Quasiparticle Configurations Research Articles

Pfaffian formulation for matrix elements of three-body operators in multiple quasiparticle configurations

We present a Pfaffian formula to calculate matrix elements of three-body operators in symmetry-restoration beyond-mean-field methods, including the case of multiple quasiparticle (qp) configurations. Detailed derivation is provided and the validity of the new formula is checked numerically. The corresponding efficiency is discussed, which turns out to be about five times (one order of magnitude) higher than the conventional method when four (less than four) qp operators are considered.

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.

Large Shape Staggering in Neutron-Deficient Bi Isotopes.

The changes in the mean-square charge radius (relative to ^{209}Bi), magnetic dipole, and electric quadrupole moments of ^{187,188,189,191}Bi were measured using the in-source resonance-ionization spectroscopy technique at ISOLDE (CERN). A large staggering in radii was found in ^{187,188,189}Bi^{g}, manifested by a sharp radius increase for the ground state of ^{188}Bi relative to the neighboring ^{187,189}Bi^{g}. A large isomer shift was also observed for ^{188}Bi^{m}. Both effects happen at the same neutron number, N=105, where the shape staggering and a similar isomer shift were observed in the mercury isotopes. Experimental results are reproduced by mean-field calculations where the ground or isomeric states were identified by the blocked quasiparticle configuration compatible with the observed spin, parity, and magnetic moment.

Systematic study of near-yrast band structures in odd-mass Pr125−137 and Pm127−139 isotopes

In the present work, the basis space in the triaxial projected shell model approach is expanded to include three and five quasiparticle configurations for odd-proton systems. This extension allows to investigate the high-spin band structures observed in odd-proton systems up to and including the second band crossing region, and as a first major application of this development, the high-spin properties are investigated for odd-mass $^{125-137}$Pr and $^{127-139}$Pm isotopes. It is shown that band crossings in the studied isotopes have mixed structures with first crossing dominated by one-proton coupled to two-neutron configuration for the lighter isotopes which then changes to three-proton configuration with increasing neutron number. Further, $\gamma$-bands based on quasiparticle states are also delineated in the present work, and it is predicted that these band structures built on three-quasiparticle configurations become favoured in energy for heavier systems in the high-spin region.

Description of magnetic moments within the Gogny Hartree-Fock-Bogolyubov framework: Application to Hg isotopes

While the ground state configuration is classically determined by the variational principle minimizing the binding energy of the system, we propose here a different procedure to identify the configuration of the ground state in odd-$A$ nuclei. This procedure is based on the Hartree-Fock-Bogolyubov (HFB) framework with a self-consistent blocking of the unpaired nucleon and identifies the ground state as the blocked quasiparticle configuration compatible with the observed spin and parity and, most importantly, the measured magnetic moment. The magnetic moments are calculated within the HFB framework for all odd Hg isotopes for which experimental data is available. To validate the method, a systematic comparison between the predicted and measured electric quadrupole moments and isotopic shifts is performed. For even-even isotopes, we show that the ground state deformation, and more particularly the competition between the prolate and oblate shapes, can hardly be determined through a comparison of the QRPA $\ensuremath{\beta}$-decay half-life with experiment, though this approach also calls for an observable similar to the one used for odd-$A$ isotopes, namely the spin-flip component of the isovector part of the magnetic moment operator. For even isotopes with shape coexistence, no adequate constraint could be identified, except though the charge radius. Assuming light even-even Hg isotopes to have an oblate shape, the resulting charge radii staggering observed in the Hg chain by laser spectroscopy can through this identification procedure be reproduced.

