Yrast Band Research Articles

Microscopic study of near yrast band structures in odd-mass $$^{117-127}$$I isotopes

Microscopic study of near yrast band structures in odd-mass $$^{117-127}$$I isotopes

An Investigation into Properties for (_66^156)Dy Isotope Using IBM-1 and IVBM Model

Abstract: The (_66^156)Dy isotopes in the O (6) region were investigated. The positive ground-state band of (_66^156)Dy nuclei was calculated using the interacting boson model ‎(IBM-1) and the interacting vector boson model (IVBM). The negative parity band energies of the above isotope were calculated using (IVBM) only. We plotted the ratios ((E(I+2))/(〖E(2〗_1^+)), (E(I+2))/(E(I)),r(((I+2))/I)) and the E-GOS curve as a function of the spin (I) to investigate the properties of the yrast band. Accordingly, the best-fit values of the parameters were used to construct the Hamiltonian, and the electromagnetic transition probability B(E2) of this nucleus was determined. Theoretical energy levels of dysprosium-156 isotope with a neutron number N = 90 and spin parity up to 〖30〗_1^+ were obtained using the MATLAB-20 simulation program. A comparison of these calculated energy levels with the corresponding experimentally measured ones shows a good agreement. The results also ‎draw our attention to the fact that the nucleus of interest deforms and exhibits gamma-instability ‎properties. Keywords: Dysprosium Isotopes, Even-even nuclei, Interacting Boson Model-1, Interacting Vector Boson Model, Negative parity, Yrast band. Abbreviations and Acronyms, IBM: Interacting Boson Model, IVBM: Interacting Vector Boson Model, U(5): Spherical limit, SU(3): Axially deformed shape limit O(6): γ-unstable limit, SP(12; R): the non-compact symplectic group.

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.

Indications of octupole correlation in 84Sr

Excited states in the 84Sr nucleus were investigated via the 76Ge(12C,4n)84Sr reaction at a beam energy of 58 MeV. The de-excited γ-rays were detected using the Indian National Gamma Array (INGA) spectrometer at Inter-University Accelerator Center, New Delhi. Directional Correlation from Oriented (DCO) states ratio and the polarization asymmetry (Δ) measurements were done to confirm the spin-parity of the low-lying states. Eight new γ-ray transitions were placed in the level scheme of 84Sr. The systematic behaviour of energy staggering S(I) of the γ-band (Band 1 and Band 2) was compared with the γ-bands in the mass A ≈ 80 region and the nuclei of other mass regions with similar behaviour (odd-I down). The E1 character is confirmed for strong γ-ray transitions connecting Band 3 to the Yrast band. Comparison of new results such as B(E1)/B(E2) ratio, frequency ratio ω −/ω + and energy displacement ΔE in 84Sr with those of 72Se, 150Sm, 152Gd, 220Ra and 224Th nuclei suggests the presence of octupole correlations in 84Sr.

Microscopic study of normal deformed bands in 167,169,171Lu

The normal deformed bands of [Formula: see text]Lu isotopes have been studied by using projected shell model approach. The band head spins, configurations and energies of all the normal deformed bands are reproduced well by the above said approach. The present calculations have predicted [Formula: see text] band head spin for [523]7/2− bands of [Formula: see text]Lu. The observed systematics of aligned angular momenta and the experimental differences in frequencies around the backbends for all the normal deformed bands are reproduced well by the theoretical results. Besides this, the observed backbends or upbends in these isotopes may be ascribed to the alignment of a pair of neutrons in the neutron [Formula: see text] orbital. Although the theoretical [Formula: see text] values obtained from the projected shell model wavefunctions overestimate the experimental [Formula: see text] values in [Formula: see text]Lu, yet they are close to the measured values, considering the precision of measurement. The reduction in the theoretical [Formula: see text] values around the band crossing region may be ascribed to change in nuclear structure of yrast bands due to neutron pair alignment in [Formula: see text] orbital.

