Octupole States Research Articles

Enhanced α decays to negative-parity states in even-even nuclei with octupole deformation

The $\ensuremath{\alpha}$ decays of even-even Ra, Th, U, and Pu isotopes to ground and excited states of daughter nuclei with neutron numbers of $N=130--140$ are investigated. These nuclei show some enhanced $\ensuremath{\alpha}$-branching ratios to negative-parity states $({1}^{\ensuremath{-}},$ ${3}^{\ensuremath{-}})$, compared with the decays to positive-parity states $({4}^{+})$ of comparable energy. This enhancement correlates with appearance of static octupole deformation, rather than spherical nuclear shapes or dynamic asymmetric vibrational states. The highly enhanced branching ratios occur for $\ensuremath{\alpha}$ decays to the ${1}^{\ensuremath{-}}$ and ${3}^{\ensuremath{-}}$ states of the Ra isotopes with $N=134, 136, 138$, then to ${1}^{\ensuremath{-}}$ state in Th $(N=134--140)$ and to the ${3}^{\ensuremath{-}}$ state in Rn $(N=132--136)$ isotopes.

Quadrupole and octupole states in 152Sm using the proton–neutron interacting boson model

A scheme of solving the proton–neutron interacting boson model (IBM-2) in terms of the SU(3) basis is introduced, by which the IBM-2 coupled with an octupole boson is applied to describe the low-energy structure of the critical point nucleus, 152Sm. The results indicate that the spectral properties of both the positive-parity bands and negative-parity bands in this nucleus can be well captured by the IBM-2 calculations through a simple Hamiltonian, thus providing an example of the IBM-2 in a unified description of quadrupole and octupole states in a transitional system. In addition, a statistical analysis of the low-spin states in the model is also provided.

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.

Nuclear collective motion of heavy nuclei with axial quadrupole and octupole deformation

A quadrupole-octupole axially symmetric model is constructed for the unified description of alternate parity bands corresponding to octupole vibration or a stable deformation. The model depends on two parameters whose clear physical meaning allows a systematic description of the rotation-vibration dynamics of alternate parity bands analyzed for isotopic sequences of Ra, Th, U, and Pu nuclei. A critical point is identified in the $A=224--228$ mass region of the Ra and Th nuclei marking different stages of the transition between static and dynamic octupole deformation. Model predictions are performed for energies of unobserved states of the yrast sequence and of the excited bands as well as for the $E1, E2$, and $E3$ transition rates, which reproduce the available experimental data and exhibit a specific spin dependence for the transitional nuclei.

Beta decay studies and search for octupole deformation in the A ∼ 225 Po-Fr nuclei

In the landscape of nuclear shapes, dominated by reflection-symmetric forms leading to either spherical or axially deformed arrangements, the occurrence of asymmetric pear-like nuclei has long been searched for. Evidence for static octupole deformation has only been found in selective areas of the nuclear chart, in the mass regions A ∼ 222 and A ∼ 146, the so-called “Islands of Octupole Deformation” (IOD). This paper is focused on β decay studies in the Po-Fr nuclei in the 220 ≤ A ≤ 230 island of octupole deformation exploiting the FRS+DESPEC setup at GSI in Spring 2021. The experimental setup and the analysis techniques employed to perform this study are here shown and discussed, together with preliminary results from the on-going analysis.

Exchange interactions, Jahn-Teller coupling, and multipole orders in pseudospin one-half 5d2 Mott insulators