Nuclear matrix elements of neutrinoless double- β decay in the triaxial projected shell model

The nuclear matrix elements of neutrinoless double-$\beta$ decay for nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd are studied within the triaxial projected shell model, which incorporates simultaneously the triaxial deformation and quasiparticle configuration mixing. The low-lying spectra and the $B(E2:0^+\rightarrow2^+)$ values are reproduced well. The effects of the quasiparticles configuration mixing, the triaxial deformation, and the closure approximation on the nuclear matrix elements are studied in detail. For nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd, the nuclear matrix elements are respectively reduced by the quasiparticle configuration mixing by 6%, 7%, 2%, 3%, and 4%, and enhanced by the odd-odd intermediate states by 7%, 4%, 11%, 20%, and 14%. Varying the triaxial deformation $\gamma$ from $0^\circ$ to $60^\circ$ for the mother and daughter nuclei, the nuclear matrix elements change by 41%, 17%, 68%, 14%, and 511% respectively for $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd, which indicates the importance of treating the triaxial deformation consistently in calculating the nuclear matrix elements.

Self-focusing hybrid skyrmions in spatially varying canted ferromagnetic systems

Magnetic skyrmions are quasiparticle configurations in a magnetic film that can act as information carrying bits for ultrasmall, all-electronic nonvolatile memory. The skyrmions can be nucleated and driven by spin-orbit torque from a current driven in a heavy metal underlayer. Along its gyrotropic path, a Magnus force can cause a skyrmion to be annihilated at the boundaries. By combining interfacial and bulk Dzyaloshinskii-Moriya interactions (DMIs), for instance by using a B20 material on top of a heavy metal layer with high spin-orbit coupling, it is possible to engineer a hybrid skyrmion that will travel parallel to the racetrack with zero Magnus force. We show that by using a spatially varying interfacial DMI, a hybrid skyrmion will automatically self-focus onto such a track as its domain angle evolves along the path. Furthermore, using a gate driven voltage controlled magnetic anisotropy, we can control the trajectory of the hybrid skyrmion and its eventual convergence path and lane selection in a racetrack geometry.

Microscopic study of nuclear structure of odd-odd 128–138I nuclei within the framework of projected shell model for positive- and negative-parity states

We have done the microscopic study of neutron-rich odd-odd iodine isotopes within the framework of projected shell model. Odd-odd nuclei are the best candidates for studying possible structure variations away from the valley of stability. We used the projected shell model, in which the deformed Nilsson single-particle states are being used for the construction of model basis. We studied the band properties of odd-odd I[Formula: see text](Z [Formula: see text] 53) isotopes with neutron numbers N [Formula: see text] 75, 77, 79, 81, 83 and 85. Using model analysis, we presented the low-lying positive- and negative-parity states of these nuclei. In these isotopes, the band structures have been analyzed in terms of quasi-particle configurations and comparative presentation of yrast levels is discussed. The phenomenon of yrast energy splitting is also studied in this work.

Revealing multiple band structures in Xe131 from α -induced reactions

The excited states in the transitional nucleus $^{131}\mathrm{Xe}$ have been populated by using $\ensuremath{\alpha}$-induced fusion-evaporation reaction and the de-exciting $\ensuremath{\gamma}$ rays were detected with the Compton suppressed clover detector setup of the Indian National Gamma Array coupled to digital data acquisition system. The existing level structure of $^{131}\mathrm{Xe}$ has been significantly extended with the observation and placement of 72 new $\ensuremath{\gamma}$-ray transitions. The use of light-ion ($\ensuremath{\alpha}$) beam helped to identify several new band structures in $^{131}\mathrm{Xe}$ with different quasiparticle (qp) configurations. The multipolarities of the observed $\ensuremath{\gamma}$ rays have been determined on the basis of the directional correlation from oriented states ratio and polarization asymmetry measurements. The yrast negative-parity band has been confirmed up to ${35/2}^{\ensuremath{-}}$ spin and the highly nonyrast signature partner of this band has been identified for the first time. The positive-parity band, based on the ${3/2}^{+}$ ground state, has been extended up to ${23/2}^{+}$ with the observation of a signature inversion, which signifies a pair of particle alignment around the spin of 15/2 $\ensuremath{\hbar}$. A dipole band, consisting of $M1$ transitions has been identified and assigned a 5-qp configuration. A new band structure built on a 3-qp ${23/2}^{+}$ state has been observed with a large signature splitting. A comparison in the isotopic and isotonic chains reveals the transitional nature of the $N=77$ nuclei. Total Routhian surface calculations have been performed to understand the structure of $^{131}\mathrm{Xe}$ associated with different configurations.

