Triaxial Rotor Research Articles

A novel approach for the anomalous collectivity in the neutron-deficient Os isotopes

Abstract An algebraic model with three-body boson interactions is proposed to incorporate the different quadrupole modes in nuclear collectivity. It is shown that the recently observed anomalous collective structure characterized by $B_{4/2}=B(E2;4_1\rightarrow2_1)/B(E2;2_1\rightarrow0_1)<1.0$ and $R_{4/2}= E(4_1)/E(2_1)\geq2.0$, which cannot yet be explained by any other microscopic nuclear models, naturally emerge in the present model due to the inclusion of triaxial rotor modes.
This description is further extended to describe the odd-$A$ nuclei by including the coupling to the Fermion degree of freedom. That allows us to give a unified explanation of the anomalous $B(E2)$ strengths in both even-even and even-odd systems which seemed to indicate different behaviors. As examples, the model is applied to describe the spectroscopy and $E2$ transition properties of $^{168,169,170,171}$Os. All recent measurements of those isotopes can be well reproduced on the same footing which suggests that the anomalous collectivity persists even in the odd-$A$ systems.

Octupole correlations in stable nucleus 153Eu within reflection-asymmetric particle rotor model

Abstract The observed low-lying K=5/2± positive- and negative-parity bands in the stable nucleus 153Eu are investigated by the reflection-asymmetric triaxial particle rotor model. The experimental energy spectra, the energy staggering parameters, as well as the intraband E2 and M1 transition probabilities are well reproduced. It is found that the calculated interband B(E1) values depend sensitively on the octupole deformation parameter β30, although the energy spectra and intraband E2 and M1 transitions can be reproduced without the octupole degree of freedom. The observed enhanced E1 transition probabilities can be reproduced with β30=0.05. The detailed analysis of the intrinsic wave functions shows these nearly degenerate positive- and negative-parity bands are built on two individual proton configurations, i.e., dominated by πg9/2[Ω=5/2] and πh11/2[Ω=5/2], respectively, which differs from the parity doublet bands built on a single parity-mixed configuration.

Schrödinger equation for the chiral geometry in atomic nuclei

The dynamical and spectral features of the chiral geometry in atomic nu clei are described by means of a triaxial rigid rotor Hamiltonian cranked by quasiparticle alignments. The problem is treated alternatively in the space of angular momentum states and using a Schr¨odinger equation for a continuous variable associated with an angular momentum projection. The later is con structed using a semiclassical approach. Numerical applications performed for various deformation and alignment conditions with both methods are compared in terms of energy levels and wave functions.

Reevaluation of structures in Se70 from combined conversion-electron and γ -ray spectroscopy

In the selenium isotopes various shape phenomena are present, in particular, the emergence of a dominant oblate deformation in the most neutron-deficient isotopes has been observed. The scenario of shape coexisting oblate and prolate bands has been proposed across the isotopic chain, with the crossing point of such bands being located near Se70, where no coexistence has yet been identified. To determine the presence or absence of any low-lying 0+ state in Se70, confirm the level structure, and interpret the nuclear deformation with theoretical models. A combined internal-conversion-electron and γ-ray spectroscopy study was undertaken with the SPICE and TIGRESS spectrometers at the TRIUMF-ISAC-II facility. Nuclear models were provided by the generalized triaxial rotor model (GTRM) and the collective generalised Bohr Hamiltonian (GBH). Despite a comprehensive search, no evidence was found for the existence of a 0+ state below 2 MeV in Se70. Significant discrepancies to the previously established positive-parity-level scheme were found. GBH calculations using UNEDF1 mass parameters were found to reproduce the revised low-lying level structure well. Se70 does not have a well-defined axial shape. The 22+ state at 1601 keV resembles a quasi-γ excitation rather than a member of a shape coexisting band; the presence of such a band is all but ruled out.Published by the American Physical Society2024

First observation of excited states in 120La and its impact on the shape evolution in the A ≈ 120 mass region

Excited states have been observed for the first time in the very neutron-deficient odd-odd nucleus 57120La63. The observed γ rays have been assigned based on coincidences with lanthanum X rays measured with the JUROGAM 3 array and with A=120 fusion-evaporation residues measured with the MARA separator. The observed γ rays form a rotational band which decays to the ground state via a cascade of four low-energy transitions. Based on the systematic comparisons with the heavier odd-odd La isotopes we assign spin-parity 4+ to the ground state and a πh11/2⊗νh11/2 configuration to the rotational band. The nuclear shape has been investigated by the cranked Nilsson-Strutinsky model. Two quasiparticle plus triaxial rotor model calculations including the np interaction nicely reproduce the spin of the inversion between the even- and odd-spin cascades of E2 transitions, giving credit to the np interaction as an important parameter responsible for the mechanism inducing the inversion. The position of the Fermi levels, in particular for neutrons, also has a strong impact on the observed inversion in the chain of lanthanum nuclei.

