Octupole Correlations Research Articles

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.

Alignment effects in the medium-spin level structure of Se78

The excited states of $^{78}\mathrm{Se}$ were populated using the $^{76}\mathrm{Ge}(\ensuremath{\alpha},2n)$ fusion evaporation reaction. The deexcited gamma rays were detected using the Indian National Gamma Array (INGA) spectrometer comprising clover and low-energy photon spectrometer (LEPS) detectors. The ground state band of $^{78}\mathrm{Se}$ has been extended up to ${E}_{x}$ = 8.5 MeV and $J$ = $16\ensuremath{\hbar}$; this excitation regime is very close to the $\ensuremath{\pi}(1{g}_{9/2}^{2})$ crossing frequency. Several newly observed in-band and intraband transitions belonging to the other bands of $^{78}\mathrm{Se}$ have also been placed in the level scheme based on their coincidence relationships. From the newly identified $E1$ transitions, an enhancement in the $B(E1)$/$B(E2)$ values with spin has been observed which indicates the onset of octupole correlations in the band structure built on the ${3}^{\ensuremath{-}}$, 2508-keV state. Persistence of triaxial shape up to the highest observed spin of the ground state band has been observed and the feature of successive $1{g}_{9/2}^{2}$ quasiparticle alignments due to protons and neutrons has been unveiled. The consequences arising due to the occurrence of the neutron $1{g}_{9/2}$ quasiparticle alignments in the other observed correlated band structures are also presented. The results are interpreted in terms of total Routhian surface (TRS) calculations and the level structure systematic of the neighboring nuclei.

Evolution of nuclear structure through isomerism in Fr216

Three new isomers have been identified in the transitional odd-odd $^{216}\mathrm{Fr}$ nucleus. The properties of the $({11}^{+})$ isomer with ${T}_{1/2}$ = 9.6(14) ns are compared with those of the similar isomeric states in neighboring doubly-odd nuclei. The experimental results are compared with predictions of shell-model calculations and a fair agreement is observed between the experimental and calculated excitation energies of the $({11}^{+})$ isomeric state and the states to which it decays. The deviation between the measured and calculated reduced transition probabilities suggests contribution from effects other than the single-particle degrees of freedom in these states. Evidence of two high-spin $[{J}^{\ensuremath{\pi}}>({18}^{+})]$ isomers above 2.2 MeV excitation energy with ${T}_{1/2}=7.8(14)$ and 89(9) ns is also presented. These isomers at high excitation energies reflect a pronounced change in the structure above the previously established level scheme, where moderate quadrupole collectivity and octupole correlations were evident.

Shape coexistence and octupole correlations in Se72

In the present paper, we report the results from the study of excited states in the $^{72}\mathrm{Se}$ nucleus using the $^{50}\mathrm{Cr}(^{28}\mathrm{Si}, \ensuremath{\alpha}2p)^{72}\mathrm{Se}$ fusion evaporation reaction at a beam energy of 90 MeV. The deexciting $\ensuremath{\gamma}$ rays were detected using the Indian National Gamma Array (INGA). A total of ten new $\ensuremath{\gamma}$-ray transitions have been identified using the $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence technique. The ${K}^{\ensuremath{\pi}}={0}_{2}^{+}$ band based on an isomeric state has been extended up to a (${10}^{+}$) state at 5.473 MeV excitation energy, and four new interconnecting transitions have been placed between this band and yrast band. Further, the enhanced interconnecting $E1$ transitions between positive- and negative-parity bands suggest the existence of octupole correlations in this nucleus. The characteristics of the observed bands in the experiment have been interpreted in terms of the total Routhian surface (TRS) calculations.

Evidence of Quadrupole and Octupole Deformations in ^{96}Zr+^{96}Zr and ^{96}Ru+^{96}Ru Collisions at Ultrarelativistic Energies.

