Γ-soft Nuclei Research Articles

Relative variation between γ coordinate and the potential of the Bohr Hamiltonian producing X(4) from Z(4)

In this paper, four degree of freedom γ-rigid solutions of the Bohr Hamiltonian at γ 0 = π/6 are obtained. The relative variation between γ and the potential of the Hamiltonian is employed to retrieve X(4) from Z(4). γ is varied in the interval 0 ≤ γ 0 ≤ π/6 while the potential minimum, β 0, is varied in the interval 0 ≤ β 0 ≤ ∞ . Very small value of β 0 yields Z(4) while a large value of β 0 produces X(4) and SU(3) is realized at β 0 ≈ ∞ . The solutions at γ 0 = 0 correspond to X(4) while the solutions at γ 0 = π/6 yield Z(4): a dynamic link between Z(4) and X(4) critical point symmetries (CPSs) has been provided. The fact that γ and β 0 of the potential play the same role in the dynamical link between Z(4) and X(4) shows that β 0 also measures the departure from axial symmetry to other shapes as γ does. In the experimental realization of the model, the conformation of 192Pt and 194Pt isotopes to the present Z(4) model shows that the present model can be employed in the description of triaxial rotors and γ-soft isotopes. 194Pt is shown to be the best choice for triaxial rigid rotor candidacy. 130Xe, a critical point isotope, which belongs to the class of γ-soft nuclei, reproduces this present model very well in all the states. Consequently, this present model can serve as a critical point model. 40,0 − β 0 distribution for Z(4) and X(4) candidate isotopes shows a significant interval between the two models where the T(4) CPS lies.

On the mechanism of chromium-nickel two-phase alloy strengthening and fracture

The mechanism of strengthening of a two-phase chromium-nickel alloy 65Cr-(31-35)Ni–Ti–V–W depends on the heat treatment mode: the lattice periods of the α-phase (alloy matrix is a solid solution of Ni in Cr) in the hardened and equilibrium conditions are almost the same; level of strength and ductility properties of alloy determines dispersion and amount of γ-soft nuclei released during heat treatment (solid solution of Cr in Ni), its hardness is less than that of α-phase. Quenching from single-phase area from 1250°C and tempering at 800−900°C provides a higher strength than annealed alloy and increases the start temperature of high temperature failure. The nature of the destruction depends on the temperature. The influence of γ-phase is manifested more significantly at temperatures below equicohesive.

Role of the quadrupole deformation in γ-soft nuclei: The case of 124−134Xe

Observation of the scissors mode in the γ-soft and transition nuclei provides the reasoning for investigating the possibility of quadrupole deformation in such nuclei. Using a deformed-based model for an investigation of the scissors mode, the goal of this work was to analyze the effects associated with quadrupole deformation for the so-called “γ-soft” nuclei in the example of even-even 124−134Xe isotopes. Here, the well-known properties of the scissors mode were investigated using just the quadrupole deformed-based rotational, invariant quasiparticle random phase approximation (QRPA) method. The properties of the scissors mode were clearly seen for all the investigated xenon isotopes, demonstrating that quadrupole deformed-based models can easily explain the nature of the low-lying M1 strength for γ-soft nuclei and indicating that quadrupole deformation plays a non-negligible role in the formation of the low-lying dipole strength for such nuclei.

Beta decay of the axially asymmetric ground state of 192Re

The β decay of 75192Re117, which lies near the boundary between the regions of predicted prolate and oblate deformations, has been investigated using the KEK Isotope Separation System (KISS) in RIKEN Nishina Center. This is the first case in which a low-energy beam of rhenium isotope has been successfully extracted from an argon gas-stopping cell using a laser-ionization technique, following production via multi-nucleon transfer between heavy ions. The ground state of 192Re has been assigned Jπ=(0−) based on the observed β feedings and deduced logft values towards the 0+ and 2+ states in 192Os, which is known as a typical γ-soft nucleus. The shape transition from axial symmetry to axial asymmetry in the Re isotopes is discussed from the viewpoint of single-particle structure using the nuclear Skyrme-Hartree-Fock model.

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.

