Multi-quasiparticle States Research Articles

Three-quasineutron γ-band in 127Xe

Structures of negative parity multi-quasiparticle states in 127Xe have been investigated through in-beam γ-ray spectroscopy. Excited states were populated via the 122Sn(9Be, 4nγ)127Xe fusion-evaporation reaction at E beam = 48 MeV. Two new negative parity bands have been identified and their structures have been discussed using the triaxial projected shell model (TPSM) approach. One of the bands is established above the I π = 27/2− state at 3702 keV and based on the experimental inferences and TPSM results, this band is interpreted as a γ-band built on a three-quasineutron configuration. The second sequence, found above I π = 31/2− state at 4848 keV, is proposed to have a two-proton aligned configuration (), considering the properties of this band with the neighbouring isotopes. The analysis of the TPSM wave function substantiates the proposed interpretation of this band.

Description of Nb93 stellar electron-capture rates by the projected shell model

Capture of electrons by nuclei is an important process in stellar environments where excited nuclear states are thermally populated. However, accurate treatment for excited configurations in electron capture (EC) rates has been an unsolved problem for medium-heavy and heavy nuclei. In this work, we take the $^{93}$Nb $\rightarrow$ $^{93}$Zr EC rates as the example to introduce the Projected-Shell-Model (PSM) in which excited configurations are explicitly included as multi-quasiparticle states. Applying the prevalent assumption that the parent nucleus always stays in its ground state in stellar conditions, we critically compare the obtained PSM results with the recently-measured Gamow-Teller transition data, and with the previous calculations by the conventional shell model and the quasiparticle random-phase approximation. We discuss important ingredients that are required in theoretical models used for stellar EC calculations, and demonstrate effects of the explicit inclusion of excited nuclear states in EC rate calculations, especially when both electron density and environment temperature are high.

Phenomenological description of non-axial shapes of some doubly even neutron deficient barium isotopes

The evolution of non-axial shapes and rotational structure in even–even 122–132Ba isotopes has been investigated microscopically with the application of a triaxial projected shell model (TPSM). Based on calculations, the shape instability and softness towards γ deformation are predicted for these isotopes. In the present work, the application of three-dimensional angular-momentum projection on multi-quasiparticle configurations, constructed from the triaxially deformed mean field, provides a reliable description of the yrast and near yrast structure in these nuclei. The theoretically obtained backbends demonstrate the importance of decoupling of multi-quasiparticle states for these nuclei. The uniform behaviour of transition probabilities B(E), shown by the present calculations, authenticate the global validity of Grodzin’s product rule. Besides this, the deformation systematics and odd–even staggering in γ bands have also been discussed in the present work.

Negative parity three-quasiparticle band in 127I

The excited states of 127I were populated via 124Sn(7Li, 4n $\gamma$ ) fusion-evaporation reaction at $ E_{beam} = 33$ MeV. A strongly coupled $\Delta I = 1$ band has been established above 2423keV state with $J^{\pi} = 19/2^{-}$ as bandhead, likely to be associated with the three-quasiparticle configuration. Spin and parity of these multi-quasiparticle states have been confirmed from DCO ratio and linear polarization asymmetry of depopulating $\gamma$ -rays. The parity of these states have been found altered from their previous assignment.

Rotational structure of odd-proton 103, 105, 107, 109, 111Tc isotopes

A systematic study of the yrast band structure for the neutron-rich odd-mass 103-111Tc nuclei is carried out using Projected Shell Model. The rotational band structure has been studied up to a maximum spin of $ 59/2^{+}$ . Excellent agreement with available experimental data for all isotopes is obtained. The energy spectra and electromagnetic transition strengths in terms of the configuration mixing of the angular-momentum projected multi-quasiparticle states are studied in detail. Signature splitting in the yrast rotational band is well described in the perspective of nuclear structure physics. The back-bending phenomenon is also well described for these nuclei in the present work.

