Collective Octupole Research Articles

Robustness of the octupole collectivity in $${^{144}\textrm{Ba}}$$ within the cranking covariant density functional theory in 3D lattice

Robustness of the octupole collectivity in $${^{144}\textrm{Ba}}$$ within the cranking covariant density functional theory in 3D lattice

Evolution of quadrupole-octupole collectivity in the even–even 54 ≤ Z ≤ 58 nuclei

We explore the quadrupole-octupole collectivity in the mass region of even–even 54 ≤ Z ≤ 58 (Xe, Ba and Ce) nuclei by analysing the fine structure of energy spectra. As a basic criterion for the presence of reflection-asymmetric degree of freedom we consider the formation of alternating-parity level-sequences. As a clear-cut criterion for the emergence of pronounced octupole deformation we consider the reduction of the parity-shift at certain angular momentum and the formation of a single energy sequence which can be interpreted as an octupole band. Applying these criteria we select out alternating-parity bands (APBs) in the region of Xe, Ba and Ce isotopes for which a manifestation of pronounced octupole collectivity can be considered. Their fine structure is probed in a collective quadrupole-octupole rotation model (QORM) providing a detailed analysis in terms of odd–even staggering diagrams. The obtained model descriptions of the energy levels and staggering patterns reveal the most characteristic features of the quadrupole-octupole deformations in this mass region and outline a clearly determined area of manifestation of nuclear reflection-asymmetric shapes.

Enhanced Schiff and magnetic quadrupole moments in deformed nuclei and their connection to the search for axion dark matter

Deformed nuclei possess enhanced moments violating time reversal invariance ($T$) and parity ($P$). Collective magnetic quadrupole moments (MQM) appear in nuclei with a quadrupole deformation (which have ordinary $T$,$P$-conserving collective electric quadrupole moments). Nuclei with an octupole deformation have a collective electric octupole moment, electric dipole moment (EDM), Schiff moment and MQM in the intrinsic frame which rotates with the nucleus. In a state with definite angular momentum in the laboratory frame, these moments are forbidden by $T$ and $P$ conservation, meaning their expectation values vanish due to nuclear rotation. However, nuclei with an octupole deformation have doublets of close opposite parity rotational states with the same spin, which are mixed by $T$,$P$-violating nuclear forces. This mixing polarises the orientation of the nuclear axis along the nuclear spin, and all moments existing in the intrinsic frame appear in the laboratory frame (provided the nuclear spin $I$ is sufficiently large to allow such a moment). Such a mechanism produces enhanced $T$,$P$-violating nuclear moments. This enhancement also takes place in nuclei with a soft octupole vibration mode. In this paper we present updated estimates for the enhanced Schiff moment in isotopes of Eu, Sm, Gd, Dy, Er, Fr, Rn, Ac, Ra, Th, Pa, U, Np and Pu in terms of the CP-violating $\pi$-meson--nucleon interaction constants $\bar{g}_{0},\bar{g}_{1}$ and $\bar{g}_{2}$, the QCD parameter $\bar{\theta}$ and the quark chromo-EDMs. The implications of the enhanced $T$,$P$-violating moments to the search for axion dark matter in solid state experiments are also discussed, with potential alternative candidate compounds in which we may expect enhanced effects suggested.

Microscopic formulation of the interacting boson model for reflection asymmetric nuclei

Reflection asymmetric, octupole shapes in nuclei are a prominent aspect of nuclear structure, and have been recurrently studied over the decades. Recent experiments using radioactive-ion beams have provided evidence for stable octupole shapes. A variety of nuclear models have been employed for the related theoretical analyses. We review recent studies on the nuclear octupole shapes and collective excitations within the interacting boson model. A special focus is placed on the microscopic formulation of this model by using the mean-field method that is based on the framework of nuclear density functional theory. As an illustrative example, a stable octupole deformation, and a shape phase transition as a function of nucleon number that involves both quadrupole and octupole degrees of freedom are shown to occur in light actinides. Systematic spectroscopic studies indicate enhancement of the octupole collectivity in a wide mass region. Couplings between the octupole and additional degrees of freedom are incorporated in a microscopic manner in the boson system, and shown to play a crucial role in the description of the related intriguing nuclear structure phenomena such as the shape coexistence.