Relative variation between γ coordinate and the potential of the Bohr Hamiltonian producing X(4) from Z(4)

In this paper, four degree of freedom γ-rigid solutions of the Bohr Hamiltonian at γ 0 = π/6 are obtained. The relative variation between γ and the potential of the Hamiltonian is employed to retrieve X(4) from Z(4). γ is varied in the interval 0 ≤ γ 0 ≤ π/6 while the potential minimum, β 0, is varied in the interval 0 ≤ β 0 ≤ ∞ . Very small value of β 0 yields Z(4) while a large value of β 0 produces X(4) and SU(3) is realized at β 0 ≈ ∞ . The solutions at γ 0 = 0 correspond to X(4) while the solutions at γ 0 = π/6 yield Z(4): a dynamic link between Z(4) and X(4) critical point symmetries (CPSs) has been provided. The fact that γ and β 0 of the potential play the same role in the dynamical link between Z(4) and X(4) shows that β 0 also measures the departure from axial symmetry to other shapes as γ does. In the experimental realization of the model, the conformation of 192Pt and 194Pt isotopes to the present Z(4) model shows that the present model can be employed in the description of triaxial rotors and γ-soft isotopes. 194Pt is shown to be the best choice for triaxial rigid rotor candidacy. 130Xe, a critical point isotope, which belongs to the class of γ-soft nuclei, reproduces this present model very well in all the states. Consequently, this present model can serve as a critical point model. 40,0 − β 0 distribution for Z(4) and X(4) candidate isotopes shows a significant interval between the two models where the T(4) CPS lies.

Triaxial rotor in the O(6) limit of the interacting boson model

A mapping from the triaxial rotor Hamiltonian to that of the O(6) limit in the interacting boson model (IBM) is established, which is achieved by introducing the symmetry-conserving high-order interactional terms The validity of the proposed mapping scheme is further examined for the cases with γ = 0 and γ = π/6, respectively. It is shown that the rotor model results can be well reproduced in its O(6) image especially for the low-spin states. It thus provides an alternative way to understand the triaxiality in the finite-N systems and additional insight into the O(6) IBM theory.

Wobbling motion for a triaxial rotor plus a single quasiparticle*

Abstract Wobbling motion in a system comprising a triaxial rotor and a single quasiparticle is studied employing the particle-rotor model. The energy spectra, wobbling frequencies, electromagnetic transition probabilities, g-factors, angular momentum components, spin coherent state maps, and static quadrupole moments are investigated. These investigations were conducted with regard to the Fermi surface transitioning from the lowest orbit to the highest one. As the Fermi surface increases, notable transformations occur in the wobbling mode. Initially, the mode exhibits a transverse revolution around the short axis of the nucleus. However, as the Fermi surface continues to increase, the mode gradually shifts to a longitudinal revolution around the intermediate axis. Eventually, it transitions to a transverse revolution around the long axis. Notably, the stability of the long axis transverse mode diminishes relative to its counterpart along the short axis as the total angular momentum increases at .

Rotational spectroscopies of reflection-asymmetric nuclei within particle rotor model

The rotational spectroscopic properties of reflection-asymmetric nuclei investigated by the reflection-asymmetric axial or triaxial particle rotor model are briefly reviewed. The status of observations of the alternated parity bands in even–even nuclei and the parity doublet bands in odd-[Formula: see text] and odd–odd nuclei for the [Formula: see text] mass region are summarized. The reflection-asymmetric axial particle rotor model has been used to systematically describe the parity doublet bands of the odd-[Formula: see text] nuclei in this region. With the triaxial degree of freedom included, the reflection-asymmetric triaxial particle rotor model shows the ability to study the multiple chiral doublet bands with octupole correlations and explore the possible chirality-parity quartet bands.

