Particle-rotor Model Research Articles

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.

Three-Dimension Calculation for the Scattering Problem for Non-Spherical Potential

The interaction of the 238U with a neutron is studied. Correct accounting for the non-spherical shape of the uranium nucleus is in focus. The optical potential is used as a model. It is shown that the spherically symmetric and non-spherical potentials give different scattering patterns, in particular different resonance features of the cross-section. The possibility of using the method as an extension of the particle–rotor model of the nucleus is illustrated.

Evidence for Chiral Wobbler in Nuclei.

Three ΔI=1 bands with the πg_{9/2}⊗νg_{9/2} configuration have been identified in _{35}^{74}Br_{39}. Angular distribution, linear polarization, and lifetime measurements were performed to determine the multipolarity, type, mixing ratio, and absolute transition probability of the transitions. By comparing these experimental observations with the corresponding fingerprints and the quantum particle rotor model calculations, the second and third lowest bands are, respectively, suggested as the chiral partner and one-phonon wobbling excitation built on the yrast band. The evidence indicates the first chiral wobbler in nuclei.

Pairing effect on critical spin in chiral rotation

The critical spin Ic (or critical frequency ħωc) represents the minimum spin (or rotational frequency) required for stable chiral solutions in nuclear systems. The effect of pairing on the critical spin has been examined for the particle-hole configuration π(1h11/2)⊗ν(1h11/2)−1 with a triaxial deformation parameter of γ=30∘ using the particle rotor model, which treats the total angular momentum as a good quantum number. Increasing pairing interaction keeps the critical spin Ic constant, but decreases the critical rotational frequency ħωc. This is due to that the enhanced pairing interaction causes valence nucleons angular momenta to align preferentially along the medium axis, resulting in a larger effective collective moment of inertia and facilitating the emergence of chiral rotation at a lower frequency. However, even with an increase in pairing gap from 0.0 to 2.0MeV, the resulting increase in medium axis alignment is less than 1ħ, which is insufficient to change the value of the critical spin Ic. This study suggests that the critical spin remains robust against the influence of pairing interaction.

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 .

Electromagnetic properties of Λ hypernuclei with a beyond relativistic mean-field approach

We present a microscopic study of electromagnetic properties of the low-lying states of single-Λ hypernucleus Λ9Be using a quantum-number projected generator coordinate method (HyperGCM) based on covariant density functional theory. All the configurations are restricted to have axial symmetry, with the Λ hyperon in the lowest-energy state. The results are compared to the predictions of a simple particle-rotor model (PRM), for which analytic expressions are available. We show that the electromagnetic properties of Λ9Be from the HyperGCM calculation are close to those by the PRM. In particular, it is found that the magnetic moments and M1 transition strengths are less sensitive to the coupling strengths of the ΛN interaction than the electric quadrupole transition strengths. The latter may provide additional constraints on the ΛN interaction.

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.

Wobbling Motion in Nuclei

Wobbling motion as an exotic collective mode in nuclei without axial symmetry, was intensively discussed during the last few years. The observation of the newly proposed transverse wobbling, first reported in 135Pr and soon after in nuclei from other mass regions, was considered as a significant discovery in low-spin nuclear structure. However, both the reported experimental results and the proposed theoretical models were actively questioned in work devoted to the study of the low-spin wobbling mode in the same nuclei. We recently re-measured the electromagnetic character of the ΔI=1 transitions connecting the one- to zero-phonon and the two- to one-phonon wobbling bands in 135Pr, showing their predominant M1 magnetic character, which is in contradiction with the wobbling interpretation. These new experimental results, which were reproduced by either the quasiparticle-plus-triaxial-rotor model and interacting boson-fermion model calculations, are against the previously proposed wobbling nature of the low-spin bands in 135Pr. On the other hand, we obtained conclusive experimental evidence for the theoretically proposed transverse wobbling bands at medium spin in 136Nd. The comparison of the experimental data with calculations using the triaxial projected shell model as well as a new particle-rotor model with frozen orthogonal geometry of the active nucleons, supports the description in terms of transverse wobbling of medium-spin bands in triaxial even-even nuclei.