Reflection-asymmetric mode in the structure of heavy nuclei

The properties and description of the reflection-asymmetric mode in heavy nuclei are discussed. Two approaches based on the collective octupole degree of freedom and the mass asymmetry mode are presented. Angular momentum dependence of the parity splitting, phase transition in alternating parity rotational band, stabilization of the reflection-asymmetric deformation with angular momentum increase and the rigidity of the reflection-asymmetric deformation are considered.

Quadrupole and octupole collectivity in the semi-magic nucleus [formula omitted]Hg126

The first low-energy Coulomb-excitation measurement of the radioactive, semi-magic, two proton-hole nucleus 206Hg, was performed at CERN's recently-commissioned HIE-ISOLDE facility. Two γ rays depopulating low-lying states in 206Hg were observed. From the data, a reduced transition strength B(E2;21+→01+)=4.4(6) W.u. was determined, the first such value for an N=126 nucleus south of 208Pb, which is found to be slightly lower than that predicted by shell-model calculations. In addition, a collective octupole state was identified at an excitation energy of 2705 keV, for which a reduced B(E3) transition probability of 30−13+10 W.u. was extracted. These results are crucial for understanding both quadrupole and octupole collectivity in the vicinity of the heaviest doubly-magic nucleus 208Pb, and for benchmarking a number of theoretical approaches in this key region. This is of particular importance given the paucity of data on transition strengths in this region, which could be used, in principle, to test calculations relevant to the astrophysical r-process.

Investigation of octupole collectivity near the A=72 shape-transitional point

Enhanced octupole collectivity is expected in the neutron-deficient Ge, Se and Kr isotopes with neutron number $N \approx 40$ and has indeed been observed for $^{70,72}$Ge. Shape coexistence and configuration mixing are, however, a notorious challenge for theoretical models trying to reliably predict octupole collectivity in this mass region, which is known to feature rapid shape changes with changing nucleon number and spin of the system. To further investigate the microscopic configurations causing the prolate-oblate-triaxial shape transition at $A \approx 72$ and their influence on octupole collectivity, the rare isotopes $^{72}$Se and $^{74,76}$Kr were studied via inelastic proton scattering in inverse kinematics. While significantly enhanced octupole strength of $\sim 32$ Weisskopf units (W.u.) was observed for $^{72}$Se, only strengths of $\sim 15$ W.u. were observed for $^{74,76}$Kr. In combination with existing data, the new data clearly question a simple origin of enhanced octupole strengths around $N = 40$. The present work establishes two regions of distinct octupole strengths with a sudden strength increase around the $A=72$ shape transitional point.

Coulomb excitation of Rn222

The nature of quadrupole and octupole collectivity in Rn222 was investigated by determining the electric-quadrupole (E2) and octupole (E3) matrix elements using subbarrier, multistep Coulomb excitation. The radioactive Rn222 beam, accelerated to 4.23 MeV/u, was provided by the HIE-ISOLDE facility at CERN. Data were collected in the Miniball γ-ray spectrometer following the bombardment of two targets, Sn120 and Ni60. Transition E2 matrix elements within the ground-state and octupole bands were measured up to 10ℏ and the results were consistent with a constant intrinsic electric-quadrupole moment, 518(11)efm2. The values of the intrinsic electric-octupole moment for the 0+→3− and 2+→5− transitions were found to be respectively 2360−210+300efm3 and 2300−500+300efm3 while a smaller value, 1200−900+500efm3, was found for the 2+→1− transition. In addition, four excited non-yrast states were identified in this work via γ−γ coincidences.6 MoreReceived 10 December 2021Accepted 8 February 2022DOI:https://doi.org/10.1103/PhysRevC.105.024323Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectromagnetic transitionsNuclear structure & decaysPropertiesA ≥ 220Nuclear Physics