Triaxiality and the nature of low-energy excitations in Ge76

The deformation properties of the low-lying states in Ge76 have been investigated following a safe-energy Coulomb excitation measurement with the GRETINA tracking array and CHICO2 heavy-ion counter at the ATLAS accelerator facility at Argonne National Laboratory. A comprehensive set of transition and static E2 matrix elements were extracted from the measured differential Coulomb cross sections and compared with results of configuration-interaction shell-model calculations and computations carried out within the framework of the generalized triaxial rotor model. The remarkable agreement between the calculated and experimental data supports a near-maximum triaxial deformation for the ground state of Ge76. In addition, the degree of softness of the asymmetry in Ge76 and Se76 was investigated using rotational invariants generated from configuration-interaction shell-model wave functions computed with the jj44b and JUN45 effective interactions. The resulting invariants are shown to be consistent with a stiff triaxial deformation in Ge76 and a predominantly soft triaxial potential for Se76, in agreement with the conclusions of recent works by this collaboration.5 MoreReceived 27 January 2023Accepted 3 April 2023DOI:https://doi.org/10.1103/PhysRevC.107.044314©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear reactionsNuclear structure & decaysNucleon distributionProperties59 ≤ A ≤ 89TechniquesCollective modelsShell modelNuclear Physics

New perspective of the role of the triaxiality parameter γ for γ–g B(E2)s

Recently, from the study of the absolute [Formula: see text] values for the ([Formula: see text]–[Formula: see text]) [Formula: see text]2 transitions, the different roles of the triaxiality parameter [Formula: see text] and [Formula: see text] parts were pointed out. Here, the use of the triaxial rotor model expressions for the [Formula: see text]2)s in producing the bell-shaped curve of [Formula: see text] is illustrated. The variation of certain ([Formula: see text]–[Formula: see text]) [Formula: see text] ratios versus [Formula: see text] for the states [Formula: see text] and [Formula: see text] are illustrated, reflecting the two regions of [Formula: see text]. The inter relation of the [Formula: see text] and [Formula: see text] variables is illustrated for the Os isotopes.

The Particle-Rotor-Quadrupole-Coupling Model for Transitional Odd-A Nuclei

The particle-rotor-quadrupole-coupling model, in which the quadrupole–quadrupole interaction of the even-even core is described by a triaxial rotor with a single-j particle, is adopted to describe low-lying spectra of odd-A nuclei within the vibrational to triaxial transition region. In contrast to the particle-plus-rotor-model, the quadrupole–quadrupole interaction introduced in the particle-rotor-quadrupole-coupling model keeps the rotational symmetry in the collective model framework without approximation. To demonstrate the usability, low-lying level energies, reduced E2 transition probabilities, and ground-state quadrupole moments of 135Ba and 131Xe are fit by the model, of which the results are compared with the experimental data and those of other models. It is shown that the fitting results of the particle-rotor-quadrupole-coupling model to the low-lying level energies, reduced E2 transition probabilities, and ground-state electric quadrupole moments of 135Ba and 131Xe are the best, of which the model parameters of the even-even core are determined by the triaxial rotor model in fitting the low-lying spectra of 134Ba and 130Xe. In comparison with the E(5/4) model results of 135Ba, it is also shown that the quadrupole–quadrupole interaction of the even-even core with the single particle adopted can indeed reproduce the E(5/4) critical point behavior. The fitting quality of the reduced E2 transition probabilities among low-lying states by the particle-rotor-quadrupole-coupling model is also noticeably improved. Thus, it can be concluded that the particle-rotor-quadrupole-coupling model is suitable to describe low-lying properties of odd-A nuclei within the transitional region.

Triaxiality explored by an odd quasi-particle

The microscopic origin of the $\gamma$-softness (fluctuations in the triaxiality parameter $\gamma$ of the nuclear shape) observed in atomic nuclei is studied in the framework of the triaxial projected shell model approach, which is based on the deformed mean-field picture with multi-quasiparticle configuration space. It is demonstrated that the coupling to quasiparticle excitations drives the system from a $\gamma$-rigid to a $\gamma$-soft pattern. As an illustrative example for a $\gamma$-soft nucleus, a detailed study has been performed for the $^{104}$Ru nucleus. The experimental energies and a large sample of measured $E2$ matrix elements available for this nucleus are reproduced quite accurately. The shape invariant analysis of the calculated $E2$ matrix elements elucidates the $\gamma$-soft nature of $^{104}$Ru.