Possible antimagnetic rotational band in In114

High-spin states of $^{114}\mathrm{In}$ were populated using the reaction $^{110}\mathrm{Pd}\phantom{\rule{4pt}{0ex}}(^{7}\mathrm{Li}, 3n)^{114}\mathrm{In}$ at a beam energy of 26 MeV. More than 30 new $\ensuremath{\gamma}$ transitions and 20 new levels are identified in $^{114}\mathrm{In}$. In total, three new bands and a short cascade are observed, among which a new negative-parity $\mathrm{\ensuremath{\Delta}}I=2$ band built on the $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}2}{d}_{5/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ configuration before the backbend and the $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}2}{d}_{5/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}^{3}$ configuration after the backbend is established. The properties of this band are discussed based on the classical particle-rotor model calculations. The predicted $B(E2)$ and ${\ensuremath{\mathfrak{I}}}^{(2)}/B(E2)$ ratios indicate that the $\mathrm{\ensuremath{\Delta}}I=2$ band after the backbend, has the characteristics of antimagnetic rotation. Meanwhile, the two-shears-like mechanism for the possible antimagnetic rotational band is examined by investigating the orientation of the angular momenta. A new positive-parity $\mathrm{\ensuremath{\Delta}}I=1$ band with the configuration of $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}({g}_{7/2}/{d}_{5/2}){h}_{11/2}^{2}$ is observed.

Examination of nuclear chirality with a magnetic moment measurement of the I=9 isomeric state in Cs128

The $g$ factor of the isomeric $I={9}^{+}$ bandhead of the yrast states in $^{128}\mathrm{Cs}$ is obtained from the time differential perturbed angular distribution measurement performed with the electromagnet at IPN Orsay. An external magnetic field of 2.146 T at the target position was attained with GAMIPE reaction chamber surrounded by four high-purity germanium detectors, of which two were low-energy photon spectrometer type. The results are in accordance with $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}I={9}^{+}$ bandhead assignment and are discussed in the context of chiral interpretation of the $^{128}\mathrm{Cs}$ nucleus as a composition of the odd proton, odd neutron, and even-even core with their angular momentum vectors. The obtained $g$-factor value was compared with predictions of the particle-rotor model. The experimental $g$ factor corresponds to the nonchiral geometry of the isomeric bandhead. This observation indicates the existence of the chiral critical frequency in $^{128}\mathrm{Cs}$ and may explain the absence of the chiral doublet members for $I<13\ensuremath{\hbar}$.

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.

Possible wobbling motion in multiple chiral doublets

The analysis of mixing ratios δ of the ΔI =1 linking transitions in the chiral and multiple chiral doublet bands with the ideal case are theoretically performed for the first time by employing the quantum particle rotor model. The calculated E2 fraction extracted from the mixing ratio show that the ΔI =1 linking transitions in the lowest and excited chiral doublet bands are of the pure M1 character, while those connecting the excited to lowest chiral doublet bands are of M1/E2 character with a relatively large E2 admixture. The further analysis of the angular momentum geometry and azimuthal plots reveals that the excited chiral doublet bands represents a chiral geometry with a wobbling motion of the core. This provides a possible figure of wobbling motion in multiple chiral doublets.

Possible multiple antimagnetic rotational bands in odd-A 103,105Pd and 109Cd nuclei * *Supported by the Science and Technology Research Planning Project of Jilin Provincial Department of Education (JJKH20220965KJ), and the National Natural Science Foundation of China (12175086, 11775098, U1867210, 11405072) and the Fundamental Research Funds for the Central Universities

The positive-parity signature partner bands in 103,105Pd and 109Cd nuclei are investigated using the classical particle-rotor model. Based on the systematic study of neighbouring nuclei, the signature partner bands of 105Pd are assigned to the configuration, and this assignment is also supported by the present calculations. Furthermore, the calculated values of such bands of 105Pd reproduce the experimental values well and exhibit a decrease with increasing angular momentum, suggesting that these two bands may originate from antimagnetic rotation. Similar signature partner bands are also found in the neighboring 103Pd and 109Cd nuclei. The properties of both bands are in general agreement with the fingerprints of antimagnetic rotation, and thus the signature partner bands of 103Pd and 109Cd are suggested to be candidates for the multiple antimagnetic rotational bands of 105Pd. In addition, the evolution of the two-shears-like mechanism for possible multiple antimagnetic rotational bands in 103,105Pd and 109Cd nuclei is examined by investigating the orientation of the angular momenta.