Quadrupole-octupole coupling and the evolution of collectivity in neutron-deficient Xe, Ba, Ce, and Nd isotopes

The evolution of quadrupole and octupole collectivity in neutron-deficient Xe, Ba, Ce, and Nd nuclei near the ``octupole magic'' neutron number $N=56$ is investigated within the mapped $sdf$-IBM framework. Microscopic input is obtained via quadrupole and octupole constrained Hartree-Fock-Bogoliubov calculations, based on the parametrization D1M of the Gogny energy density functional. Octupole-deformed mean-field ground states are predicted for Ba and Ce isotopes near $N=56$. Excitation energies of positive- and negative-parity states as well as electric transition rates are computed with wave functions resulting from the diagonalization of the mapped IBM Hamiltonian. The parameters of the Hamiltonian are determined via the mapping of the mean-field potential energy surfaces onto the expectation value of the Hamiltonian in the condensate state of the $s$, $d$, and $f$ bosons. Enhanced octupolarity is predicted for Xe, Ba, and Ce isotopes near $N=56$. The shape/phase transition from octupole-deformed to strongly quadrupole-deformed near $N=60$ is analyzed in detail.

Quadrupole-octupole collectivity in the Xe, Ba, Ce and Nd isotopic chains described with mean field and beyond approaches

The impact of quadrupole and octupole collectivity in the dynamic of low-lying collective states is discussed for a set of Xe, Ba, Ce and Nd isotopes with neutron numbers 54 ⩽ N ⩽ 96. Mean field based methods including pairing are used in our microscopic description along with the Gogny D1M force. Starting with a set of Hartree–Fock–Bogoliubov constrained states we consider dynamic fluctuations of the collective variables by using the generator coordinate method. Related quantities like reduced electromagnetic transition probabilities B(E1) and B(E3) and negative-parity excitation energies and their behavior with neutron number are discussed and compared with the available experimental data. The coupling between the quadrupole and octupole degrees of freedom is found to be rather weak in all the considered nuclei and therefore the properties of the negative parity states can be reasonably well described in terms of the octupole degree of freedom alone. The results of the calculations point towards dynamically enhanced octupole correlations around the ‘octupole magic’ neutron numbers N = 56 and N = 88.

Evolution of octupole deformation and collectivity in neutron-rich lanthanides

The onset of octupole deformation and its impact on related spectroscopic properties is studied in even-even neutron-rich lanthanide isotopes Xe, Ba, Ce, and Nd with neutron number $86\leqslant N\leqslant 94$. Microscopic input comes from the Hartree-Fock-Bogoliubov approximation with constrains on the axially symmetric quadrupole and octupole operators using the Gogny-D1M interaction. At the mean-field level, reflection asymmetric ground states are predicted for isotopes with neutron number around $N=88$. Spectroscopic properties are studied by diagonalizing the interacting boson model Hamiltonian, with the parameters obtained via the mapping of the mean-field potential energy surface onto the expectation value of the Hamiltonian in the $s$, $d$, and $f$ boson condensate state. The results obtained for low-energy positive- and negative-parity excitation spectra as well as the electric dipole, quadrupole, and octupole transition probabilities indicate the onset of pronounced octupolarity for $Z\approx 56$ and $N\approx 88$ nuclei.

Collective and noncollective states in Zn66

Excited states in the $^{66}\mathrm{Zn}$ nucleus were populated via a $^{56}\mathrm{Fe}(^{12}\mathrm{C},2p\ensuremath{\gamma}$) fusion-evaporation reaction at a beam energy of $\ensuremath{\approx}62$ MeV. The deexciting $\ensuremath{\gamma}$ rays were detected using the Indian National Gamma Array (INGA). The level scheme of the $^{66}\mathrm{Zn}$ nucleus has been updated by placing several new $\ensuremath{\gamma}$ rays as well as by assigning the spin and parity of various excited states from the present spectroscopic results. The microscopic structure of the observed states have been investigated in the light of large shell-model calculations. The shape of this nucleus in the low-spin regime has been studied under the framework of total Routhian surface (TRS) calculations. The lifetime of first ${3}^{\ensuremath{-}}$ state at 2826 keV is experimentally measured using the Doppler-shift attenuation method and the deduced $B(E1)$ value indicates the presence of octupole collectivity in this nucleus.