We develop a microscopic theory of multipole interactions and orderings in $5{d}^{2}$ transition metal ion compounds. In a cubic environment, the ground state of $5{d}^{2}$ ions is a non-Kramers ${E}_{g}$ doublet, which is nonmagnetic but hosts quadrupole and octupole moments. We derive low-energy pseudospin one-half Hamiltonians describing various spin-orbital exchange processes between these ions. Direct overlap of the ${t}_{2g}$ orbitals results in bond-dependent pseudospin interactions similar to those for ${e}_{g}$ orbitals in manganites, except for different orientations of the pseudospin easy axes. On the other hand, the superexchange process, where two different ${t}_{2g}$ orbitals communicate via oxygen ions, generates new types of pairwise interactions. In perovskites with ${180}^{\ensuremath{\circ}}$ bonding, we find nearly equal mixture of Heisenberg and ${e}_{g}$ orbital compass-type couplings. The ${90}^{\ensuremath{\circ}}$ superexchange in compounds with edge-shared octahedra is most unusual: Despite highly anisotropic shapes of the ${E}_{g}$ wave functions, the pseudospin interactions have no bond dependence. We consider the ${E}_{g}$ pseudospin models on various lattices and obtain their ground state properties using analytical and numerical methods. On the honeycomb lattice, we observe a duality with the extended Kitaev model, and use it to uncover a critical point where the quadrupole and octupole states are exactly degenerate. On the triangular lattice, an exotic pseudospin state, corresponding to the coherent superposition of vortex-type quadrupole and ferri-type octupole orders, is realized due to geometrical frustration. This state breaks both spatial and time-reversal symmetries, but possesses no dipolar magnetism. We also consider Jahn-Teller coupling effects and lattice mediated interactions between ${E}_{g}$ pseudospins, and find that they support quadrupole order. Possible implications of the results for recent experiments on double perovskite osmates are discussed, including effects of local distortions on the pseudospin wave functions and interactions.

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.

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.

Enhanced nuclear Schiff moment in stable and metastable nuclei

Nuclei with static intrinsic octupole deformation or a soft octupole vibrational mode lead to strongly enhanced collective nuclear Schiff? moments. Interaction between electrons and these Schiff moments produce enhanced time reversal (T) and parity (P) violating electric dipole moments (EDM) in atoms and molecules. Corresponding experiments may be used to test CP-violation theories predicting T,P-violating nuclear forces and to search for axions. Nuclear octupole deformations are predicted in many short lived isotopes. This paper investigates octupole deformations in stable and very long lifetime nuclei such as 153Eu, 235U, 237Np and 227Ac, which can ease atomic experiments substantially. The estimates of the enhanced Schiff? moments, atomic electric dipole momentsand T, P-odd interaction constants in molecules containing these nuclei are presented.

Systematics of alpha decay hindrance factors in doubly-even nuclei

In present work, we have calculated the hindrance factors of 182 even-even alpha emitters using Preston’s formulation of alpha decay probabilities and presented HFs systematics of 1 - and 3 - states in reflection asymmetric even-even quadruple-octupole deformed nuclides (A~216-230). The calculated HFs of both 1 - and 3 - states decrease with reduction in neutron number and this decrease is attributed to onset of intrinsic reflection asymmetry. There is a trend reversal for 1 - states at N=132 ( 218 Ra) and N=134 ( 220 Rn), which might be a possible indication of departure from static octupole deformation. Similarly, HFs systematics is discussed for 224-230 Th and 232-236 U isotopic chains along with 2 + states observed in daughter nuclei in N=132-146 isotonic chains.

Magnetoelectric Response in Electric Octupole State: Possible Hidden Order in Cuprate Superconductors

Motivated by recent studies of odd-parity multipole order in condensed matter physics, we theoretically study magnetoelectric responses in an electric octupole state. Investigating the Edelstein effect and spin Hall effect in a locally noncentrosymmetric bilayer Rashba model, we clarify characteristic properties due to parity violation in the electric octupole state. Furthermore, a possible realization of electric octupole order in bilayer high-Tc cuprate superconductors is proposed. Our calculation of magnetic torque is consistent with recent experimental observation of a kink above the superconducting transition temperature. We also show significant enhancement of the in-plane anisotropy in spin susceptibility due to the superconductivity, and propose an experimental test by means of the nuclear magnetic resonance in the superconducting state. A spin-orbit coupled metal state in Cd2Re2O7 is also discussed.