Multi-quasiparticle excitations of 91Ru * * Supported by National Natural Science Foundation of China (U1632137)

The level structure in neutron-deficient nucleus 91Ru was investigated via the 58Ni (36Ar, 2p1n ) 91Ru reaction at a beam energy of 111 MeV. Charged particles, neutrons, and -rays were emitted in this reaction and detected by the DIAMANT CsI ball, Neutron Wall, and the EXOGAM Ge clover array, respectively. In addition to the previously reported levels in 91Ru, new low-to-medium spin states were observed. Angular correlation and linear polarization measurements were performed to unambiguously determine spins and parities of the excited states in 91Ru. The low-spin states of 91Ru exhibit a scheme of multi-quasiparticle excitations, which is very similar to that of the neighboring isotone. These excitations have been interpreted in terms of the shell model. The calculations performed in the configuration space reproduce the experimental excitation energies reasonably well, supporting the interpretation of the newly assigned positive-parity states in terms of the three quasiparticle configurations and .

Berry Phase and Model Wave Function in the Half-Filled Landau Level.

We construct model wave functions for the half-filled Landau level parametrized by "composite fermion occupation-number configurations" in a two-dimensional momentum space, which correspond to a Fermi sea with particle-hole excitations. When these correspond to a weakly excited Fermi sea, they have a large overlap with wave functions obtained by the exact diagonalization of lowest-Landau-level electrons interacting with a Coulomb interaction, allowing exact states to be identified with quasiparticle configurations. We then formulate a many-body version of the single-particle Berry phase for adiabatic transport of a single quasiparticle around a path in momentum space, and evaluate it using a sequence of exact eigenstates in which a single quasiparticle moves incrementally. In this formulation the standard free-particle construction in terms of the overlap between "periodic parts of successive Bloch wave functions" is reinterpreted as the matrix element of a "momentum boost" operator between the full Bloch states, which becomes the matrix elements of a Girvin-MacDonald-Platzman density operator in the many-body context. This allows the computation of the Berry phase for the transport of a single composite fermion around the Fermi surface. In addition to a phase contributed by the density operator, we find a phase of exactly π for this process.

Observation of multiple doubly degenerate bands in 195Tl

The High-spin states in 195Tl, populated through the 185,187Re(13C, xn) fusion evaporation reaction at the beam energy of 75 MeV, were studied using the Indian National Gamma Array (INGA). More than 50 new γ transitions have been placed in the proposed level scheme which is extended up to the excitation energy of ≈ 5.6 MeV and spin=22.5ħ. Two pairs of degenerate bands based on two different quasi-particle configurations have been identified in this nucleus indicating the first observation of such bands in an odd-A nucleus in A∼190 region and signify the first evidence of multiple chiral bands in a nucleus in this region. The total Routhian surface calculations predict triaxial shapes for both the configurations and thereby, support the experimental observation. The importance of multiple neutron holes in the i13/2 orbital and the stability of shapes for these two configurations have been discussed.

Projected Shell Model Description of Positive Parity Band of 130Pr Nucleus

Theoretical investigation of positive parity yrast band of odd-odd 130Pr nucleus is performed by applying the projected shell model. The present study is undertaken to investigate and verify the very recently observed side band in 130Pr theoretically in terms of quasi-particle (qp) configuration. From the analysis of band diagram, the yrast as well as side band are found to arise from two-qp configuration πh 11/2 ⊗ νh 11/2. The present calculations are viewed to have qualitatively reproduced the known experimental data for yrast states, transition energies, and B(M1) / B(E2) ratios of this nucleus. The recently observed positive parity side band is also reproduced by the present calculations. The energy states of the side band are predicted up to spin 25+, which is far above the known experimental spin of 18+ and this could serve as a motivational factor for future experiments. In addition, the reduced transition probability B(E2) for interband transitions has also been calculated for the first time in projected shell model, which would serve as an encouragement for other research groups in the future.

