In this work we examine the possibility to describe yrast positive- and negative-parity excitations of deformed even-even nuclei through a collective rotation model in which the nuclear surface is characterized by triaxial quadrupole and octupole deformations. The nuclear moments of inertia are expressed as sums of quadrupole and octupole parts. By assuming an adiabatic separation of rotation and vibration degrees of freedom we suppose that the structure of the positive- and negative- parity bands may be determined by the triaxial-rigid-rotor motion of the nucleus. By diagonalizing the Hamiltonian in a symmetrized rotor basis with embedded parity we obtain a model description for the yrast positive- and negative-parity bands in several actinide nuclei. We show that the energy displacement between the opposite-parity sequences can be explained as the result of the quadrupole-octupole triaxiality.

A model of strongly coupled quadrupole and octupole vibrations and rotations is applied to describe non-yrast alternating-parity sequences in even-even nuclei and split parity-doublet spectra in odd-mass nuclei. In even-even nuclei the yrast alternating-parity sequence includes the ground-state band and the lowest negative-parity levels with odd angular momenta, while the non-yrast sequences include excited beta-bands and higher negative-parity levels. In odd-mass nuclei the yrast levels are described as low-energy rotation-vibration modes coupled to the ground single-particle (s.p.) state, while the non-yrast parity-doublets are obtained as higher-energy rotation-vibration modes coupled to excited s.p. configurations. We show that the extended model scheme describes the yrast and non-yrast quadrupole-octupole spectra in both even-even and odd-A nuclei. The involvement of the reflection-asymmetric deformed shell model to explain the single-particle motion and the Coriolis interaction in odd nuclei is discussed.

The model of coherent quadrupole and octupole motion (CQOM) is applie d to describe non-yrast split parity-doublet spectra in odd-mass nuclei. T h yrast levels are described as low-energy rotation-vibration modes coupled to the g round single-particle state, while the non-yrast parity-doublet structures are o btained as higher-energy rotation-vibration modes. It is shown that the extende d model scheme describes both the yrast and non-yrast quasi-parity doublet spectra and the related B(E1) and B(E2) transition rates in different regions of heav y odd-A nuclei. The involvement of the reflection-asymmetric deformed shell mo del to describe the single-particle motion and the Coriolis interaction on a deeper lev el is discussed.

A further extension of a model of coherent quadrupole–octupole vibrations and rotations and its application to alternating-parity spectra in heavy even–even nuclei is presented. Within the model the yrast alternating-parity sequence includes the ground state band and the lowest negative parity levels with odd angular momenta, while the non-yrast sequences include excited β-bands and higher negative-parity levels. Electric transition operators reflecting the complex shape characteristics associated with the quadrupole–octupole vibration modes are introduced. By using them B(E1), B(E2) and B(E3) reduced transition probabilities within and between the different energy sequences are calculated. It is shown that the model successfully reproduces yrast and non-yrast alternating-parity bands together with the attendant B(E1)–B(E3) transition rates in the nuclei 154 Sm , 156 Gd and 100 Mo .

The model of coherent quadrupole and octupole motion is applied to describe non-yrast split parity-doublet spectra in odd-mass nuclei. The yrast levels are described as low-energy rotation-vibration modes coupled to the ground single-particle (s.p.) state, while the non-yrast parity-doublet structures are obtained as higher-energy rotation-vibration modes coupled to excited s.p. states. It is shown that the extended model scheme describes both the yrast and non-yrast quasi parity-doublet spectra and the related B(E1) and B(E2) transition rates in different regions of heavy odd-A nuclei. The involvement of the reflection-asymmetric deformed shell model to describe the single-particle motion and the Coriolis interaction on a deeper level is discussed.

Effects of the parity-mixed single-particle (s.p.) state on the collective properties of odd nuclei with reflection-asymmetric degrees of freedom are studied. The Coriolis strength and the average s.p. parity in the nuclei 219 Ra , 225 Ra , 225 Th and 241 Cm are examined in dependence on axial quadrupole and octupole deformation parameters β2 and β3 within a reflection-asymmetric deformed shell model. The obtained behaviour of the Coriolis decoupling factor in the (β2, β3)-plane is compared with values fitted in a collective quadrupole-octupole model, which allows one to determine physically reasonable deformation regions for the considered nuclei. The study provides a relation between deformation parameters, Coriolis interaction strength and the structure of collective spectra in odd-mass nuclei with quadrupole-octupole deformations.

The Coriolis decoupling strength in nuclear single-particle (s.p.) states with mixed parity is examined within a reflection-asymmetric deformed shell model. A strong coupling scheme between the parity mixed s.p. state and a coherent quadrupole–octupole vibration mode in the core is considered for odd-mass nuclei. The Coriolis decoupling factor is obtained in a projected form corresponding to good total parity of the system. The average parity of the s.p. state and the decoupling factor are evaluated in several nuclei as functions of the quadrupole and octupole deformation parameters β2 and β3. It is found that the average s.p. parity obtains various dominant values in the (β2, β3)-plane. It is shown that by comparing the behaviour of the decoupling factor in the (β2, β3)-plane to values obtained in a collective quadrupole–octupole model and by requiring consistency between the calculated dominant parity and the experimentally established parity in the ground state one can determine physically reasonable deformation regions for the considered odd-A nuclei.

The effect of parity mixing in the single particle (s.p.) states of odd-mass nuclei with quadrupole-octupole deformations is examined through a reflection-asymmetric deformed shell model. A strong coupling scheme between the parity mixed s.p. state and a coherent quadrupole-octupole vibration mode in the core is considered. The Coriolis decoupling factor is obtained in a projected form corresponding to the good total parity of the system. The average parity of the s.p. state and the decoupling factor are evaluated in several nuclei as functions of the quadrupole and octupole deformation parameters β2 and β3. It is found that the average s.p. parity obtains various dominant (+ or −) values in the (β2,β3)-plane, while the s.p. wave function is strongly fragmented into components with different parities. It is shown that by comparing the behaviour of the decoupling factor in the (β2,β3)-plane to values obtained in a collective quadrupole-octupole model one can determine physically reasonable regions for the deformation parameters.

Based on a recent application of the collective model of coherent quadrupole–octupole oscillations and rotations in odd-mass nuclei we develop an algorithm for a microscopic calculation of the Coriolis interaction strength. It is realized by using the reflection asymmetric deformed shell model. The single-particle (s.p.) wavefunction is obtained in the basis of the axially deformed harmonic oscillator (ADHO). The Coriolis interaction strength is calculated after transforming the ADHO decomposition coefficients of the wavefunction into coefficients in the basis of the spherical harmonic oscillator (SHO). The transformation brackets relating the ADHO and SHO basis functions are numerically integrated. Calculations were implemented for several nuclei in which the parity doublet spectra are known or supposed to be built on a single-particle orbital with Ω = 1/2. The results show the applicability of this approach to study the effects of Coriolis interaction in nuclei with quadrupole and octupole deformations as well as to examine their s.p. and shape characteristics.

The collective model of nuclear coherent quadrupole-octupole oscillations and ro- tations gives a specific test for the influence of Coriolis interaction between the even-even core and the unpaired nucleon on the split parity-doublet spectra in odd-mass nuclei. It provides model estimations for the angular momentum projection K on the intrinsic symmetry axis and the related intrinsic nuclear structure. Based on this result we propose a study of the con- nection between collective shape characteristics and the intrinsic reflection-asymmetric shell structure of the nucleus. The analysis of the Coriolis interaction with deformed reflection- asymmetric shell-model calculations shows consistency with the results of the model of co- herent quadrupole-octupole motion.