Quadrupole-octupole coupling and the onset of octupole deformation in actinides

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 $130\leqslant N\leqslant 150$. 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.

Large-scale nuclear shell-model calculations of isotopes in the southwest region of 208Pb

Abstract Large-scale nuclear shell-model calculations are performed in the neutron- and proton-deficient Pt, Au, Hg, and Tl isotopes ($Z < 82$ and $N \le 126$) near $^{208}$Pb. All the single-particle levels in the one-major shells, six neutron ($2p_{1/2}$, $1f_{5/2}$, $2p_{3/2}$, $0i_{13/2}$, $1f_{7/2}$, and $0h_{9/2}$) orbitals and five proton ($2s_{1/2}$, $1d_{3/2}$, $0h_{11/2}$, $1d_{5/2}$, and $0g_{7/2}$) orbitals are considered. For an effective two-body interaction, one set of the multipole pairing, quadrupole–quadrupole interactions is employed for all the nuclei considered. These phenomenological interactions are determined to reproduce the experimental energy spectra. Some of the isomeric states are analyzed in terms of the shell-model configurations. Octupole correlated states are discussed in terms of a collective octupole excitation on top of each shell model state.

Octupole correlations in light actinides from the interacting boson model based on the Gogny energy density functional

The quadrupole-octupole coupling and the related spectroscopic properties have been studied for the even-even light actinides $^{218-238}$Ra and $^{220-240}$Th. The Hartree-Fock-Bogoliubov approximation, based on the Gogny-D1M energy density functional, has been employed as a microscopic input, i.e., to obtain (axially symmetric) mean-field potential energy surfaces as functions of the quadrupole and octupole deformation parameters. The mean-field potential energy surfaces have been mapped onto the corresponding bosonic potential energy surfaces using the expectation value of the $sdf$ Interacting Boson Model (IBM) Hamiltonian in the boson condensate state. The strength parameters of the $sdf$-IBM Hamiltonian have been determined via this mapping procedure. The diagonalization of the mapped IBM Hamiltonian provides energies for positive- and negative-parity states as well as wave functions which are employed to obtain transitional strengths. The results of the calculations compare well with available data from Coulomb excitation experiments and point towards a pronounced octupole collectivity around $^{224}$Ra and $^{226}$Th.

Experimental study of lifetimes of excited states in the Kπ = 0− octupole band and γ-vibrational band in 228Th

Lifetimes of excited states in the Kπ = 0− octupole band and γ-vibrational of 228Th have been measured using the fast timing setup at the University of the West of Scotland (UWS). The setup consists of two cerium doped LaBr3 fast scintillators placed equidistant from the radioactive source 232Th. The states of interest have been analysed by doing the triple γ – γ – time coincidence analysis and using the fast-timing technique, mirror-symmetric centroid difference method. Octupole collectivity in 228Th nucleus is also investigated by calculating the enhanced electric dipole moments and transition rates in excited states followed by lifetime measurements in octupole band.

Quadrupole and octupole collectivity in Ba143

Author(s): Morse, C; MacChiavelli, AO; Crawford, HL; Zhu, S; Wu, CY; Wang, YY; Meng, J; Back, BB; Bucher, B; Campbell, CM; Carpenter, MP; Chen, J; Clark, RM; Cromaz, M; Fallon, P; Henderson, J; Janssens, RVF; Jones, MD; Khoo, TL; Kondev, FG; Lauritsen, T; Lee, IY; Li, J; Potterveld, D; Santamaria, C; Savard, G; Seweryniak, D; Stolze, S; Weisshaar, D | Abstract: The neutron-rich barium nuclei have been the subject of intense interest due to the enhanced octupole correlations they are predicted to exhibit. The observation of enhanced octupole collectivity in Ba144,146 as measured in sub-barrier Coulomb excitation, consistent with static octupole deformation, has further heightened this interest. In the present work, these studies are extended to the neighboring odd-mass Ba143 to investigate the interplay between single-particle and collective octupole degrees of freedom. A new measurement of the first 92 - state lifetime is also presented. Reflection-Asymmetric Triaxial Particle Rotor Model calculations indicate that the negative-parity bands in Ba143 can be understood as a decoupled structure of νh9/2 parentage, while the positive-parity bands are built on a decoupled octupole phonon. No evidence for E3 excitation is observed in this work, but an upper limit is placed on the E3 matrix element to the lowest octupole band.

