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Register a new userEvidence for rotational to vibrational evolution along the yrast line in the odd-A rare-earth nuclei
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The phase transition of nuclei to increasing angular momentum (or spin) and excitation energy is one of the most fundamental topics of nuclear structure research. The odd-N nuclei with A equal 160 are widely considered belonging to the well-deformed region, and their excitation spectra are energetically favored to exhibit the rotational characteristics. In the present work, however, there is evidence indicating that the nuclei can evolve from rotation to vibration along the yrast lines while increasing spin. The simple method, named as E-Gamma Over Spin (E-GOS) curves, would be used to discern the evolution from rotational to vibrational structure in nuclei as a function of spin. In addition, in order to get the insight into the rotational-like properties of nuclei, theoretical calculations have been performed for the yrast bands of the odd-A rare-earth nuclei using the total Routhian surfaces (TRS) model. The TRS plots indicate that the 165Yb and 157Dy isotopes have stable prolate shapes at low spin states. At higher rotational frequency (larger than 0.50 MeV), a distinct decrease in the quadrupole deformation is predicted by the calculations, and the isotopes becomes rigid in the gamma deformation.
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The yrast lines in Kr isotopes with $N=42$, 44, and 46 are investigated in a beyond mean field framework with both prolate-oblate coexistence and quasiparticle alignment taken into account. Quasiparticle orbitals with high-$j$ and low-$Omega$ on the oblate side are shown to be responsible for the sharp backbending observed in $^{82}$Kr, by driving the yrast shape from prolate to oblate. This suggests that quasiparticle alignment may not be neglected in the investigation of the shape evolution along the yrast line.
Distribution of the two phonon $gamma$ vibrational collectivity in the rotating triaxial odd-$A$ nucleus, $^{103}$Nb, that is one of the three nuclides for which experimental data were reported recently, is calculated in the framework of the particle vibration coupling model based on the cranked shell model plus random phase approximation. This framework was previously utilized for analyses of the zero and one phonon bands in other mass region and is applied to the two phonon band for the first time. In the present calculation, three sequences of two phonon bands share collectivity almost equally at finite rotation whereas the $K=Omega+4$ state is the purest at zero rotation.
We present an outline of an extensive study of the effects of collective couplings and nuclear deformations on integrated cross sections as well as on angular distributions in a consistent manner for neutron-induced reactions on nuclei in the rare-earth region. This specific subset of the nuclide chart was chosen precisely because of a clear static deformation pattern. We analyze the convergence of the coupled-channel calculations regarding the number of states being explicitly coupled. A model for deforming the spherical Koning-Delaroche optical potential as function of quadrupole and hexadecupole deformations is also proposed, inspired by previous works. We demonstrate that the obtained results of calculations for total, elastic, inelastic, and capture cross sections, as well as elastic and inelastic angular distributions are in remarkably good agreement with experimental data for scattering energies around a few MeV.
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.
Inspired by the recent work by Dietrich et al., substantiating validity of the adiabatic assumption in coupled-channel calculations, we explore the possibility of generalizing a global spherical optical model potential (OMP) to make it usable in coupled-channel calculations on statically deformed nuclei. The generalization consists in adding the coupling of the ground state rotational band, deforming the potential by introducing appropriate quadrupole and hexadecupole deformation and correcting the OMP radius to preserve volume integral of the spherical OMP. We choose isotopes of three rare-earth elements (W, Ho, Gd), which are known to be nearly perfect rotors, to perform a consistent test of our conjecture on integrated cross sections as well as on angular distributions for elastic and inelastic neutron scattering. When doing this we employ the well-established Koning-Delaroche global spherical potential and experimentally determined deformations without any adjustments. We observe a dramatically improved agreement with experimental data compared to spherical optical model calculations. The effect of changing the OMP radius to preserve volume integral is moderate but visibly improves agreement at lower incident energies. We find that seven collective states need to be considered for the coupled-channel calculations to converge. Our results for total, elastic, inelastic, and capture cross sections, as well as elastic and inelastic angular distributions are in remarkable agreement with experimental data. This result confirms that the adiabatic assumption holds and can extend applicability of the global spherical OMP to rotational nuclei in the rare-earth region, essentially without any free parameter. Thus, quite reliable coupled-channel calculations can be performed on such nuclei even when the experimental data, and consequently a specific coupled-channel potential, are not available.
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