Evidence of transverse wobbling motion in Eu151

Transverse wobbling was investigated in the Eu151 nucleus by populating the excited states using Nd148(Li7, 4n)Eu151 at a beam energy of 30 MeV. Three new interconnecting transitions have been placed between the two negative parity bands. The M1/E2 character of the interconnecting ΔI=1 transitions between the negative parity bands was extracted from the mixing ratios using the RDCO and linear polarization method. The spin and parity of the states of different bands have also been assigned. The dominant E2 character of the interlinking transitions between the yrast and first phonon wobbling band and the dominant M1 character between the yrast band and its signature partner band indicate the presence of transverse wobbling in the Eu151 nucleus. It is further demonstrated that the triaxial projected shell model approach describes the observed experimental properties.7 MoreReceived 21 December 2022Revised 22 January 2023Accepted 8 May 2023DOI:https://doi.org/10.1103/PhysRevC.107.054310©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsNuclear structure & decaysProperties150 ≤ A ≤ 189TechniquesSpectrometers & spectroscopic techniquesNuclear Physics

Axial and triaxial degrees of freedom in 72Zn

The unstable N=42 nucleus 72Zn has been studied using multiple safe Coulomb excitation in inverse kinematics. The experiment was performed at the REX-ISOLDE facility at CERN making first use of the silicon detector array C-REX in combination with the γ-ray spectrometer Miniball. The high angular coverage of C-REX allowed to determine the reduced transition strengths for the decay of the yrast 01+, 21+ and 41+ as well as of the 02+ and 22+ states in 72Zn. The quadrupole moments of the 21+, 41+ and 22+ states were extracted. Using model independent quadrupole invariants, the ground state of 72Zn was found to have an average deformation in the γ degree of freedom close to maximum triaxiality. In comparison to experimental data in zinc isotopes with N<40, the collectivity of the 41+ state in neutron-rich 72Zn is significantly larger, indicating a collective yrast band based on the ground state of 72Zn. In contrast, a low experimental B(E2;02+→21+) strength was determined, indicating a different structure for the 02+ state. Shell-model calculations propose a 02+ state featuring a larger fraction of the (spherical) N=40 closed-shell configuration in its wave function than for the 01+ ground state.The results were also compared with beyond mean field calculations which corroborate the large deformation in the γ degree of freedom, while pointing to a more deformed 02+ state. These experimental and theoretical findings establish the importance of the γ degree of freedom in the ground state of 72Zn, located between the 68,70Ni nuclei that have spherical ground states, and 76Ge, which has a rigid triaxial shape.

Investigation of the high-spin yrast band structure of Pu236–246 isotopes

The available data on some actinide nuclei point to certain significant features of the rotational yrast band and other excited bands. The rotational properties of plutonium isotopes ($^{236--346}\mathrm{Pu}$) were studied via projected shell model (PSM). Calculations are based on the Hamiltonian of the PSM which includes the formed part of a single particle, the $Q\ensuremath{-}Q$ force, and the residual interaction of monopole and quadrupole pairings. The results of the calculated energy levels of the yrast band are then compared with available experimental data and a good agreement has been found. The crossing between two-quasiparticle (2qp) excited bands and the ground state band (g band) in the high-spin regions has been analyzed in terms of band diagrams. The upbendings observed in the kinematic moments of inertia (${j}^{(1)}$ MOI) curves for $^{236--346}\mathrm{Pu}$ isotopes are due to the effect of two aligning nucleons that occupy excited bands and the $\ensuremath{\nu}({j}_{15/2}$), $\ensuremath{\pi}({i}_{13/2}$) high-$j$ intruder orbits. The PSM successfully reproduces the observed upbending in ${j}^{(1)}$ as well as the upturning and downturning in ${j}^{(2)}$. For the $^{240}\mathrm{Pu}$ isotope, the PSM predicts a simultaneous alignment of neutrons ${\ensuremath{\nu}}^{2} [1/2,\ensuremath{-}7/2] {K}^{\ensuremath{\pi}}$ = ${4}^{+}$ and protons ${\ensuremath{\pi}}^{2} [\ensuremath{-}3/2,5/2] {K}^{\ensuremath{\pi}}$ = ${1}^{+}$ bands cross the g band at spin $I=22$. We expect it to be mainly responsible for the disagreement at $I=22$. Furthermore, electric quadrupole transition probabilities $B(E2)$ and the gyromagnetic factor ($g$ factor) for the yrast band energy levels are also studied.