Spectroscopy of Ti54 and the systematic behavior of low-energy octupole states in Ca and Ti isotopes

Excited states of the $N=32$ nucleus $^{54}$Ti have been studied, via both inverse-kinematics proton scattering and one-neutron knockout from $^{55}$Ti by a liquid hydrogen target, using the GRETINA $\gamma$-ray tracking array. Inelastic proton-scattering cross sections and deformation lengths have been determined. A low-lying octupole state has been tentatively identified in $^{54}$Ti for the first time. A comparison of $(p,p')$ results on low-energy octupole states in the neutron-rich Ca and Ti isotopes with the results of Random Phase Approximation calculations demonstrates that the observed systematic behavior of these states is unexpected.

Description of octupole degrees of freedom in the U(5) ↔ SO(13) transitional region

In this paper, we discuss the problem of describing the collective states with negative parity in even-even nuclei by adding f boson to the usual sd-interacting boson model. The sdf -interacting boson model, which includes monopole ( $s, L=0$ ), quadrupole ( $d, L=2$ ) and octupole ( $f, L=3$ ) degrees of freedom, enables analyzing the electric transitions of atomic nuclei. We proposed a solvable extended transitional Hamiltonian based on affine SU(1,1) Lie algebra within the framework of the sdf -interacting boson model to describe the low-lying octupole states between the spherical and deformed gamma-unstable shapes. Numerical extraction to low-lying energy levels and transition probabilities within the control parameters of this evaluated Hamiltonian are presented for various N values. By reproducing the experimental results, the extended interacting boson model calculations provide a better description of Pd isotopes in this transitional region.

High spin spectroscopy in Ra219 : Search for the lower mass boundary of the region of statically octupole-deformed nuclei

We report the results of a study of rotational bands in $^{219}\mathrm{Ra}$ via the $^{208}\mathrm{Pb}(^{14}\mathrm{C},3n)$ reaction to look for evidence that this nucleus is statically octupole deformed. We add 19 $\ensuremath{\gamma}$ rays not previously observed to the level scheme and extend the two most strongly populated alternating parity bands to $J=51/2$ and 45/2. The magnitude of the energy splitting between the spin-parity doublets in the two bands appears to exclude the possibility that $^{219}\mathrm{Ra}$ has a static octupole deformation.

Influence of neutron transfer channels on fusion enhancement in sub-barrier region

Fusion cross-section measurements were performed for system 40 Ca + 70 Zn around the Coulomb barrier energies using Heavy Ion Reaction Analyzer (HIRA). The observed enhancement in experimental fusion cross-sections was investigated via coupled-channels formalism. The coupling of inelastic excitations alone could not reproduce the experimental data, however, the effect of octupole state of the projectile was observed to be significant. The multi-neutron positive Q-value transfer channels were also included in the calculations using semi-classical model. It was observed that two neutrons pick-up channel gave a major contribution to the fusion enhancement and successfully reproduce the experimental data at above as well as below barrier energies. The coupling of more than two neutrons transfer could not give any significant enhancement to subbarrier fusion.

Examining the role of transfer coupling in sub-barrier fusion ofTi46,50+Sn124

In this study, the presence of neutron transfer channels with positive Q values can enhance sub-barrier fusion cross sections. Recent measurements of the fusion excitation functions for 58Ni+132,124Sn found that the fusion enhancement due to the influence of neutron transfer is smaller than that in 40Ca +132,124Sn although the Q values for multineutron transfer are comparable. The purpose of this study is to investigate the differences observed between the fusion of Sn + Ni and Sn + Ca. Methods: Fusion excitation functions for 46,50Ti +124Sn have been measured at energies near the Coulomb barrier. As a result, a comparison of the barrier distributions for 46Ti+124Sn and 40Ca+124Sn shows that the 40Ca+124Sn system has a barrier strength resulting from the coupling to the very collective octupole state in 40Ca at an energy significantly lower than the uncoupled barrier. In conclusion, the large sub-barrier fusion enhancement in 40Ca induced reactions is attributed to both couplings to neutron transfer and inelastic excitation, with the octupole vibration of 40Ca playing a major role.