Lifetime measurements in 80Br and a new region for observation of chiral electromagnetic selection rules

Level lifetimes for the candidate chiral doublet bands of 80Br were extracted by means of the Doppler-shift attenuation method. The absolute transition probabilities derived from the lifetimes agree well with the M1 and E2 chiral electromagnetic selection rules, and are well reproduced by the triaxial particle rotor model calculations. Such good agreements among the experimental data, selection rules of chiral doublet bands and theoretical calculations are rare and outstanding in researches of nuclear chirality. Besides odd-odd Cs isotopes, odd-odd Br isotopes in the A≈ 80 mass region represent another territory that exhibits the ideal selection rules expected for chiral doublet bands.

Beyond the harmonic approximation description of wobbling excitations in even-even nuclei with frozen alignments

The wobbling motion in even-even nuclei is investigated by means of a collective Hamiltonian constructed from a semiclassical treatment applied to a triaxial rotor with a rigidly aligned pair of quasiparticles. The limits of distinct wobbling regimes are discussed in connection to the dynamic evolution of the wobbling excitations and corresponding electromagnetic properties. Model calculations are performed for the description of transverse wobbling bands in $^{130}\mathrm{Ba}, ^{134}\mathrm{Ce}$, and $^{136,138}\mathrm{Nd}$ nuclei.

Symmetry solutions at γ 0 = π/6 for nuclei transition between γ 0 = 0 and γ 0 = π/3 via a variational procedure

A Bohr Hamiltonian model suitable for triaxial shapes is found via inverse square potentials in the part and the solutions of the part are obtained via a harmonic oscillator, centered around The symmetry solutions from a triaxial vibrator to a rigid triaxial rotator are achieved through variational procedure. The solutions of some selected symmetry candidates are fitted and compared with the available experimental data.

Interpretation of enhanced electric dipole transitions in Br73 by the reflection-asymmetric triaxial particle rotor model

The recently observed positive and negative parity bands in $^{73}\mathrm{Br}$ are investigated by the reflection-asymmetric triaxial particle rotor model. The experimental energy spectra as well as the electric transition probabilities $B(E1), B(E2)$, and the ratio $B(E1)/B(E2)$ are well reproduced by the theoretical calculations. It is found that the enhanced interband $E1$ transitions between the opposite-parity bands, a crucial evidence for octupole correlations, are mainly contributed by the intrinsic single-particle electric dipole matrix elements.

Rigid Triaxial Rotor Model Description of γγ-Band in Some Even Nuclei

Rigid Triaxial Rotor Model Description of γγ-Band in Some Even Nuclei

Influence of moments of inertia on transverse wobbling mode in odd-mass nuclei

The reported transverse wobbling band in odd-mass $^{105}$Pd has been reinvestigated by the triaxial particle rotor model. Employing different parameter sets of moment of inertia (MOI), several calculated results could be in good agreement with the experimental data, which show distinct modes of rotational excitation, respectively. These modes are sensitive to the ratio between the MOI at intermediate and short axis. With the increase of this ratio, a wobble about the short axis of the total angular momentum is gradually changed to a wobble about the intermediate axis. In addition, it is exhibited that precession and tunneling are two aspects of the quantum wobbling motion. The tunneling aspect dominates in the yrare states of $^{105}$Pd. The present results in $^{105}$Pd show the complexity of the transverse wobbling mode.

Evidence of octupole correlation in Se79

Two opposite parity bands I and II with eight new parity changing transitions have been identified in $^{79}\mathrm{Se}$ using the fusion-evaporation reaction $^{76}\mathrm{Ge}(^{9}\mathrm{Be}$, $\ensuremath{\alpha}2n$) at ${E}_{\mathrm{Lab}}\ensuremath{\approx}31$ MeV. The $B(M1)$ and $B(E2)$ rates of bands I and II as well as $B(E1)$ values of the linking transitions between the two bands have been determined from lifetime measurements and are compared with reflection asymmetric triaxial particle rotor model calculations. The large $B(E1)$/$B(E2)$ ratios and $B(E1)$ transition rates indicate the existence of a strong octupole correlation in the $^{79}\mathrm{Se}$ nucleus. This is also supported by the calculated potential energy surface, based on the covariant density functional theory within the three-dimensional lattice approach, which is very soft for the octupole shape degree of freedom ${\ensuremath{\beta}}_{30}$. Extracted values of the intrinsic dipole moments $|{D}_{0}|$ from the $B(E1)$ rates for the lower spin states also indicate the octupole correlation in $^{79}\mathrm{Se}$.