Direct measurement of the intrinsic electric dipole moment in pear-shaped thorium-228

It is now well established that atomic nuclei composed of certain combinations of protons and neutrons can adopt reflection-asymmetric, or octupole-deformed, shapes at low excitation energy. These nuclei show promise in the search for a permanent atomic electric dipole moment, the existence of which has implications for physics beyond the Standard Model. Theoretical studies have suggested that certain isotopes of thorium may have the largest octupole deformation. However, due to experimental challenges, the extent of the octupole collectivity in the low-energy states in these thorium nuclei has not yet been demonstrated. This paper reports measurements of the lifetimes of low-energy states in 228Th (Z = 90) undertaken using the mirror symmetric centroid difference method, which is a direct electronic fast-timing technique. Lifetime measurements of the low-lying Jp = 1- and 3- states, which are the first for a thorium isotope, have allowed the B(E1) rates and the intrinsic dipole moment to be determined. The results are in agreement with those of previous theoretical calculations allowing the extent of the octupole deformation of 228Th to be estimated. This study indicates that the nuclei 229Th and 229Pa (Z = 91) may be good candidates for the search for a permanent atomic electric dipole moment.

Octupole states in Tl207 studied through β decay

The β decay of 207Hg into the single-proton-hole nucleus 207Tl has been studied through γ-ray spectroscopy at the ISOLDE Decay Station (IDS) with the aim of identifying states resulting from coupling of the πs−11/2, πd−13/2, and πh−111/2 shell model orbitals to the collective octupole vibration. Twenty-two states were observed lying between 2.6 and 4.0 MeV, eleven of which were observed for the first time, and 78 new transitions were placed. Two octupole states (s1/2-coupled) are identified and three more states (d3/2-coupled) are tentatively assigned using spin-parity inferences, while further h11/2-coupled states may also have been observed for the first time. Comparisons are made with state-of-the-art large-scale shell model calculations and previous observations made in this region, and systematic underestimation of the energy of the octupole vibrational states is noted. We suggest that in order to resolve the difference in predicted energies for collective and noncollective t=1 states (t is the number of nucleons breaking the 208Pb core), the effect of t=2 mixing may be reduced for octupole-coupled states. The inclusion of mixing with t=0,2,3 excitations is necessary to replicate all t=1 state energies accurately.

Evidence for octupole collectivity in ^{172}{mathrm {Pt}}

Excited states in the extremely neutron-deficient nucleus ^{172}{mathrm {Pt}} were populated via ^{96}mathrm {Ru}(^{78}mathrm {Kr},2p) and ^{92}mathrm {Mo}(^{83}mathrm {Kr},3n) reactions. The level scheme has been extended up to an excitation energy of approx 5~hbox {MeV} and tentative spin-parity assignments up to I^pi = 18^+. Linear polarization and angular distribution measurements were used to determine the electromagnetic E1 character of the dipole transitions connecting the positive-parity ground-state band with an excited side-band, firmly establishing it as a negative-parity band. The lowest member of this negative-parity structure was firmly assigned spin-parity 3^-. In addition, we observed an E3 transition from this 3^- state to the ground state, providing direct evidence for octupole collectivity in ^{172}{mathrm {Pt}}. Large-scale shell model (LSSM) and total Routhian surface (TRS) calculations have been performed, supporting the interpretation of the 3^- state as a collective octupole-vibrational state.