Particle-rotor Model Research Articles

105Tc nuclear structure and systematic evolution of states of 1/2+[431] intruder band in odd-A 95,97,99,101,103,105,107Tc isotopes

Previously observed negative and positive parity states of 105Tc were studied in the framework of the particle-rotor model. Transition properties and experimental energies were compared to the predictions of model calculations. A systematic study of the evolution of the intruder π1/2+[413] band in the nuclear structure of odd-A technetium isotopes 95,97,99,101,103,105,107Tc is presented as well. The existence of this intruder band has been argued previously in 95,97,99,101,103Tc isotopes (partially populated) and fully observed and confirmed in 105Tc. It will be shown that changes in deformation and subsequently the position of the Fermi level, vis a vis the 1/2+[431] intruder orbital originating from the π(d5/2, g7/2) subshells, predominantly affect these systematic changes. All four interpreted experimental rotational bands are naturally predicted by the rotational model as bands build on states of good Ω originating from the 5/2+[422], 5/2–[303], 3/2–[301], and 1/2+[431] orbitals near the Fermi level in deformed 105Tc (strong coupling). Further experimental investigation about missing data are needed for those observed in low lying states in both 105Tc and 103Tc to confirm the presence of the 1/2–[301] rotational band that is well defined in lighter 95,97,99,101Tc isotopes.

Coexistence of planar and aplanar rotations in 195Tl

The chirality suggested for the doublet bands B2 and B2a in 195Tl in A∼190 region is reexamined. The potential-energy curves and the configurations together with the deformation parameters are obtained by the constrained covariant density functional theory. The corresponding experimental energy spectra, energy differences between doublet bands, and the available B(M1)/B(E2) values are investigated by the fully quantal particle rotor model. Analysis on the basis of the angular momentum components, the K-plots, and the azimuthal plots suggest a planar rotation interpretation for the bands B2 and B2a. Hence, it coexists with the aplanar rotation in the other doublet bands B4 and B4a in 195Tl.

Analysis of the 18Fg,m(d,p)F19 reactions in the rotational model

Spectroscopic strengths for the ${}^{18}{\mathrm{F}}^{g,m}(d,p)\phantom{\rule{0.16em}{0ex}}^{19}\mathrm{F}$ reactions to members of the ground-state band in $^{19}\mathrm{F}$ are interpreted in the rotational model. The analysis considers two different coupling schemes, namely, the strong and decoupled limits of the particle rotor model to describe the ground and isomeric states of $^{18}\mathrm{F}$, as well as the transitions to the ground-state band in $^{19}\mathrm{F}$. Our results, obtained using Nilsson amplitudes for the neutron levels $\frac{1}{2}[220], \frac{3}{2}[211]$, and $\frac{5}{2}[202]$ calculated at a deformation ${\ensuremath{\epsilon}}_{2}=0.32$ are in agreement with the measurements and USDB shell-model calculations.

Longitudinal Wobbling Motion in Au187

The rare phenomenon of nuclear wobbling motion has been investigated in the nucleus ^{187}Au. Alongitudinal wobbling-bands pair has been identified and clearly distinguished from the associated signature-partner band on the basis of angular distribution measurements. Theoretical calculations in the framework of the particle rotor model are found to agree well with the experimental observations. This is the first experimental evidence for longitudinal wobbling bands where the expected signature partner band has also been identified, and establishes this exotic collective mode as a general phenomenon over the nuclear chart.

Observation of signature partner bands in Sb117

Rotational band structures and low-lying single-particle levels in $^{117}\mathrm{Sb}$ have been populated using reaction $^{115}\mathrm{In}(\ensuremath{\alpha}$, $2n)^{117}\mathrm{Sb}$ at a beam energy of 28 MeV and investigated using $\ensuremath{\gamma}$-ray spectroscopic techniques. The existing level scheme has been extended with the observation of 31 new transitions. The signature partner of the band structure based on the configuration of $\ensuremath{\pi}{g}_{7/2}\phantom{\rule{4pt}{0ex}}\ensuremath{\bigotimes}\phantom{\rule{4pt}{0ex}}2\mathrm{p}\text{\ensuremath{-}}2\mathrm{h}$ of the $^{116}\mathrm{Sn}$ core has been established in $^{117}\mathrm{Sb}$ for the first time. Several single-particle nonyrast transitions connecting to various band structures have also been identified. Measurements of the DCO ratios, polarization asymmetry and angular distribution of the observed $\ensuremath{\gamma}$ rays have been carried out to assign the spin-parities to the levels of all the band structures and the low-lying single-particle states, populated in the present work. The spin-parities are also determined for the states of the two previously unassigned bands. The lower-spin structures have been interpreted on the basis of large-scale shell-model calculations using OXBASH. Particle Rotor Model (PRM) calculations have been carried out to explain the large signature splitting of the observed signature partner bands.

