number of selected nuclei in the rare earth region. As another application we try to describe, for the first time, the two-neutron aligned band in $^{164}$Er, which crosses the ground state band and becomes the yrast states at higher spins. Fairly good overall agreements with the experimental data are achieved; for nuclei, where the pairing correlations are properly described, the agreements are excellent. This confirms that the previously proposed method is really useful for study of the nuclear rotational motion.
The survey of different configurations near Fermi surface of 138Nd results in 12 lowest configurations, at both positive- and negative-deformations. These are calculated to be the energetically lowest configurations. The results show that, for both EDFs, the rotational states based on positive-minimum, which is at gamma~35, are lower than the respective configurations with negative-deformation. The general trends of the spin-versus-omega curve, and the energy-versus-spin curve reproduce well those of the experimental data. Further, for the observed bands `T1-T8, the calculated results using SLy4L allows the configurations of the observed bands to be assigned. The calculations predict transitional quadrupole moments, which can be used to compare with future experimental data. The current cranked self-consistent mean-field calculations of the near-yrast high-spin rotational bands in 138Nd reproduce well the experimental data. The results suggest that the experimentally observed bands can be assigned to the calculated bands with various configurations at the positive-deformation. The predictions of the current calculations are complementary to that of the well-know macroscopic-microscopic calculations, both of which await future experiment to verify.
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