Identification of low-energy isovector octupole states in 144Nd

Recently, first candidates for low-lying isovector states in the octupole sector were suggested. The unambiguous identification of those states will contribute to the decomposition of the octupole-octupole residual interaction in an isoscalar and isovector part. This will help us understand the octupole degree of freedom. In 144Nd the 3− state at 2778 keV is a good candidate for such a “mixed-symmetry’' octupole state. In order to clarify the nature of this state, a 143Nd(n, γ)-experiment was conducted with the EXILL-setup. Following neutron capture the 3− states are populated and EXILL provides the opportunity to determine the multipole-mixing ratios of the 3i−→31- transitions. For the transition from the “mixed-symmetry” octupole state to the symmetric 31− state we expect a strong M1 component.

Octupole strength in the neutron-rich calcium isotopes

Low-lying excited states of the neutron-rich calcium isotopes $^{48-52}$Ca have been studied via $\gamma$-ray spectroscopy following inverse-kinematics proton scattering on a liquid hydrogen target using the GRETINA $\gamma$-ray tracking array. The energies and strengths of the octupole states in these isotopes are remarkably constant, indicating that these states are dominated by proton excitations.

Microscopic study ofCa40+Ni58,64fusion reactions

Background: Heavy-ion fusion reactions at energies near the Coulomb barrier are influenced by couplings between the relative motion and nuclear intrinsic degrees of freedom of the colliding nuclei. The time-dependent Hartree-Fock (TDHF) theory, incorporating the couplings at the mean-field level, as well as the coupled-channels (CC) method are standard approaches to describe low energy nuclear reactions. Purpose: To investigate the effect of couplings to inelastic and transfer channels on the fusion cross sections for the reactions $^{40}$Ca+$^{58}$Ni and $^{40}$Ca+$^{64}$Ni. Methods: Fusion cross sections around and below the Coulomb barrier have been obtained from coupled-channels (CC) calculations, using the bare nucleus-nucleus potential calculated with the frozen Hartree-Fock method and coupling parameters taken from known nuclear structure data. The fusion thresholds and neutron transfer probabilities have been calculated with the TDHF method. Results: For $^{40}$Ca+$^{58}$Ni, the TDHF fusion threshold is in agreement with the most probable barrier obtained in the CC calculations including the couplings to the low-lying octupole $3_1^{-}$ state for $^{40}$Ca and to the low-lying quadrupole $2_1^{+}$ state for $^{58}$Ni. This indicates that the octupole and quadrupole states are the dominant excitations while neutron transfer is shown to be weak. For $^{40}$Ca+$^{64}$Ni, the TDHF barrier is lower than predicted by the CC calculations including the same inelastic couplings as those for $^{40}$Ca+$^{58}$Ni. TDHF calculations show large neutron transfer probabilities in $^{40}$Ca+$^{64}$Ni which could result in a lowering of the fusion threshold. Conclusions: Inelastic channels play an important role in $^{40}$Ca+$^{58}$Ni and $^{40}$Ca+$^{64}$Ni reactions. The role of neutron transfer channels has been highlighted in $^{40}$Ca+$^{64}$Ni.

Nuclear fusion as a probe for octupole deformation inRa224

$\textit{Background}$: Nuclear fusion has been shown to be a perfect probe to study the different nuclear shapes. However, the possibility of testing octupole deformation of a nucleus with this tool has not been fully explored yet. The presence of a stactic octupole deformation in nuclei will enhanced a possible permanent electric dipole moment, leading to a possible demonstration of parity violation. $\textit{Purpose}$: To check whether static octupole deformation or octupole vibration in fusion give qualitatively different results so that both situations can be experimentally disentangled. $\textit{Method}$: Fusion cross sections are computed in the Coupled-Channels formalism making use of the Ingoing-Wave Boundary Conditions (IWBC) for the systems $^{16}$O+$^{144}$Ba and $^{16}$O+$^{224}$Ra. $\textit{Results}$: Barrier distributions of the two considered schemes show different patterns. For the $^{224}$Ra case, the octupole deformation parameter is large enough to create a sizeable difference. $\textit{Conclusions}$: The measurement of barrier distributions can be an excellent probe to clarify the presence of octupole deformation.