Study of normal deformed bands in light Lutetium isotopes

The projected shell model has been employed to study the energy levels and alignment frequencies of the normally deformed bands of light lutetium isotopes. Band head spins and configurations have been reproduced for all the positive parity bands of 161−165Lu isotopes and negative parity bands of 163Lu. The theoretical aligned angular momenta reasonably reproduced the observed backbends and their corresponding rotational frequencies for all the experimentally observed normally deformed bands. Moreover, I = 7/2− state is predicted as band head spin for negative parity yrast bands of 161,165Lu. The negative parity yrast bands of 161,165Lu are predicted to have 1π1h11/2[523]7/2− configuration. Further, the calculated B(E2) values of 165Lu show reasonable agreement with the available experimental data. The dip predicted in the B(E2) values may be interpreted due to the alignment of a pair of neutrons in the neutron 1i13/2 orbital of all yrast bands of 161−165Lu.

Effective and efficient algorithm for the Wigner rotation matrix at high angular momenta

The Wigner rotation matrix ($d$ function), which appears as a part of the angular-momentum-projection operator, plays a crucial role in modern nuclear-structure models. However, it is a longstanding problem that its numerical evaluation suffers from serious errors and instability, which hinders precise calculations for nuclear high-spin states. Recently, Tajima [Phys. Rev. C 91, 014320 (2015)] has made a significant step toward solving the problem by suggesting the high-precision Fourier method, which however relies on formula-manipulation softwares. In this paper we propose an effective and efficient algorithm for the Wigner $d$ function based on the Jacobi polynomials. We compare our method with the conventional Wigner method and the Tajima Fourier method through some testing calculations, and demonstrate that our algorithm can always give stable results with similar high-precision as the Fourier method, and in some cases (for special sets of $j,m,k$, and $\ensuremath{\theta}$) ours are even more accurate. Moreover, our method is self-contained and less memory consuming. By taking the $^{156}\mathrm{Dy}$ yrast band as an example, we show that with the $d$ function calculated by our proposed Jacobi method in the angular-momentum projector, the realistic projected-shell-model calculation can be aggressively extended to the high-spin region where the conventional Wigner method collapses completely. A related testing code and subroutines for the three algorithms of $d$ function are provided as Supplemental Material in the present paper.

Octupole correlations in collective excitations of neutron-rich N≈56 nuclei

Octupole correlations in the low-energy collective states of neutron-rich nuclei with the neutron number $N\approx56$ are studied within the interacting boson model (IBM) that is based on the nuclear density functional theory. The constrained self-consistent mean-field (SCMF) calculations using a universal energy density functional and a pairing interaction provide the potential energy surfaces in terms of the axially-symmetric quadrupole and octupole deformations for the even-even nuclei $^{86-94}$Se, $^{88-96}$Kr, $^{90-98}$Sr, $^{92-100}$Zr, and $^{94-102}$Mo. The SCMF energy surface is then mapped onto the energy expectation value of a version of the IBM in the boson condensate state, which consists of the neutron and proton monopole $s$, quadrupole $d$, and octupole $f$ bosons. This procedure determines the strength parameters of the IBM Hamiltonian, which is used to compute relevant spectroscopic properties. At the SCMF level, no octupole deformed ground state is obtained, while the energy surface is generally soft in the octupole deformation at $N\approx56$. The predicted negative-parity yrast bands with the bandhead state $3^-_1$ weakly depend on $N$ and become lowest in energy at $N=56$ in each of the considered isotopic chains. The model further predicts finite electric octupole transition rates between the lowest negative- and the positive-parity ground-state bands.

Questioning the wobbling interpretation of low-spin bands in γ -soft nuclei within the interacting boson-fermion model

An alternative interpretation of the recently reported low-lying excited bands in $\gamma$-soft odd-mass nuclei as wobbling bands is presented in terms of the interacting boson-fermion model. The model Hamiltonian is determined based on the mean-field calculations with the nuclear energy density functionals. The predicted mixing ratios of the $\Delta{I}=1$ electric quadrupole to magnetic dipole transition rates between yrast bands and those yrare bands previously interpreted as wobbling bands in $^{135}$Pr, $^{133}$La, $^{127}$Xe, and $^{105}$Pd are consistently smaller in magnitude than the experimental values on which the wobbling interpretation is based. These calculated mixing ratios indicate predominant magnetic character in agreement with the new experimental data. The earlier wobbling assignments are severely questioned.

