Quadrupole-octupole Deformation Research Articles

Th229m isomer from a nuclear model perspective

The physical conditions for the emergence of the extremely low-lying nuclear isomer $^{229m}$Th at approximately 8 eV are investigated in the framework of our recently proposed nuclear structure model. Our theoretical approach explains the $^{229m}$Th-isomer phenomenon as the result of a very fine interplay between collective quadrupole-octupole and single-particle dynamics in the nucleus. We find that the isomeric state can only appear in a rather limited model space of quadrupole-octupole deformations in the single-particle potential, with the octupole deformation being of a crucial importance for its formation. Within this deformation space the model-described quantities exhibit a rather smooth behaviour close to the line of isomer-ground state quasi-degeneracy determined by the crossing of the corresponding single-particle orbitals. Our comprehensive analysis confirms the previous model predictions for reduced transition probabilities and the isomer magnetic moment, while showing a possibility for limited variation in the ground-state magnetic moment theoretical value. These findings prove the reliability of the model and suggest that the same dynamical mechanism could manifest in other actinide nuclei giving a general prescription for the search and exploration of similar isomer phenomena.

Shape and electromagnetic properties of the229mTh isomer

We examine the physical conditions, and specifically the role of the quadrupole-octupole deformation, for the emergence of the 8 eV “clock” isomer229mTh. Our nuclear structure model suggests that such an extremely low-energy state can be the result of a very fine interplay between the shape and single-particle (s.p.) dynamics in the nucleus. We find that the isomer can only appear in a rather limited region of quadrupoleoctupole deformation space close to a line along which the ground-state and isomer s.p. orbitals 5/2[633] and 3/2[631], respectively, cross each other providing the isomer-formation quasi-degeneracy condition. The crucial role of the octupole deformation in the formation mechanism is pointed out. Our calculations within the outlined deformation region show a smooth behaviour of the229Th electromagnetic properties, including the isomer decay rate, allowing for their more precise theoretical determination

Vibrational-rotational spectra of even–even nuclei with quadrupole and octupole deformations

Vibrational-rotation levels of the yrast and first nonyrast alternating-parity bands of the lanthanide [Formula: see text]Nd, [Formula: see text]Sm, [Formula: see text]Gd, [Formula: see text]Er and actinide [Formula: see text]Th, [Formula: see text]U, [Formula: see text]Pu nuclei are studied in the framework of a nonadiabatic collective model of even–even nuclei with quadrupole and octupole deformations. The theoretical spectra are obtained through the use of Gauss and harmonic-oscillator (HO) potentials in the radial part of the Schrödinger equation which is taken in polar coordinates. The change of the surface deformation of the nucleus with the collective excitation energy is taken into account. The [Formula: see text] staggering structure of the yrast alternating-parity bands is also considered. The theoretically obtained energy bands and staggering diagrams are in good agreement with the corresponding experimental data and point out the soft character of the collective quadrupole–octupole deformation mode manifesting in these nuclei.

Beyond mean-field approach for pear-shaped hypernuclei

We develop both relativistic mean field and beyond approaches for hypernuclei with possible quadrupole-octupole deformation or pear-like shapes based on relativistic point-coupling energy density functionals. The symmetries broken in the mean-field states are recovered with parity, particle-number, and angular momentum projections. We take $^{21}_\Lambda$Ne as an example to illustrate the method, where the $\Lambda$ hyperon is put on one of the two lowest-energy orbits (labeled as $\Lambda_s, \Lambda_p$), respectively. We find that the $\Lambda$ hyperon in both cases disfavors the formation of a reflection-asymmetric molecular-like $^{16}$O$+\alpha$ structure in $^{20}$Ne, which is consistent with the Nilsson diagram for the hyperon in $(\beta_2, \beta_3)$ deformation plane. In particular, we show that the negative-parity states with the configuration $^{20}$Ne($K^\pi=0^-)\otimes \Lambda_s$ are close in energy to those with the configuration $^{20}$Ne($K^\pi=0^+)\otimes \Lambda_p$, even though they have very different structures. The $\Lambda_s$ ($\Lambda_p$) becomes more and more concentrated around the bottom (top) of the "pear" with the increase of octupole deformation.

Alternating Parity Band in Octupole-Soft 140Xe with Axial Vibrational-Rotational Model and Triaxial Rigid Rotor Model**Supported by the National Natural Science Foundation of China under Grant Nos 11675094 and 11622540, and the Young Scholars Program of Shandong University under Grant No 2015WHWLJH01.

Energies of the yrast positive- and negative-parity excited states in 140Xe are reproduced by two different models considering quadrupole-octupole deformations, namely the axial vibrational-rotational model and the triaxial rigid rotor model, and compared with the stable octupole-deformed 222Th. The origin of the energy difference between the opposite parity sequences is considered from two different mechanisms, the vibration in axial deformed energy minima and the rotation considering the effective triaxial deformation. The success of reproducing the data in both the models implies that these two mechanisms are equivalent on some level for the octupole-soft nuclei. By investigating the probability distributions for projection of total angular momentum in the triaxial rigid rotor model, it is found that such an energy difference is associated with the difference of orientation of the rotational axis.

Effects of the shape and Coriolis interaction in nuclear electromagnetic properties

We study the manifestation of collective vibrations and rotations coupled to single-particle motion in odd-mass nuclei with the presence of axial quadrupole-octupole deformations. Our model incorporates K-mixing effects stemming from the Coriolis interaction between the odd nucleon and the even-even core and thus takes into account the probabilities for otherwise forbidden due to the axial symmetry electromagnetic transitions between excited states built on different intrinsic configurations. We demonstrate these effects in the quasi-parity-doublet spectrum of the nucleus 221Fr in which a strong Coriolis interaction manifests. The model successfully describes the available intra- and interband E1, E2 and M1 transition rates giving an insight into the mechanism which allows the K-suppressed transitions in axially symmetric nuclei.

