Quadrupole Pairing Research Articles

Installation and performance of the Budapest–Hamburg proton microprobe

A new scanning proton microprobe has been installed at the 5MV Van de Graaff accelerator of the KFKI Research Institute for Particle and Nuclear Physics. It is the energy-upgraded version of the Hamburg proton microprobe dismantled in 2001. The probe forming system includes a pair of focusing quadrupoles and an additional quadrupole pair in front of it, which is applied to increase the proton beam divergence. The average probe size at 2.5MeV proton energy is 2.2μm×1.1μm. The test results on stability and the preliminary experiments on cement corrosion and fish otoliths are also presented.

Microscopic Mechanism of Large Fluctuation in Odd-Even Differences in Momentsof Inertia for Actinide Nuclei

The experimental large fluctuation in odd-even differences in moments ofinertia of deformed actinide nuclei is investigated using the particle-numberconserving (PNC) method for treating the cranked shell model with monopole andquadrupole pairing interactions. PNC calculations show that the large odd-evendifference in moments of inertia mainly comes from the interferencecontributions j(μν) from particles in high j intruder orbitals μand ν quite near the Fermi surface, which have no counterpart in the BCSformalism. The effective monopole and quadrupole pairing interaction strengthsare determined to fit the experimental odd-even differences in bindingenergies and bandhead moments of inertia. The experimental results for thevariation of moments of inertia with rotational frequency ω arereproduced well by the PNC calculation. The nearly identical experimentalmoments of inertia between 236U(gsb) and 238U(gsb) at lowfrequencies ℏω⩽0.20 MeV are also reproduced quite well.

The i13/2 proton intruder orbital and the identical superdeformed bands in 193, 194, 195Tl

The microscopic mechanism of the identical bands in odd-odd nucleus Tl-194 and its neighbor odd-A nuclei Tl-193,Tl-195 is investigated using the particle-number-conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. It is found that the blocking effect of the high-j intruder orbital plays an important role in the variation of moments of inertia (J((1)) and J((2))) with rotational frequency for the superdeformed bands and identical bands. The omega variation of the occupation probability of each cranked orbital and the contributions to moment of inertia from each cranked orbital are presented.

Neutron–proton interaction and backbending in 48,50Cr nuclei

The high-spin state properties of the neutron–proton (n–p) residual effective interaction are analysed in 48,50Cr nuclei, where the experiments have observed anomalous rotational alignment. The self-consistent microscopic Hartree–Fock–Bogoliubov equations have been solved by employing monopole and quadrupole pairing plus quadrupole–quadrupole interaction. We have studied the mechanism of backbending in yrast energies in terms of moment of inertia and angular frequencies, E2 transition probabilities and quadrupole moments as a function of the angular momentum states. It is shown that the self-consistent theory with variation after angular momentum projection describes well overall trends of experimental data with n–p residual interaction strength decreasing from 0.0795 in a N = Z nucleus to 0.0495 MeV b−4 in a N = Z + 2 nucleus. However, the strong n–p residual interaction force is quite important in explaining the experimental data in N ≈ Z.

Blocking Effect and Moments of Inertia of K=1/2 Rotational Band in 171Yb**The project supported by National Natural Science Foundation of China under Grant Nos. 10147205 and 10375001

The rotational band in is investigated using the particle number conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. The experimental moments of inertia of (signature ) are reproduced well by the PNC calculation, in which no free parameter is involved. The difference in the contribution to the moment of inertia between protons and neutrons is mainly due to the blocking effect of neutron normal orbitals. The variation of the occupation probability of each cranked orbital and the contribution to the moment of inertia from each major shell and from each cranked orbital are investigated.

Simple modeling of dipolar coupled 7Li spins and stimulated-echo spectroscopy of single-crystalline β-eucryptite

Stimulated-echo spectroscopy has recently been applied to study the ultra-slow dynamics of nuclear spin-3/2 probes such as 7Li and 9Be in solids. Apart from the dominant first-order quadrupolar interaction in the present article also the impact of the homonuclear dipolar interactions is considered in a simple way: the time evolution of a dipole coupled pair of spins with I=3/2 is calculated in an approximation, which takes into account that the satellite transitions usually do not overlap. Explicit analytical expressions describing various aspects of a coupled quadrupolar pair subjected to a Jeener–Broekaert pulse sequence are derived. Extensions to larger spin systems are also briefly discussed. These results are compared with experimental data on a single-crystalline Li ion conductor.

Identical Bands and Alignment in 193,194Tl

The microscopic mechanism of the identical bands in odd–oddnucleus 194Tl and its neighbour odd-A nucleus 193Tl areinvestigated using the particle-number conserving methodwith monopole and quadrupole pairing interaction. It is found thatthe blocking effect plays an important role in the variation ofmoments of inertia (J(1) and J(2)) with rotationalfrequency for the superdeformed bands and identical bands. The alignmentof 194Tl bands with respect to the 193Tl(1) band used asa reference is also discussed.