A systematic study of band structure and electromagnetic properties of neutron rich odd mass Eu isotopes in the projected shell model framework

The positive and negative parity rotational band structure of the neutron rich odd mass Eu isotopes with neutron numbers ranging from 90 to 96 are investigated up to the high angular momentum. In the theoretical analysis of energy spectra, transition energies and electromagnetic transition probabilities we employ the projected shell model. The calculations successfully describe the formation of the ground and excited band structures from the single particle and multi quasiparticle configurations. Calculated excitation energy spectra, transition energies, exact quantum mechanically calculated B(E2) and B(M1) transition probabilities are compared with experimental data wherever available and a reasonably good agreement is obtained with the observed data. The change in deformation in the ground state band with the increase in angular momentum and the increase in neutron number has also been established.

Pygmy and Giant Dipole Resonances in Proton-Rich Nuclei 17,18Ne**Supported by the National Natural Science Foundation of China under Grant Nos 11375022, 11575060, 11505058 and 11435014.

The pygmy and giant dipole resonances in proton-rich nuclei 17,18Ne are investigated with a fully self-consistent approach. The properties of ground states are calculated in the Skyrme Hartree–Fock with the Bardeen–Cooper–Schrieffer approximation to take into account the pairing correlation. The quasiparticle random phase approximation (QRPA) method is used to explore the properties of excited dipole states. In the calculations the SLy5 Skyrme interaction is employed. In addition to the giant dipole resonances, pygmy dipole resonances (PDR) are found to be located in the energy region below 10 MeV in both 17,18Ne. The strength and transition density show that the low-lying states are typical PDR states. However, analyzing the QRPA amplitudes of proton and neutron 2 quasiparticle (2qp) configurations for a given low-lying state in 17,18Ne, we find that the PDR state is less collective, more like a single 2qp excitation.

Systematic study of multi-quasiparticleK-isomeric bands in tungsten isotopes by the extended projected shell model

Background: The interplay between collective and single-particle degrees of freedom is an important structure aspect to study. The nuclei in theA ≈ 180 mass region are often denoted as good examples to study such problems because these nuclei are known to exhibit many rotational bands based on multi-quasiparticle K isomers. Purpose: A large set of high-quality experimental data on high-K isomeric states in the A ≈ 180 mass region has accumulated. A systematic description of them is a theoretical challenge as it requires a method going beyond the usual mean field with multi-quasiparticle configurations built in the shell-model basis. The K-isomer data provide an ideal testing ground for theoretical models. Method: The recently extended projected shell model (PSM) by the Pfaffian method is employed with a sufficiently large configuration space including up to 10 quasiparticles. The restoration of rotational symmetry which is broken in the deformed mean field is obtained by means of angular-momentum projection. With axial symmetry in the basis deformation, each multi-quasiparticle state, classified by a K quantum number, represents the major component of a rotational K band. Shell-model diagonalization in such a projected basis defines the K mixing, which is the key ingredient of the present method. Results: Quasiparticle structure and rotational properties of high-K isomers in even-even neutron-rich 174−186W isotopes are described. The rotational evolution of the yrast and near-yrast bands is discussed with successive band crossings. Multi-quasiparticle K isomers and associated rotational bands in each W isotope are studied with detailed quasiparticle configurations given. Electromagnetic transition properties are also studied and the calculated B(E2), B(M1), and g-factors are compared with experiment if data exist. Conclusions: Many nuclei of the A ≈ 180 mass region exhibit properties of an axially symmetric shape and K is approximately a good quantum number. For such nuclei, the extended PSM assuming an axially symmetric basis but including K mixing through diagonalization of the two-body Hamiltonian is an appropriate method to study multi-quasiparticle K isomers and K violations in these states. For special examples where one finds highly K-forbidden transitions the present model needs to be further improved.