In the hydrodynamic model description of heavy-ion collisions, the elliptic flow v_{2} and triangular flow v_{3} are sensitive to the quadrupole deformation β_{2} and octupole deformation β_{3} of the colliding nuclei. Therelations between v_{n} and β_{n} have recently been clarified and were found to follow a simple parametric form. The STAR Collaboration has just published precision v_{n} data from isobaric ^{96}Ru+^{96}Ru and ^{96}Zr+^{96}Zr collisions, where they observe large differences in central collisions v_{2,Ru}>v_{2,Zr} and v_{3,Ru}<v_{3,Zr}. Using a transport model simulation, we show that these orderings are a natural consequence of β_{2,Ru}≫β_{2,Zr} and β_{3,Ru}≪β_{3,Zr}. We reproduce the centrality dependence of the v_{2} ratio qualitatively and v_{3} ratio quantitatively and extract values of β_{2} and β_{3} that are consistent with those measured at low-energy nuclear structure experiments. STAR data provide the first direct evidence of strong octupole correlations in the ground state of ^{96}Zr in heavy-ion collisions. Our analysis demonstrates that flow measurements in high-energy, heavy-ion collisions, especially using isobaric systems, are a new precision tool to study nuclear structure physics.

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 $^{79}\mathrm{Se}$.

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.

Erratum: Possible octupole correlation in Pr147 and πh11/2 bands in Pr149,151 [Phys. Rev. C 62 , 044303 (2000)

Erratum: Possible octupole correlation in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Pr</mml:mi><mml:mprescripts /><mml:none /><mml:mn>147</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>π</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mrow><mml:mn>11</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> bands in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Pr</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>149</mml:mn><mml:mo>,</mml:mo><mml:mn>151</mml:mn></mml:mrow></mml:mmultiscripts></mml:math> [Phys. Rev. C <b>62</b> , 044303 (2000)

Microscopic description of octupole collective excitations near N=56 and N=88

Octupole deformations and related collective excitations are analyzed using the framework of nuclear density functional theory. Axially-symmetric quadrupole-octupole constrained self-consistent mean-field (SCMF) calculations with a choice of universal energy density functional and a pairing interaction are performed for Xe, Ba, and Ce isotopes from proton-rich to neutron-rich regions, and neutron-rich Se, Kr, and Sr isotopes, in which enhanced octupole correlations are expected to occur. Low-energy positive- and negative-parity spectra and transition strengths are computed by solving the quadrupole-octupole collective Hamiltonian, with the inertia parameters and collective potential determined by the constrained SCMF calculations. Octupole-deformed equilibrium states are found in the potential energy surfaces of the Ba and Ce isotopes with $N\approx 56$ and 88. The evolution of spectroscopic properties indicates enhanced octupole correlations in the regions corresponding to $N\approx Z\approx 56$, $Z\approx 88$ and $Z\approx 56$, and $N\approx 56$ and $Z\approx 34$. The average $\beta_{30}$ deformation parameter and its fluctuation exhibit signatures of octupole shape phase transition around $N=56$ and 88.

Octupole correlations in 127I

In-beam [Formula: see text]-ray spectroscopy of [Formula: see text]I was carried out following [Formula: see text]Sn(7Li, 4n[Formula: see text]) fusion-evaporation reaction at a beam energy of 33 MeV. Ratio of the electric dipole (E1) and electric quadrupole (E2) transition probabilities [B(E1)/B(E2)] for the transitions depopulating from the [Formula: see text] states have been extracted from this study. Existence of enhanced E1 transition rates between the opposite parity bands, associated dominantly with [Formula: see text] and [Formula: see text] configurations, provides an indication of octupole correlations in this nucleus