Configurations and decay hindrances of high- K states in Hf180

Multi-quasiparticle high-K states, several of which are isomeric, were observed in Hf-180 with the Gammasphere array. We determined the lifetimes in the ns-μs range using centroid-shift and decay measurements within a mu s coincidence time window. The configurations of high-K states involve two and four quasiparticles, with states up to Kπ = (18-) established. High-K excitations are found to be progressively more favored with increasing excitation energy. The K quantum number is quite robust up to the highest spins observed, as evidenced by the large values of the reduced hindrance for isomeric decays. Furthermore, rotational bands built on three high-K states are identified, and the measured branching ratios in these sequences enable the assignment of underlying configurations. Multi-quasiparticle calculations using the Lipkin-Nogami approach for pairing, with blocking included, reproduce the observed high-K energies quite well.

Magnetic moment of the13/2+isomeric state inCu69: Spin alignment in the one-nucleon removal reaction

We report on a new measurement of the g factor of the (13/2(+)) isomeric state in the neutron-rich nucleus Cu-69. This study demonstrates the possibility of obtaining considerable nuclear spin alignment for multi-quasiparticle states in single-nucleon removal reactions. The time-dependent perturbed angular distribution (TDPAD) method was used to extract the gyromagnetic factor of the (13/2(+)) [T-1/2 = 351(14) ns] isomeric state of Cu-69. Its g factor was obtained as g(13/2(+)) = 0.248( 9). The experimentally observed spin alignment for the state of interest was deduced as A = -3.3(9)%.

A systematic analysis of 131−139Pm nuclei in a self-consistent approach

Projected shell model is used to study the negative parity yrast states in odd mass 131−139Pm isotopes. Some nuclear structure properties like yrast spectra, back bending in moment of inertia, band-diagrams and electric quadrupole transitions [B(E2)] have been deduced and compared with the experimentally available data. The calculated results on these physical quantities have been explained in the perspectives of good physics and the yrast states are found to arise not only from single quasi-particle states but from multi quasi-particle states also.

Multi-quasiparticle high-K isomeric states in deformed nuclei

In the past years, we have made many theoretical investigations on multi-quasiparticle high- K isomeric states. A deformation-pairing-configuration self-consistent calculation has been developed by calculating a configuration-constrained multi-quasiparticle potential energy surface (PES). The specific single-particle orbits that define the high- K configuration are identified and tracked (adiabatically blocked) by calculating the average Nilsson numbers. The deformed Woods-Saxon potential was taken to give single-particle orbits. The configuration-constrained PES takes into account the shape polarization effect. Such calculations give good results on excitation energies, deformations and other structure information about multi-quasiparticle high- K isomeric states. Many different mass regions have been investigated.

Decay spectroscopy of 160Sm: The lightest four-quasiparticle K isomer

The decay of a new four-quasiparticle isomeric state in 160Sm has been observed using γ-ray spectroscopy at the RIBF, RIKEN. The four-quasiparticle state is assigned a 2π⊗2νπ52−[532], π52+[413], ν52−[523], ν72+[633] configuration. The half-life of this (11+) state is measured to be 1.8(4) μs. The (11+) isomer decays into a rotational band structure, based on a (6−) ν52−[523]⊗ν72+[633] bandhead, consistent with the gK−gR values. This decays to a (5−) two-proton quasiparticle state, which in turn decays to the ground state band. Potential energy surface and blocked-BCS calculations were performed in the deformed midshell region around 160Sm. They reveal a significant influence from β6 deformation and that 160Sm is the best candidate for the lightest four-quasiparticle K isomer to exist in this region. The relationship between reduced hindrance and isomer excitation energy for E1 transitions from multiquasiparticle states is considered with the new data from 160Sm. The E1 data are found to agree with the existing relationship for E2 transitions.