“Staggering” Effect in Even-even Nuclei with Quadrupole and Octupole Deformations

The ∆I = 1 "staggering" effect is investigated in the energy spectrum of positive and negative parities of the yrast band of even-even actinide nuclei. The "staggering" effect is described by the formula proportional to the discrete approximation of the fourth-order derivative of the function ∆E(I). It is shown that the "staggering" effect is characterized by the "zigzag" behavior and does not vanish within the observed range of angular momenta.

Nucleon-pair shell model: Effect of non-collective pairs for odd 123−129Sn

In this paper, odd-mass isotopic chain of [Formula: see text]Sn has been studied within the framework of nucleon-pair shell model (NPSM) with the noncollective pair originating from the alignment of two neutrons in the [Formula: see text]h11/2 orbit included. It was found that NPSM can reproduce the properties of the yrast bands satisfactorily, it is crucial to include the noncollective pair in the NPSM. The band structure can be explained as the backbending or the phase transition from vibrational limit to the rotational limit. The mechanism of the yrast band can be explained as band crossing between the ground state band and the S band constructed from the neutron alignment in the [Formula: see text]h11/2 orbit. Our results also suggest that the mechanism of the band structure of those four Sn isotopes can also be interpreted as the competition and transition between collective and noncollective phase.

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.

Triaxial projected shell model study of γ-bands in even even 104−122Cd nuclei

A systematic study of the nuclear observables related to the triaxial nature of the even-even 104−122Cd isotopes is presented microscopically using multi-quasiparticle triaxial projected shell model (TPSM) approach. In the present work, we have performed a detailed study of γ-bands in cadmium isotopes in addition to the yrast band. The present calculations are found to reproduce the observed systematics of the R42=[E(41+)/E(21+)], E-GOS plots and B(E2) values for 104−122Cd isotopic mass chain. The E-GOS plots along with the R42 ratios predict the quasi-deformed structure for these bands. Besides this, odd-even staggering in γ bands, inter band and intra band reduced transition probabilities and g-factors have also been discussed in the present work and it is shown that TPSM approach provides a reasonable description of the measured properties.

Magnetic rotational band in 116Sb

The excited states of 116Sb have been populated using the α induced reaction 115In(α, 3n)116Sb at a beam energy of 40 MeV and investigated via in-beam gamma spectroscopic techniques. A positive parity sequence (B1) of strong M1 transitions with relatively weak crossover E2 transitions, connected to the yrast negative parity rotational band (B2) of 116Sb, has been observed. The experimental B(M1)/B(E2) values for band B1 are found to decrease with angular momentum (I). The origin of this band (B1) has been interpreted in terms of Magnetic Rotation (MR) under the framework of Semi-Classical Model (SCM) and Shears mechanism with Principal Axis Cranking (SPAC) formalism and is assigned a four quasiparticle configuration of π(g9/2)−1 ⊗ ν(g7/2/d5/2)(h11/2)2. The yrast rotational band B2 is extended up to the band crossing region.

Systematics of Yrast Bands in the Region of Heavy and Superheavy Even-Even Nuclei

Systematics of Yrast Bands in the Region of Heavy and Superheavy Even-Even Nuclei

High-Spin States of Yrast Bands in Even Pu, Cm, Fm, and No Isotopes

High-Spin States of Yrast Bands in Even Pu, Cm, Fm, and No Isotopes

Gradual loss of collectivity in rotational bands in N = 89 isotones

In the present work, we investigate the general properties of low-lying experimental bands in three isotones, 155Dy , 156Ho , 157Er , at high spin within the cranked Nilsson-Strutinsky formalism. The excitation energies of the yrast bands have been compared with the experimental findings, and good agreements are observed. Our calculations show that with increasing total nuclear spin, the collectivity decreases gradually leading to the termination. In addition, nuclei with 10–12 particles outside the closed core terminate within configurations with no hole in the core.