Nuclear alternating parity bands and transition rates in a model of coherent quadrupole–octupole motion in neutron-rich barium isotopes

Deformed even–even nuclei Barium isotopes with quadrupole–octupole deformations are investigated on the basis of a collective model. The model describes energy levels of the yrast band with alternating parity in the neutron-rich \(^{140,142,144,146,148}\)Ba. The structure of the alternating parity bands is examined by odd–even \((\Delta I =1)\) staggering diagrams. An analytical method of the collective model is proposed for the calculation of E2 transition probabilities in alternating spectra of the nuclei \({}^{140,142,144,146}\)Ba.

Octupole deformations in high-Kisomeric states of heavy and superheavy nuclei

We study the effects of quadrupole-octupole deformations on the energy and magnetic properties of high-K isomeric states in even-even heavy and superheavy nuclei. The neutron two-quasiparticle (2qp) isomeric energies and magnetic dipole moments are calculated within a deformed shell model with the Bardeen-Cooper- Schrieffer (BCS) pairing interaction over a wide range of quadrupole and octupole deformations. We found that in most cases the magnetic moments exhibit a pronounced sensitivity to the octupole deformation, while the 2qp energies indicate regions of nuclei in which the presence of high-K isomeric states may be associated with the presence of octupole softness or even with octupole deformation. In the present work we also examine the influence of the BCS pairing strength on the energy of the blocked isomer configuration. We show that the formation of 2qp energy minima in the space of quadrupole-octupole and eventually higher multipolarity deformations is a subtle effect depending on nuclear pairing correlations.

Magnetic moments of K isomers as indicators of octupole collectivity

The relation between the quadrupole-octupole deformation and the structure of high-K isomers in heavy even-even nuclei is studied through a reflection asymmetric deformed shell model including a BCS procedure with constant pairing interaction. Two-quasiparticle states with K π = 4−, 5−, 6−, 6+ and 7− are considered in the region of actinide nuclei (U, Pu and Cm) and rare-earth nuclei (Nd, Sm and Gd). The behaviour of two-quasiparticle energies and magnetic dipole moments of these configurations is examined over a wide range in the plane of quadrupole and octupole deformations (β 2 and β 3. In all considered actinide nuclei, the calculations show that there is pronounced sensitivity of the magnetic moments to the octupole deformation. In the rare-earth nuclei, the calculations for 154, 156Gd show stronger sensitivity of the magnetic moment to the octupole deformation than in the other considered cases.

PARITY EFFECTS IN NUCLEAR COLLECTIVE AND SINGLE PARTICLE MOTION

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.

Parity mixing in the single particle states of quadrupole-octupole deformed 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.

Complex shape effects in nuclear rotational spectra

We study the evolution of collectivity in the structure of nuclear rotational bands based on complex quadrupole-octupole shapes. We apply an extended version of a quadrupole-octupole rotation model capable of reproducing both the low-lying states of alternating parity bands interpreted on the basis of octupole vibrations and the higher spin states considered as members of a single octupole rotational band. In such a way, the complicated odd-even staggering effects observed in light actinide nuclei are described successfully. The implemented model analysis suggests a unified mechanism in which the octupole band structure is formed as the result of the transition from an octupole vibration (soft) mode to a rotation of a shape with a stable quadrupole-octupole deformation.

Shell model configurational trends in odd-odd nuclei beyond208Pb

Experimental information on the energy distribution of states in the lowest lying configurations of selected odd-odd nuclei just beyond ${}^{208}$Pb is summarized. In ${}^{210}$Bi the $\ensuremath{\pi}{0h}_{9/2}\ensuremath{\bigotimes}\ensuremath{\nu}{1g}_{9/2}$ configuration and other low lying configurations all have the inverted parabola shape in a plot of energy versus spin. When additional pairs of protons and/or neutrons are added, leading to heavier odd-odd nuclei, the inverted parabola becomes more compressed. Before these trends can be completed, however, quadrupole-octupole deformation sets in. Using the generalized intermediate coupling model, it is possible to reproduce these experimental trends and then to carry them to completion in the reversed parabola (of energy versus spin) resulting from the configuration $\ensuremath{\pi}{0h}_{9/2}\ensuremath{\bigotimes}\ensuremath{\nu}{(1g}_{9/2}{)}^{\ensuremath{-}1}$ or $\ensuremath{\pi}{(0h}_{9/2}{)}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{1g}_{9/2}.$

Definition of the actinide region of static quadrupole-octupole deformation

Ground state spins of odd- A nuclei in the region just beyond 208Pb are compiled. They are compared with the theoretically predicted spins of an axially symmetric, reflection asymmetric nucleus with octupole deformation ϵ 3 = 0.08 to determine the region of static quadrupole-octupole deformation. Coexistence of different shapes and the corresponding spectra in the same nucleus are predicted in the transition regions.

Self-consistent calculation of the quadrupole-octupole deformation energy surface of 222Ra

The Hartree-Fock + BCS quadrupole-octupole deformation energy surface of 222Ra, calculated with the Skyrme SIII interaction, presents a minimum for a non-zero value of the octupole moment. Our results suggest the existence of a quadrupole coupling which may account for the observed differences between the moments of inertia of the positive- and negative-parity bands.