Octupole correlations near Te110

The lifetime of the 2+ and 9−, 11−, 13−, 15− states in the neutron-deficient Te110 was measured for the first time using the recoil distance Doppler shift technique. The reported value of the reduced transition probability B(E2;0g.s+→2+)=4.3(8)×103e2fm4 supports the systematic for even-mass Te isotopes and was interpreted in the framework of the large-scale shell model and cranked shell model calculations. The measured reduced transition probabilities in the negative-parity yrast band revealed the upward trend towards the high spins. The enhanced collectivity is discussed in terms of the tilted axis cranking approach and the symmetry configuration mixing method with the Gogny D1S interaction.6 MoreReceived 10 September 2020Revised 8 December 2020Accepted 3 February 2021DOI:https://doi.org/10.1103/PhysRevC.103.044321©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsLifetimes & widthsNuclear forcesNucleon-nucleon interactionsProperties90 ≤ A ≤ 149Nuclear Physics

Alternating-parity bands of U236,238 and Pu238,240 in a particle-number-conserving method based on the cranked shell model

The particle-number-conserving (PNC) method in the framework of cranked shell model (CSM) is developed to deal with the reflection-asymmetric nuclear system by applying the ${S}_{x}$ symmetry. Based on an octupole-deformed Nilsson potential, the alternating-parity bands in $^{236,238}\mathrm{U}$ and $^{238,240}\mathrm{Pu}$ are investigated. The experimental kinematic moments of inertia (MoI) and the angular momentum alignments of all studied bands are reproduced well in the PNC-CSM calculations. The striking difference of rotational behaviors between U and Pu isotopes can be linked to the strength of octupole correlations. The upbendings of the alternating-parity bands in $^{236,238}\mathrm{U}$ are due to the alignments of pairs of nucleons occupying $\ensuremath{\nu}{g}_{9/2}, \ensuremath{\pi}{f}_{7/2}$ orbitals and $\ensuremath{\nu}{j}_{15/2}, \ensuremath{\pi}{i}_{13/2}$ high-$j$ intruder orbitals. In particular, the interference terms of nucleon occupying the octupole-correlation pairs of ${\ensuremath{\nu}}^{2}{j}_{15/2}{g}_{9/2}$ and of ${\ensuremath{\pi}}^{2}{i}_{13/2}{f}_{7/2}$ give a very important contribution to the suddenly gained alignments.

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.

Investigating the structure of the low–lying states in 140Ba

The neutron–rich 144–146Ba isotopes have been studied recently in terms of their experimental B(E3) values [1, 2]. Although featuring large uncertainties, the results were found to be significantly larger than any theoretical calculation. Similar questions exist for the slightly lighter isotope 140Ba, which is particularly interesting since it is located at the onset of octupole correlations. The lifetimes of the lower–lying states are completely unknown, with the sole exception of the first 2+ state [3].In this work, we report on the outcome of a short test run, attempting to populate the states of interest using the 138Ba(18O,16O)140Ba reaction. The experiment was carried out at IFIN–HH using a specially manufactured nat Ba target sandwiched between two Au layers. This was considered imperative due to Barium’s quick oxidation in air. Four beam energies (61,63,65,67 MeV) below the Coulomb barrier have been tested. The subsequent γ decay was measured using the Bucharest ROSPHERE array, consisting of 15 Ge detectors and 10 LaBr3(Ce) scintillators.The preliminary results from the test run report on the level population strengths and the limits in lifetime measurements, which are expected to provide new information on the structural effects in neutron–rich barium isotopes, especially regarding quadrupole and octupole degrees of freedom. The findings are also expected to act as stringent tests to theoretical modeling in this mass regime.

Recent progress in multiple chiral doublet bands * * Supported by the Shandong Natural Science Foundation, China (JQ201701) and the National Natural Science Foundation of China (11622540)

Recent progress regarding multiple chiral doublet bands ( ) is reviewed from the experimental and theoretical perspectives. In particular, the experimental findings, theoretical predictions, selection rule for electromagnetic transitions, with octupole correlations, and some related topics are highlighted. Based on these discussions, it is of great scientific interest to search for the other , as well as possible chiral wobblers, chirality-parity quartet bands, and chirality-pseudospin triplet (or quartet) bands in the nuclear system.