Transverse wobbling in an even-even nucleus

Two new bands built on the two-quasiparticle $\pi(h_{11/2})^2$ configuration of the even-even nucleus $^{130}$Ba are investigated using constrained triaxial covariant density functional theory combined with quantum particle rotor model calculations. The energy difference between the two bands, as well as the available electromagnetic transition probabilities $B(M1)_{\textrm{out}}/B(E2)_{\textrm{in}}$ and $B(E2)_{\textrm{out}}/B(E2)_{\rm{in}}$, are well reproduced. The analysis of the angular momentum geometry reveals that the higher band represents transverse wobbling motion of a two-quasiparticle configuration. This is the first example of two-quasiparticle wobbling bands in an even-even nucleus.

Global microscopic calculations of odd-odd nuclei

The macroscopic-microscopic finite-range droplet model is combined with a particle-rotor coupling model in order to systematically describe low-energy spectra of odd-odd nuclei. The odd proton and neutron are allowed to interact through effective nuclear forces representing the residual neutron-proton interaction. In particular, ground-state spins and parities are calculated and compared to data, where all 268 axially symmetric nuclei which have reliable spin and parity assignments in the Nubase 2016 database are considered. Using a residual neutron-proton interaction composed of both central and tensor terms the agreement with experimental ground-state spins and parities reaches 41% for spherical nuclei and 31% for deformed nuclei. The model is applied to study possible $\ensuremath{\alpha}$-decay chains in superdeformed odd-odd nuclei, and ${Q}_{\ensuremath{\alpha}}$ values are calculated considering favored decay-paths as compared to ground-state paths.

Properties of platinum isotopes in framework of particle rotor model and IBM

We introduce a model that consists of an axially symmetric core plus two particles occupying the lowest two sublevels i13/2 orbital. The exact solution of this model has been calculated by diagonalizing 4×4 matrices. By fitting the experimental single particle spectrum in these nuclei, a new set of Nilsson parameters and deformation parameter are proposed. Since the excitation energy spectrum of the core is very difficult to simulate through any simple energy angular momentum relationship, we use the variable moment of inertia (VMI) core formalism. The calculated kinematic moment of inertia, rotational frequency and the component of angular momentum along an axis perpendicular to the symmetry axis reproduce quite well the backbending of the yrast band in 180–192Pt. Nuclei exhibit an anomaly along the yrast line around angular momentum 10+ to 12+. An apparent change of structure occurs when transiting from 186Pt to 188Pt.It is more appropriate to describe Pt nuclei within the IBM Hamiltonian based on the intrinsic coherent state to generate the potential energy surfaces (PES's) to identify the shape transition. The equilibrium values of shape parameter β are obtained by minimizing the PES and also the location of the critical points are obtained. The isotopic chain 180–192Pt evolves from prolate to oblate shapes between 186Pt (prolate) and 188Pt (oblate). The PES's for both 188,190Pt are γ-soft having the minimum on the oblate side.

Chirality of Nd135 reexamined: Evidence for multiple chiral doublet bands

One new pair of positive-parity chiral doublet bands have been identified in the odd-A nucleus Nd135 which together with the previously reported negative-parity chiral doublet bands constitute a third case of multiple chiral doublet (MχD) bands in the A≈130 mass region. The properties of the MχD bands are well reproduced by constrained covariant density functional theory and particle rotor model calculations. The newly observed MχD bands in Nd135 represents an important milestone in supporting the existence of MχD in nuclei.Received 6 April 2019Revised 23 May 2019DOI:https://doi.org/10.1103/PhysRevC.100.024314©2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsCollective modelsElectromagnetic transitionsNuclear spin & parityNuclear structure & decaysNuclear Physics

Behavior of the collective rotor in nuclear chiral motion

The behavior of the collective rotor in the chiral motion of triaxially deformed nuclei is investigated using the particle rotor model by transforming the wave functions from the $K$-representation to the $R$-representation. After examining the energy spectra of the doublet bands and their energy differences as functions of the triaxial deformation, the angular momentum components of the rotor, proton, neutron, and the total system are investigated. Moreover, the probability distributions of the rotor angular momentum ($R$-plots) and their projections onto the three principal axes ($K_R$-plots) are analyzed. The evolution of the chiral mode from a chiral vibration at the low spins to a chiral rotation at high spins is illustrated at triaxial deformations $\gamma=20^\circ$ and $30^\circ$.