The odd-even staggering in 122–124Xe and 124–128Ba nuclei

The γ-band energy staggering in low-spin, low-energy spectra of even-even 122–124Xe and 124–128Ba nuclei are discussed. The energy levels of ground and gamma band are calculated by the Soft Rotor Formula (SRF). The staggering is a function of spin has been analyzed in order to derive the information on the type of triaxiality present in 122–124Xe and 124–128Ba nuclei. The staggering indices of γ-soft and triaxial nuclei are also calculated by this SRF formula. It is found that these staggering indices have opposite signs and provide clear distinction between γ-soft and triaxial nuclei.

Collective motion in complex nuclei

We present the implementation in the (β,γ) plane of the generator coordinate method with full triaxial angular momentum and particle number projected wave functions using the Gogny force. We apply the method to the study of 24Mg, the calculated energies of excited states as well as the transition probabilities are compared to the available experimental data showing a good overall agreement. In addition we also show preliminary results for the γ-soft nucleus 126Xe.

Extension of the Random-Phase Approximation for γ-soft nuclei

The variational method is formulated which extends the Random-Phase Approximation to γ-soft nuclei.

O(6)-symmetry breaking in the γ-soft nucleus Xe126 and its evolution in the light stable xenon isotopes

O(6)-symmetry breaking in the γ-soft nucleus Xe126 and its evolution in the light stable xenon isotopes

Non-yrast positive-parity structures in the γ-soft nucleus Er156

Non-yrast positive-parity structures in the γ-soft nucleus Er156

Evolution of chirality from γ soft 108Ru to triaxial 110,112Ru

Rotational bands in 108,110,112Ru have been investigated by means of γ–γ–γ and γ–γ(θ) coincidences of prompt γ rays emitted in the spontaneous fission of 252Cf. The positive parity bands are described by different versions of IBA, where 108Ru is best described as a γ-soft nucleus whereas 110,112Ru are more like rigid triaxial rotors. New ΔI=1 negative parity doublet bands are found. In case of 110,112Ru, these are interpreted as soft chiral vibrations. Many of the experimental findings can be explained by microscopic calculations that combine the TAC mean-field with random phase approximation but a simple geometrical explanation is not apparent.

Nuclear structure of 187W studied with [formula omitted] and [formula omitted] reactions

The level structure of 187W has been studied using prompt and delayed gamma–gamma coincidences from thermal neutron capture in 186W and also measuring the ( d , p ) reaction. From these data and those of previous studies a total of 170 levels (121 connected by γ transitions) have been established for energies below 2.35 MeV. Some of these levels have been grouped into rotational bands built on 14 intrinsic states of quasi-particle and quasi-particle plus phonon character. Of particular interest has been the identification of “quasi bands” with inverse spin sequence based on the newly established isomeric 11 / 2 + state at 410.1 keV. Although the DWBA analysis permitted definite spin–parity assignments for most states a large number of particle transitions have “anomalous” angular distribution shapes with respect to the DWBA which indicate an influence of strong mixing between particle and probably hole states. The exchange of phonons across the Fermi surface leads to a fine structure in the extra fragmentation of most single particle strengths and, at the same time, it produces the effect of breakdown of individual properties of Nilsson states. The total extracted l = 1 , 2 and 3 ( d , p ) strengths below 2 MeV have about the same magnitudes as in 185W that comprise a rather small fraction of the expected strengths. The observed states below 2 MeV are compared with predictions of the quasi particle phonon model. The discussion focuses on transition aspects from rigid rotors of light W to γ-soft nuclei in the Os, Pt region.

Change of the dipole strength distributions between the neighbouring γ-soft nuclei 194Pt and 196Pt

A nuclear resonance fluorescence experiment with two highly efficient EUROBALL Cluster detectors has been performed on the γ-soft nucleus 194Pt. Dipole excitations were observed between 2 and 4 MeV excitation energy. They are tentatively interpreted as the main fragments of the scissors mode based on the measured excitation strengths and a comparison to microscopic calculations in the framework of the quasiparticle random phase approximation (QRPA). The data indicate large differences to the neighbouring isotope 196Pt: a doubling of the observed dipole strength and a shift of the energy centroid by about 600 keV. None of the currently available models is able to reproduce these features consistently in both nuclei.