Quasiparticle-continuum level repulsion in a quantum magnet

A neutron scattering study of the quantum magnet BiCu2PO6 demonstrates a phenomenon known as energy-level repulsion, which occurs between a long-lived quasiparticle state and a many-particle continuum. When the energy eigenvalues of two coupled quantum states approach each other in a certain parameter space, their energy levels repel each other and level crossing is avoided1. Such level repulsion, or avoided level crossing, is commonly used to describe the dispersion relation of quasiparticles in solids2. However, little is known about the level repulsion when more than two quasiparticles are present; for example, in a strongly interacting quantum system where a quasiparticle can spontaneously decay into a many-particle continuum3,4,5. Here we show that even in this case level repulsion exists between a long-lived quasiparticle state and a continuum. In our fine-resolution neutron spectroscopy study of magnetic quasiparticles in the frustrated quantum magnet BiCu2PO6, we observe a renormalization of the quasiparticle dispersion relation due to the presence of the continuum of multi-quasiparticle states.

Effect of the reduced pairing interaction onα-decay half-lives of multi-quasiparticle isomeric states

The role of the pairing interaction in multi-quasiparticle isomeric states was examined by calculating $\ensuremath{\alpha}$-decay half-lives with the superfluid tunneling model. We found that this model reproduces the experimental $\ensuremath{\alpha}$-decay half-lives with an accuracy typical of current $\ensuremath{\alpha}$-decay models. In spite of the simplicity of the model, we are able to demonstrate how the reduction of pairing in multi-quasiparticle isomers has a remarkable effect on $\ensuremath{\alpha}$-decay half-lives. Taking this effect into account may be important for spin and parity assignments of $\ensuremath{\alpha}$-decaying multi-quasiparticle isomers.

Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states

We present new formulae for the matrix elements of one-body and two-body physical operators, which are applicable to arbitrary Hartree–Fock–Bogoliubov wave functions, including those for multi-quasiparticle excitations. The testing calculations show that our formulae may substantially reduce the computational time by several orders of magnitude when applied to many-body quantum system in a large Fock space.

Band structure of odd-mass lanthanum nuclei

Negative parity energy states in 121–131 La have been studied using Projected Shell Model (PSM). Some nuclear structure properties like yrast spectra, back-bending in moment of inertia, reduced transition probabilities and band diagrams have been described. The experimental feature of the co-existence of prolate–oblate shapes in 125–131 La isotopes has been satisfactorily explained by PSM results. Comparison of the theoretical data with their experimental counterparts has also been made. From the calculations, it is found that the yrast states arise because of multi-quasiparticle states.

Nature ofγdeformation in Ge and Se nuclei and the triaxial projected shell model description

Recent experimental data have demonstrated that ${}^{76}$Ge may be a rare example of a nucleus exhibiting rigid $\ensuremath{\gamma}$ deformation in the low-spin regime. In the present work, the experimental analysis is supported by microscopic calculations using the multi-quasiparticle triaxial projected shell model (TPSM) approach. It is shown that to best describe the data of both yrast and $\ensuremath{\gamma}$-vibrational bands in ${}^{76}$Ge, a rigid-triaxial deformation parameter $\ensuremath{\gamma}\ensuremath{\approx}{30}^{\ensuremath{\circ}}$ is required. TPSM calculations are discussed in conjunction with the experimental observations and also with the published results from the spherical shell model. The occurrence of a $\ensuremath{\gamma}\ensuremath{\gamma}$ band in ${}^{76}$Ge is predicted with the bandhead at an excitation energy of $\ensuremath{\sim}$2.5 MeV. We have also performed TPSM study for the neighboring Ge and Se isotopes and the distinct $\ensuremath{\gamma}$-soft feature in these nuclei is shown to result from configuration mixing of the ground-state with multi-quasiparticle states.