Diversity of shapes and rotations in the γ-soft 130Ba nucleus: First observation of a t-band in the A = 130 mass region

Several new bands have been identified in 130Ba, among which there is one with band-head spin 8+. Its properties are in agreement with the Fermi-aligned νh11/22, 7/2−[523]⊗9/2−[514] Nilsson configuration. This is the first observation of a two-quasiparticle t-band in the A=130 mass region. The t-band is fed by a dipole band involving two additional h11/2 protons. The odd-spin partners of the proton and neutron S-bands and the ground-state band at high spins are also newly identified. The observed bands are discussed using several theoretical models, total Routhians surfaces (TRS), tilted axis cranking (TAC), particle rotor model (PRM) and projected shell model (PSM), which strongly suggest the coexistence of prolate and oblate shapes polarized by rotation aligned two-proton and two-neutron configurations, as well as prolate collective rotations around axes with different orientations. With the new results, 130Ba presents one of the best and most complete sets of collective excitations that a γ-soft nucleus can manifest at medium and high spins, revealing a diversity of shapes and rotations for the nuclei in the A=130 mass region.

Possible Antimagnetic Rotational Band in 102Ru

Semiclassical particle-rotor model calculations have been carried out for the ground-state band of 102Ru nucleus to find out the possibility of antimagnetic rotational structure with more than two pair of proton holes in A ≈ 110 mass region. The experimental dynamic moment of inertia in the spin range of 14+ to 24+ is constant throughout the band and is found in the range of antimagnetic rotational bands. The model calculated decreasing trend of B(E2) with angular momentum and sharply increasing trend of I(2)/B(E2) indicates the antimagnetic nature of the band with higher number of proton holes. Reasonable agreements between the experiment and the calculation of spin vs. angular frequency support the adequacy of the parameters and the configuration used for the calculation.

Possible chiral doublets in 60Ni

The open problem on whether or not the chirality exists in doublet bands M1 and M4 in light-mass even-even nucleus 60Ni is studied by adopting the recently developed fully quantal four-j shells triaxial particle rotor model. The corresponding experimental energy spectra, energy differences between doublet bands, and the available B(M1)/B(E2) values are successfully reproduced. The analyses on the basis of the angular momentum components, the azimuthal plots, and the K-plots suggest that the chiral modes exist at I≥12ħ in doublet bands M1 and M4.

Multiple chiral doublet bands with octupole correlations in reflection-asymmetric triaxial particle rotor model

A reflection-asymmetric triaxial particle rotor model (RAT-PRM) with a quasi-proton and a quasi-neutron coupled with a reflection-asymmetric triaxial rotor is developed and applied to investigate the multiple chiral doublet (MχD) bands candidates with octupole correlations in 78Br. The calculated excited energies, energy staggering parameters, and B(M1)/B(E2) ratios are in a reasonable agreement with the data of the chiral doublet bands with positive- and negative-parity. It is found that both the triaxial deformation γ and octupole deformation β3 influence the calculated B(E1) values. The chiral geometry based on the angular momenta for the rotor, the valence proton and valence neutron is discussed in details.

Experimental Evidence for Transverse Wobbling in ^{105}Pd.

New rotational bands built on the ν(h_{11/2}) configuration have been identified in ^{105}Pd. Two bands built on this configuration show the characteristics of transverse wobbling: the ΔI=1 transitions between them have a predominant E2 component and the wobbling energy decreases with increasing spin. The properties of the observed wobbling bands are in good agreement with theoretical results obtained using constrained triaxial covariant density functional theory and quantum particle rotor model calculations. This provides the first experimental evidence for transverse wobbling bands based on a one-neutron configuration, and also represents the first observation of wobbling motion in the A∼100 mass region.