High-spin structure of yrast-band in 78Kr

Lifetime of levels up to 22+, have been measured in 78Kr and an oblate shape is assigned to the ground state using the CSM and the configuration dependent shell correction calculations. Calculations further show that 78Kr is highly γ-soft nucleus. The experimental Qt values coupled with theoretical calculations indicate an oblate shape for 78Kr at low spins and triaxial shape at higher spins

Transition quadrupole moments in γ-soft nuclei and the triaxial projected shell model

Transition probabilities of the ground-state bands in γ-soft nuclei are studied for the first time using the triaxial projected shell model approach. It is observed that the angular-momentum dependence of the transition quadrupole moment Q t is related to the triaxial deformation of the nuclear mean-field potential. The introduction of the γ-degree of freedom in the shell model basis is shown to have a little influence on the constant behavior of the low-spin Q t in a well-deformed nucleus. However, the increasing collectivity with spin for the low-spin states in a γ-soft nucleus can only be explained by considering the triaxial mean-field deformation.

Transition probabilities in negative parity bands of the 119I nucleus

Lifetimes in four negative-parity bands of 119I were measured using DSAM and RDM. 119I nuclei were produced in the 109Ag(13C,3n) reaction, γγ coincidences were collected using the NORDBALL array. RDDSA — a new method of RDM analysis — is described. This method allowed for the self-calibration of stopping power. From 31 measured lifetimes, 39 values of B(E2) were established. Calculations in the frame of the Core Quasi Particle Coupling (CQPC) model were focused on the problem of susceptibility of the nucleus to γ-deformation. It was established that nonaxial quadrupole deformation of 119I plays on important role. The Wilets–Jean model of a γ-soft nucleus describes the 119I nucleus in a more consistent way then the Davydov–Filippov model of a γ-rigid nucleus.

On the two-quasineutron rotational band in [formula omitted]Ba

The lifetimes of five levels of the two-quasineutron band in 128 Ba populated via the 116 Cd( 16 O ,4n) reaction were measured for the first time by means of the recoil-distance Doppler-shift method. For the data-analysis, a new version of the differential decay-curve method in singles-like mode was developed which takes into account the velocity distribution of the recoils and the effect of the Doppler-shift attenuation in the stopper. The high values of 〈K 2〉 and K eff characterising the band are confirmed by the determined B(E2 ,I→I−2) and B(M1 ,I→I−1) transition strengths. At the same time, the rigid-rotor model is not able to describe the behaviour of the experimental B(E2 ,I→I−1) and B(M1 ,I→I−1) values. A new theoretical effort seems to be needed for a consistent explanation of the intraband transition strengths within two-quasiparticle bands in γ-soft nuclei.

Microscopical Studies of the Energy Staggering in γ-Soft Nuclei**The project supported by National Natural Science Foundation of China

The energy staggering in γ-or quasi γ-band of γ-soft even-even nuclei is studied with the approximate angular moment um projection of the deformed Hartree–Fock (DHF) states. In the calculations of DHF states the modified surface δ-interaction matrix elements are used. It is found that in the K = 2 band produced by the angular momentum projection of DHF state the energy staggering appears only in certain conditions. Some points concerning with the angular momentum projection of K = 2 DHF states are discussed. The energy spectra of nuclei 74Se and 76Kr are calculated and compared with the experimental data, which show the staggering pattern of γ-soft rotor, the coincidence between them are fairly good.

Lifetime measurements of a triaxial band in133Ce

The Doppler shift attenuation method has been used to determined the transition quadrupole moment of a triaxial band belonging to the γ-soft nucleus,133Ce. Doppler broadened lineshape (DBLS) analysis has revealed the magnitude of theQ t value, to be ∼ 2.4 eb. This contribution provides new information of (i) the transition quadrupole moment of this band (ii) the life-times of in-band and sidefeeding transition and (iii) the relative deformations of coexisting nuclear shapes.

RESULTS FROM SHELL-MODEL MONTE CARLO STUDIES

▪ Abstract We review results obtained using Shell-Model Monte Carlo (SMMC) techniques. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; the resultant path integral is evaluated stochastically. After a brief review of the methods, we discuss a variety of nuclear-physics applications. These include studies of the ground-state properties of pf-shell nuclei, Gamow-Teller strength distributions, thermal and rotational pairing properties of nuclei near N = Z, γ-soft nuclei, and ββ-decay in76Ge. Several other illustrative calculations are also reviewed. Finally, we discuss prospects for further progress in SMMC and related calculations.