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Register a new userRotational bands in Quadrupole-Octupole Collective Model
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A collective bands of positive and negative parity could be composed of the vibrations and rotations. The rotations of the octupole configurations can be based either on the axial or the non-axial octupole vibrations. A consistent approach to the quadrupole-octupole collective vibrations coupled with the rotational motion enables to distinguish between various scenarios of disappearance of the E2 transitions in negative-parity bands. The here presented theoretical estimates are compared with the recent experimental energies and transition probabilities in and between the ground-state and low-energy negaive-parity bands in $^{156}$Dy. A realistic collective Hamiltonian contains the potential energy term obtained through the macroscopic-microscopic Strutinsky-like method with particle-number-projected BCS approach and deformation-dependent mass tensor defined in vibrational-rotational, nine-dimensional collective space. The symmetrization procedure ensures the uniqueness of the Hamiltonian eigensolutions with respect to the laboratory coordinate system. This quadrupole-octupole collective approach may also allow to find and/or verify some fingerprints of possible high-order symmetries (e.g. tetrahedral, octahedral,...) in nuclear collective bands.
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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.
The direct transition-matrix approach to determination of the electric polarizabilities of quantum bound systems developed in my recent work is applied to study the electric multipole polarizabilities of a two-particle bound complex with a central interaction between the particles. Expressions for the electric quadrupole and octupole polarizabilities of the deuteron are derived and their values in the case of the S-wave separable interaction potential are calculated.
A parametrization of octupole plus quadrupole deformation, in terms of intrinsic variables defined in the rest frame of the overall tensor of inertia, is presented and discussed. The model is valid for situations close to the axial symmetry, but non axial deformation parameters are not frozen to zero. The properties of the octupole excitations in the deformed Thorium isotopes Th-226, Th-228 are interpreted in the frame of this model. A tentative interpretation of octupole oscillations in nuclei close to the X(5) symmetry, in terms of an exactly separable potential, is also discussed.
The matrix elements of the quadrupole variables and canonic conjugate momenta, emerging from collective nuclear models are calculated within a $SU(1,1)times O(5)$ basis. Using a harmonic oscillator implementation of the SU(1,1) degree of freedom, it can be shown that the matrix elements of the quadrupole phonon creation and annihilation operators can be calculated in a pure algebraic way, making use of an intermediate state method.
A reflection-asymmetric triaxial particle rotor model (RAT-PRM) with a quasi-proton and a quasi-neutron coupled with a reflection-asymmetric triaxial rotor is developed and applied to investigate the multiple chiral doublet (M$chi$D) bands candidates with octupole correlations in $^{78}$Br. The calculated excited energies, energy staggering parameters, and $B(M1)/B(E2)$ ratios are in a reasonable agreement with the data of the chiral doublet bands with positive- and negative-parity. The influence of the triaxial deformation $gamma$ on the calculated $B(E1)$ is found to be significant. By changing $gamma$ from 16$^circ$ to 21$^circ$, the $B(E1)$ values will be enhanced and better agreement with the $B(E1)/B(E2)$ data is achieved. The chiral geometry based on the angular momenta for the rotor, the valence proton and valence neutron is discussed in details.
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