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Register a new userMicroscopic description of octupole shape-phase transitions in light actinides and rare-earth nuclei
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A systematic analysis of low-lying quadrupole and octupole collective states is presented, based on the microscopic energy density functional framework. By mapping the deformation constrained self-consistent axially symmetric mean-field energy surfaces onto the equivalent Hamiltonian of the $sdf$ interacting boson model (IBM), that is, onto the energy expectation value in the boson condensate state, the Hamiltonian parameters are determined. The study is based on the global relativistic energy density functional DD-PC1. The resulting IBM Hamiltonian is used to calculate excitation spectra and transition rates for the positive- and negative-parity collective states in four isotopic chains characteristic for two regions of octupole deformation and collectivity: Th, Ra, Sm and Ba. Consistent with the empirical trend, the microscopic calculation based on the systematics of $beta_{2}$-$beta_{3}$ energy maps, the resulting low-lying negative-parity bands and transition rates show evidence of a shape transition between stable octupole deformation and octupole vibrations characteristic for $beta_{3}$-soft potentials.
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The evolution of quadrupole and octupole collectivity and their coupling is investigated in a series of even-even isotopes of the actinide Ra, Th, U, Pu, Cm, and Cf with neutron number in the interval $130leqslant Nleqslant 150$. The Hartree-Fock-Bogoliubov approximation, based on the parametrization D1M of the Gogny energy density functional, is employed to generate potential energy surfaces depending upon the axially-symmetric quadrupole and octupole shape degrees of freedom. The mean-field energy surface is then mapped onto the expectation value of the $sdf$ interacting-boson-model Hamiltonian in the boson condensate state as to determine the strength parameters of the boson Hamiltonian. Spectroscopic properties related to the octupole degree of freedom are produced by diagonalizing the mapped Hamiltonian. Calculated low-energy negative-parity spectra, $B(E3;3^{-}_{1}to 0^{+}_{1})$ reduced transition rates, and effective octupole deformation suggest that the transition from nearly spherical to stable octupole-deformed, and to octupole vibrational states occurs systematically in the actinide region.
``Beat patterns are shown to appear in the octupole bands of several actinides and rare earths, their appearance being independent from the formula used in order to isolate and demonstrate them. It is shown that the recent formalism, making use of discrete approximations to derivatives of the transition energies (or of the energy levels) gives results consistent with the traditional formulae. In both regions it is seen that the first vanishing of the staggering occurs at higher values of the angular momentum I in nuclei exhibiting higher staggering at low I. Since these nuclei happen to be good rotators, the observed slow decrease of the amplitude of the staggering with increasing I is in good agreement with the parameter independent predictions of the su(3) (rotational) limit of several algebraic models. In the actinides it has been found that within each series of isotopes the odd-even staggering exhibits minima at N=134 and N=146, while a local maximum is shown at N=142, these findings being in agreement with the recent suggestion of a secondary maximum of octupole deformation around N=146.
The dynamics of nuclear collective motion is investigated in the case of reflection-asymmetric shapes. The model is based on a new parameterization of the octupole and quadrupole degrees of freedom, valid for nuclei close to the axial symmetry. Amplitudes of oscillation in other degrees of freedom different from the axial ones are assumed to be small, but not frozen to zero. The case of nuclei which already possess a permanent quadrupole deformation is discussed in some more detail and a simple solution is obtained at the critical point of the phase transition between harmonic octupole oscillation and a permanent asymmetric shape. The results are compared with experimental data of the Thorium isotopic chain. The isotope Th-226 is found to be close to the critical point.
Octupole deformations and related collective excitations are analyzed using the framework of nuclear density functional theory. Axially-symmetric quadrupole-octupole constrained self-consistent mean-field (SCMF) calculations with a choice of universal energy density functional and a pairing interaction are performed for Xe, Ba, and Ce isotopes from proton-rich to neutron-rich regions, and neutron-rich Se, Kr, and Sr isotopes, in which enhanced octupole correlations are expected to occur. Low-energy positive- and negative-parity spectra and transition strengths are computed by solving the quadrupole-octupole collective Hamiltonian, with the inertia parameters and collective potential determined by the constrained SCMF calculations. Octupole-deformed equilibrium states are found in the potential energy surfaces of the Ba and Ce isotopes with $Napprox 56$ and 88. The evolution of spectroscopic properties indicates enhanced octupole correlations in the regions corresponding to $Napprox Zapprox 56$, $Zapprox 88$ and $Zapprox 56$, and $Napprox 56$ and $Zapprox 34$. The average $beta_{30}$ deformation parameter and its fluctuation exhibit signatures of octupole shape phase transition around $N=56$ and 88.
Fission of $^{180}$Hg produces mass asymmetric fragments which are expected to be influenced by deformed shell-effects at N=56 in the heavy fragment and Z=34 in the light fragment [G. Scamps and C. Simenel, arXiv:1904.01275 (2019)]. To investigate both shell-effects and to determine which one has the main influence on the asymmetry in the region of the $^{180}$Hg, we produce a systematic of Constraint-Hartree-Fock calculations in nuclei with similar N/Z ratio than the $^{178}$Pt. It is found that N=56 determines the asymmetry of systems in this region of the nuclear chart.
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