Pseudospin symmetry and octupole correlations for multiple chiral doublets in Ba131

A reflection-asymmetric triaxial particle rotor model with three quasiparticles and a reflection-asymmetric triaxial rotor is developed, and applied to investigate the observed multiple chiral doublets (M\c{hi}D) candidates with octupole correlations in 131Ba, i.e., two pairs of positive-parity bands D3-D4 and D5-D6, as well as one pair of negative-parity bands D7-D8. The energy spectra, the energy staggering parameters, the B(M1)/B(E2) ratios, and the B(E1)/B(E2) ratios are reproduced well. The chiral geometries for these M\c{hi}D candidates are examined by the azimuthal plots, and the evolution of chiral geometry with spin is clearly demonstrated. The intrinsic structure for the positive-parity bands is analyzed and the possible pseudospin-chiral quartet bands are suggested.

Signatures of enhanced octupole correlations at high spin in Nd136

Experimental signatures of moderately enhanced octupole correlations at high spin in Nd136 are indicated for the first time. The extracted dipole moments of two negative-parity bands are only two times smaller than those of the lanthanide nuclei with N≈90 which present well-established octupole correlations. Calculations using the cranked quasiparticle random phase approximation and a model of quadrupole-octupole rotations with octupole vibrations reveal the structure of the bands and the enhanced octupole correlations at high spin in Nd136.

In-beam γ -ray and electron spectroscopy of Md249,251

The odd-$Z$ $^{251}$Md nucleus was studied using combined $\gamma$-ray and conversion-electron in-beam spectroscopy. Besides the previously observed rotational band based on the $[521]1/2^-$ configuration, another rotational structure has been identified using $\gamma$-$\gamma$ coincidences. The use of electron spectroscopy allowed the rotational bands to be observed over a larger rotational frequency range. Using the transition intensities that depend on the gyromagnetic factor, a $[514]7/2^-$ single-particle configuration has been inferred for this band, i.e., the ground-state band. A physical background that dominates the electron spectrum with an intensity of $\simeq$ 60% was well reproduced by simulating a set of unresolved excited bands. Moreover, a detailed analysis of the intensity profile as a function of the angular momentum provided a method for deriving the orbital gyromagnetic factor, namely $g_K = 0.69^{+0.19}_{-0.16}$ for the ground-state band. The odd-$Z$ $^{249}$Md was studied using $\gamma$-ray in-beam spectroscopy. Evidence for octupole correlations resulting from the mixing of the $\Delta l = \Delta j = 3$ $[521]3/2^-$ and $[633]7/2^+$ Nilsson orbitals were found in both $^{249,251}$Md. A surprising similarity of the $^{251}$Md ground-state band transition energies with those of the excited band of $^{255}$Lr has been discussed in terms of identical bands. Skyrme-Hartree-Fock-Bogoliubov calculations were performed to investigate the origin of the similarities between these bands.

Pear-shaped atomic nuclei.

This review presents the current status of experimental evidence for the occurrence of reflection-asymmetric or ‘pear’ shapes in atomic nuclei, which arises from the presence of strong octupole correlations in the nucleon–nucleon interactions. The behaviour of energy levels and electric octupole transition moments is reviewed, with particular emphasis on recent measurements. The relevance of nuclear pear shapes to measurements of fundamental interactions is also discussed.

Evidence for pseudospin-chiral quartet bands in the presence of octupole correlations

Three nearly degenerate pairs of doublet bands are identified in 131Ba. Two of them, with positive-parity, are interpreted as pseudospin-chiral quartet bands. This is the first time that a complete set of chiral doublet bands built on the pseudospin partners π(d5/2,g7/2) is observed. The chiral bands with opposite parity built on 3-quasiparticle configurations are directly connected by many E1 transitions, without involving an intermediary non-chiral configuration. The observed band structures in 131Ba have been investigated by using the reflection-asymmetric particle rotor model. The energies and the electromagnetic transition ratios of the three pairs of doublet bands observed in 131Ba are reproduced and they are interpreted as chiral doublet bands with three-quasiparticle configurations. It is the first time that multiple chiral bands are observed in the presence of enhanced octupole correlations and pseudospin symmetry.