Identification of high- K rotation in Ba130 : Testing the consistency of electromagnetic observables

The band built on the Kπ=8−,T1/2=9.4 ms isomer of Ba130 has been identified, filling the gap in the systematics of the dipole bands built on the 8− isomers in the N=74 isotones from Xe128 to Gd138. The use of the GALILEO array in conjunction with its ancillaries EUCLIDES and Neutron Wall, helped to firmly place the newly identified transitions on top of the long-lived isomer. The extracted gK and gR gyromagnetic factors are in agreement with the 7/2+[404]⊗9/2−[514] two-neutron Nilsson configuration. Particle-rotor model calculations give an understanding of the limited degree of K mixing. The experimental information on the Kπ=8− isomer of Ba130 is now the most complete among the K isomers of the N=74 isotones.1 MoreReceived 24 September 2018DOI:https://doi.org/10.1103/PhysRevC.99.014307©2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsIsomer decaysNuclear structure & decaysProperties90 ≤ A ≤ 149TechniquesCollective modelsNuclear Physics

Two-dimensional collective Hamiltonian for chiral and wobbling modes. II. Electromagnetic transitions

The intraband electromagnetic transitions in the framework of collective Hamiltonian for chiral and wobbling modes are calculated. By going beyond the mean field approximation on the orientations of rotational axis, the collective Hamiltonian provides the descriptions on both yrast band and collective excitation bands. For a system with one $h_{11/2}$ proton particle and one $h_{11/2}$ neutron hole coupled to a triaxial rotor ($\gamma=-30^\circ$), the intraband electromagnetic transitions given by the one-dimensional and two-dimensional collective Hamiltonian are compared to the results by the tilted axis cranking approach and particle rotor model. Compared with the tilted axis cranking approach, the electromagnetic transitions given by the collective Hamiltonian have a better agreement with those by the particle rotor model, due to the consideration of the quantum fluctuations.

Behavior of the collective rotor in wobbling motion

The behavior of the collective rotor in wobbling motion is investigated within the particle-rotor model for the nucleus $^{135}$Pr by transforming the wave functions from the $K$-representation to the $R$-representation. After reproducing the experimental energy spectra and wobbling frequencies, the evolution of the wobbling mode in $^{135}$Pr, from transverse at low spins to longitudinal at high spins, is illustrated by the distributions of the total angular momentum in the intrinsic reference frame (azimuthal plot). Finally, the coupling schemes of the angular momenta of the rotor and the high-$j$ particle for transverse and longitudinal wobbling are obtained from the analysis of the probability distributions of the rotor angular momentum ($R$-plots) and their projections onto the three principal axes ($K_R$-plots).

Disappearance of nuclear deformation in hypernuclei: A perspective from a beyond-mean-field study

The previous mean-field calculation [Myaing Thi Win and K. Hagino, Phys. Rev. C{\bf 78}, 054311 (2008)] has shown that the oblate deformation in $^{28,30,32}$Si disappears when a $\Lambda$ particle is added to these nuclei. We here investigate this phenomenon by taking into account the effects beyond the mean-field approximation. To this end, we employ the microscopic particle-rotor model based on the covariant density functional theory. We show that the deformation of $^{30}$Si does not completely disappear, even though it is somewhat reduced, after a $\Lambda$ particle is added if the beyond-mean-field effect is taken into account. We also discuss the impurity effect of $\Lambda$ particle on the electric quadrupole transition, and show that an addition of a $\Lambda$ particle leads to a reduction in the $B(E2)$ value, as a consequence of the reduction in the deformation parameter.

Multiple chiral doublets in four-j shells particle rotor model: Five possible chiral doublets in [formula omitted]Nd76

A particle rotor model, which couples nucleons in four single-j shells to a triaxial rotor core, is developed to investigate the five pairs of nearly degenerate doublet bands recently reported in the even-even nucleus 136Nd. The experimental energy spectra and available B(M1)/B(E2) values are successfully reproduced. The angular momentum geometries of the valence nucleons and the core support the chiral rotation interpretations not only for the previously reported chiral doublet, but also for the other four candidates. Hence, 136Nd is the first even-even candidate nucleus in which the multiple chiral doublets exist. Five pairs of chiral doublet bands in a single nucleus is also a new record in the study of nuclear chirality.