Multi-quasiparticle rotational bands in neutron-rich erbium isotopes

Multi-quasiparticle states and rotational bands in neutron-rich erbium isotopes have been investigated by the configurationconstrained pairing-deformation-frequency self-consistent total-Routhian-surface (TRS) method with particle-number-conserved pairing. Specifically, the recently observed K fy = 4− bands in 168,170,172Er have been found to experience a configuration change in our calculation. Some other multi-quasiparticle states with uncertain configuration assignments have been reinvestigated by calculating their collective rotations. The configuration-constrained TRS calculation can reproduce experimental data consistently.

Transition fission states for heated nuclei

Induced fission reactions of fissioning compound nuclei that result from the capture of various incident particles (nucleons, γ rays, multiply charged ions) by target nuclei are investigated using the generalized nucleus model and the Wigner random matrix method. The effect produced on the fission widths of the compound nucleus by the competition between the excitation energies of its collective vibrational degrees of freedom that lead to its scission into fission fragments and its rotational and multi-quasiparticle states is analyzed. Bohr’s concept of transition fission states developed for near-barrier nuclear fission is generalized to the induced fission of nuclei with the excitation energies noticeably higher than the fission barriers. The temperature of the fissioning nucleus in the vicinity of the point of its scission into fission fragments is estimated.

Isomers and excitation modes in the gamma-soft nucleus 192Os

New spectroscopic results for high-spin states in 192Os populated in deep-inelastic reactions include the identification of a 2-ns, 12+ isomeric state at 2865 keV and a 295-ns, 20+ state at 4580 keV and their associated ΔJ=2 sequences. The structures are interpreted as manifestations of maximal rotation alignment within the neutron i13/2 and proton h11/2 shells at oblate deformation. Rotational band members based on the long-lived, Kπ=10− isomer are also identified for the first time. Configuration-constrained, potential-energy-surface calculations predict that other prolate multi-quasiparticle high-K states should exist at low energy.

Isomers, nuclear structure and spectroscopy

Isomers and their roles in discovery and as probes of nuclear structure are discussed, with a focus on neutron-rich nuclei in the mass 180–190 region. Long-lived, high-K isomers are predicted in the heavy hafnium nuclei for example, some of which should be accessible by projectile fragmentation and deep-inelastic reactions. Progress with these reactions in reaching a broad range of isotopes to the right of the stability line is summarized. Recent results for isomers in the iridium and osmium isotopes produced in deep-inelastic reactions and studied with time-correlated γ-ray spectroscopy are presented as examples. These studies venture into the border region where well-deformed prolate shapes give way to soft, transitional nuclei. Prolate, oblate and triaxial structures are predicted, but with shapes that depend sensitively on the multi-particle configurations. Dynamical effects such as rotation alignment also play a significant role and produce isomeric states. In some cases, very low-lying multi-quasiparticle intrinsic states are predicted but these are possibly missed with current approaches. The prospects for the identification and characterization of such exotic isomers using new storage ring techniques, that might also provide a window into exotic states populated in their subsequent decay are outlined, as is the potential for studies with beams of isomers themselves.

Particle-number conserving analysis for the 2-quasiparticle and high-K multi-quasiparticle states in doubly-odd 174,176Lu

Two-quasiparticle bands and low-lying excited high-K four-, six-, and eight-quasiparticle bands in the doubly-odd174,176 Lu are analyzed by using the cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method, in which the blocking effects are taken into account exactly. The proton and neutron Nilsson level schemes for174,176, Lu are taken from the adjacent odd-A Lu and Hf isotopes, which are adopted to reproduce the experimental bandhead energies of the one-quasiproton and one-quasineutron bands of these odd-A Lu and Hf nuclei, respectively. Once the quasiparticle configurations are determined, the experimental bandhead energies and the moments of inertia of these two- and multi-quasiparticle bands are well reproduced by PNC-CSM calculations. The Coriolis mixing of the low-K (K=|Ω1−Ω2|) two-quasiparticle band of the Gallagher-Moszkowski doublet with one nucleon in the Ω=1/2 orbital is analyzed.