Band structures in Pd101

Excited states in the $^{101}\mathrm{Pd}$ nucleus were investigated through the $^{75}\mathrm{As}(^{31}\mathrm{P},2p3n)$ fusion-evaporation reaction at ${E}_{\mathrm{lab}}=125$ MeV by using the Indian National Gamma Array spectrometer equipped with 21 clover Ge detectors. The level scheme is considerably extended for medium spin values. New positive-parity band structures in $^{101}\mathrm{Pd}$ have been studied within the framework of the projected shell model and are found to undergo transition from single quasiparticle to high-$K$ three quasiparticle configuration after band crossing, i.e., from principal-axis rotation to tilted-axis rotation. The negative-parity band structures are discussed in the framework of the hybrid version of tilted-axis cranking shell model calculations. The observed alignment gain in the lowest excited $\ensuremath{\nu}{h}_{11/2}$ negative-parity band results from successive ${(\ensuremath{\nu}{g}_{7/2})}^{2}$ and ${(\ensuremath{\pi}{g}_{9/2})}^{2}$ pair alignments. The higher excited negative-parity bands are reproduced for the $\ensuremath{\nu}[{h}_{11/2}{({g}_{7/2}/{d}_{5/2})}^{2}]$ and ${(\ensuremath{\pi}{g}_{9/2})}^{\ensuremath{-}2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ configurations.

Isomer-delayed gamma-ray spectroscopy of neutron-rich 166Tb

This short paper presents the identification of a metastable, isomeric-state decay in the neutron-rich odd-odd, prolate-deformed nucleus 166 Tb. The nucleus of interest was formed using the in-flight fission of a 345 MeV per nucleon 238 U primary beam at the RIBF facility, RIKEN, Japan. Gamma-ray transitions decaying from the observed isomeric states in 166 Tb were identified using the EURICA gamma-ray spectrometer, positioned at the final focus of the BigRIPS fragments separator. The current work identifies a single discrete gamma-ray transition of energy 119 keV which de-excites an isomeric state in 166 Tb with a measured half-life of 3.5(4) μs. The multipolarity assignment for this transition is an electric dipole and is made on the basis internal conversion and decay lifetime arguments. Possible two quasi-particle Nilsson configurations for the initial and final states which are linked by this transition in 166 Tb are made on the basis of comparison with Blocked BCS Nilsson calculations, with the predicted ground state configuration for this nucleus arising from the coupling of the v (1 - /2)[521] and π (3 + /2) Nilsson orbitals.

Quasiparticle-random-phase approximation treatment of the transverse wobbling mode reconsidered

The quasiparticle random phase approximation is used to study the properties of the wobbling bands in $^{163}$Lu. Assuming that the wobbling mode represents pure isoscalar orientation oscillations results in too low wobbling frequencies and too strong M1 transitions between the one- and zero-phonon wobbling bands. The inclusion of an LL interaction, which couples the wobbling mode to the scissors mode, generates the right upshift of the wobbling frequencies and the right suppression of the B(M1)$_{out}$ values toward the experimental values. In analogy to the quenching of low-energy E1 transition by coupling to the Isovector Giant Dipole Resonance, a general reduction of the M1 transitions between quasiparticle configurations caused by coupling to the scissors mode is suggested.

Search for octupole correlations inNd147

Properties of excited states in $^{147}$Nd have been studied with multispectra and $\gamma \gamma$ coincidence measurements. Twenty-four new $\gamma$-lines and three new levels have been introduced into the level scheme of $^{147}$Nd. Lifetimes of eight excited levels in $^{147}$Nd, populated in the $\beta$ decay of $^{147}$Pr, have been measured using the advanced time-delayed $\beta\gamma\gamma$(t) method. Reduced transition probabilities have been determined for 30 $\gamma$-transitions in $^{147}$Nd. Potential energy surfaces on the ($\beta_{2}$,$\beta_{3}$) plane calculated for $^{147}$Nd using the Strutinsky method predict two single quasiparticle configurations with nonzero octupole deformation, with K=1/2 and K=5/2. We do not observe parity doublet bands with K=5/2. For pair of opposite parity bands that could form the K=1/2 parity doublet we were able only to determine lower limit of the dipole moment, $|D_0|\geq$0.02 e$\cdot fm$.