Single-particle and collective excitations in Zn66

Single-particle and collective excitations in $^{66}\mathrm{Zn}$ have been investigated via the multinucleon transfer reaction, $^{26}\mathrm{Mg}(^{48}\mathrm{Ca}$, $\ensuremath{\alpha}4n\ensuremath{\gamma}$) using the Gammasphere multidetector array and the Fragment Mass Analyzer. In addition to confirming and complementing the previously known low-spin structure, a new quasirotational band comprising several stretched $E2$ transitions has been established to high spins. However, due to fragmentary nature of its decay, it was not possible to link this sequence to the low-lying states and, thus, determine the absolute excitation energies, spins, and parities unambiguously. Large-scale shell-model calculations employing the JUN45 and jj44b effective interactions are able to successfully describe the low-spin structure and herewith confirm that it is dominated by single-particle excitations. The newly established rotational cascade is compared with known superdeformed bands in the $A\ensuremath{\approx}60\text{--}70$ mass region, and with results of calculations performed within the frameworks of the cranked shell model and the adiabatic and configuration-fixed constrained covariant density functional theory and the quantum particle-rotor model.

Single-particle and dipole excitations in Co62

An extensive study of the level structure of $^{62}\mathrm{Co}$ has been performed following a complex multinucleon transfer reaction, $^{26}\mathrm{Mg}(^{48}\mathrm{Ca}, 2\ensuremath{\alpha}3np\ensuremath{\gamma})^{62}\mathrm{Co}$, at beam energies of 275, 290, and 320 MeV. The combination of the Gammasphere array, the fragment mass analyzer, and a focal-plane ionization chamber was used to identify and delineate excited levels in $^{62}\mathrm{Co}$. A considerable extension to the $^{62}\mathrm{Co}$ level scheme is proposed with firm spin-parity values assigned on the basis of angular distribution and correlation analyses. Various level sequences built upon states of single-particle character have been observed, and an interpretation of these structures in the framework of the spherical shell model is presented. At moderate spins, two dipole bands have been observed and, based on their phenomenological study, a possible magnetic rotation character is suggested. However, theoretical calculations performed using the particle rotor model support magnetic rotation for only one of these dipole bands.

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.

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.

Possible antimagnetic rotation in 99Pd

The reduced electric quadrupole transition rates have been calculated for states of the negative parity band in the [Formula: see text]Pd nucleus using semiclassical particle-rotor model calculations. The calculated transition rates are found to decrease with increasing spin states. The dynamic moment of inertia [Formula: see text] of the states above I = [Formula: see text] are found to be large. The spin ([Formula: see text]) versus frequency ([Formula: see text]) plot obtained from the semiclassical model for the configuration [Formula: see text] ⊗[Formula: see text] is found to agree with the experimental data, which suggests a possible anti magnetic rotational character in the negative parity band.

Possible existence of multiple wobbling modes in A≈60 nuclei

The nuclear multiple wobbling modes in $A\ensuremath{\approx}60$ mass region are explored by the adiabatic and configuration-fixed constrained covariant density functional theory for nickel isotopes for the first time. The potential-energy curves and deformation parameters $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ of the ground and excited states of $^{57\text{--}62}\mathrm{Ni}$ are obtained to search for the possible wobbling candidates. It is shown that there are suitable triaxial deformations and high-$j$ particle(s) or hole(s) configurations in $^{57\text{--}62}\mathrm{Ni}$, which are beneficial to the appearance of wobbling motion, including the simple, longitudinal and transverse modes. Moreover, possible multiple wobbling motions based on different high-$j$ configurations might coexist in one single nucleus, which provides a promising basis for future experiments to find wobbling bands in the $A\ensuremath{\approx}60$ mass region. Finally, taking the nucleus $^{62}\mathrm{Ni}$ as an example, the experimental energy spectra, the angular momentum components, and the azimuthal plots are investigated by the combination of the covariant density functional theory and quantum particle rotor model. The transverse wobbling mode is suggested in this nucleus.

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