Band crossing and the N=7 intruder orbital in superdeformed nucleus 193Hg

The particle-number conserving method for treating the cranked shell model with monopole and quadrupole pairing interactions is used to investigate the microscopic mechanism of six superdeformed bands in 193Hg, including the occupation probability of each cranked orbital, the contributions to angular momentum alignment from the direct contributions j x ( μ) of the particle in orbital μ, and the interference contribution j x ( μν) from the particles in orbitals μ and ν. Our calculated results support the previous assignments of configuration of six superdeformed bands in 193Hg and provide a satisfactory demonstration for the crucial role of the high- N intruder orbital ν[761]3/2 in band crossing and angular momentum alignment.

Particle-number-conserving treatment for the backbending in Yb isotopes

The particle-number conserving (PNC) treatment for the cranked shell model with monopole and quadrupole pairing interactions is used to investigate the microscopic mechanism of backbending in nuclear moments of inertia of Yb isotopes, including the variation with rotational frequency ω of the occupation n μ of each cranked orbital μ, the contributions to angular momentum alignment from each unclosed major shell, and the individual contributions j x ( μ) from the particle in the orbital μ, and the interference j x ( μν) between the particles in orbitals μ and ν. PNC calculations show that the occurrence of sharp backbending in some nuclei (e.g., 170Yb), comes mainly from contribution of the interference effect between a high j intruder orbital quite near the Fermi surface and neighboring high j orbitals.

Three-dimensional roll-up of a viscoelastic mixing layer

In this paper, the three-dimensional roll-up of a viscoelastic mixing layer is numerically simulated with the pseudospectral method using the FENE-P model. An artificial diffusion is self-adaptively introduced into the constitutive equation to stabilize the time integration. In the three-dimensional mixing layer and within the parameter ranges studied, the effect of the polymer additives on the formation of the coherent structures such as the ribs and the cups is found to be negligible. The polymer normal stresses develop wherever there exist extensional strains that are produced by the coherent structures and they then hinder the development of these structures. Stretching by the quadrupoles and the ribs together gives rise to an enormous enhancement of the polymer normal stress differences in the symmetrical plane between the quadrupole pair. These normal stress differences directly or indirectly weaken all large-scale structures occurring in the flow including the quadrupoles, the cups, the ribs, the spanwise vortices which rotate in the opposite direction to that of the cups, and the thin spanwise vortical sheets. Attenuation of these large-scale structures leads to a diminution of small-scale structures after their breakdown in the secondary roll-up process of the thin sheets. There is a tendency for the small-scale structures in the core region to merge into a large-scale one in the viscoelastic case. As a result, a flat and inclined vortex forms at the end of the simulation which resembles the type of structure observed in an experimental mixing layer with surfactants injected. In addition, the results show that the extensional viscosity is an important quantity to determine the extent to which the coherent structures in a mixing layer are modified by polymer additives.

A set of molecular models for carbon monoxide and halogenated hydrocarbons

Molecular models are presented for carbon monoxide and 53 halogenated methane, ethane, and ethene derivatives, among which are important alternative refrigerants. The models are based on the two-center Lennard-Jones plus point dipole or plus point quadrupole pair potentials. The model parameters were adjusted to experimental vapor–liquid equilibria of the pure fluids using a highly efficient procedure. The application of these models to the calculation of vapor–liquid equilibria and homogeneous fluid state points by molecular simulation shows good to excellent agreement with experimental results. The present molecular models describe the vapor pressures in most cases significantly better than models available in the literature. Typical mean relative deviations between simulation results and experiments are 0.5% for the saturated liquid density, 4% for the vapor pressure, and 3% for the enthalpy of vaporization. Due to the compatibility of the presented models, the prediction of vapor–liquid equilibria of mixtures is straightforward.

Pair-truncated shell-model approach to backbending and low-lying states in132Ba

Backbending phenomena and low-lying collective states in the nucleus ${}^{132}\mathrm{Ba}$ are studied in terms of a pair-truncated shell model with the monopole and quadrupole pairing plus quadrupole-quadrupole interaction. The model reproduces well experimental energy levels, transition rates, and g factors for both low-lying states and those around the backbending region. The collective pair truncation of the shell-model space yields remarkable results for low-lying states, and the alignment of two ${0h}_{11/2}$ neutrons plays a decisive role in describing the backbending.

Pairing Field and Moments of Inertia of Superdeformed Nuclei

We have systematically analysed the dynamic moments of inertia of theexperimental superdeformed (SD) bands observed in the A = 190, 150and 60-80 mass regions as functions of rotational frequency. Bycombining the different mass regions, the dramatic features of thedynamic moments of inertia were found and explained based on thecalculations of the pairing fields of SD nuclei with the anisotropicharmonic oscillator quadrupole pairing Hartree-Fock-Bogoliubovmodel.

Microscopic mechanism of identical superdeformed bands in192,193,194Hg

The microscopic mechanism of identical superdeformed bands in ${}^{192,193,194}\mathrm{Hg}$ is investigated using the particle-number conserving treatment for the cranked shell model with monopole and quadrupole pairing interactions. In combination with the analysis for normally deformed identical bands in the rare-earth nuclei, it is shown that the identical bands observed in normally deformed rare-earth nuclei and superdeformed nuclei in the $A\ensuremath{\sim}190$ region result from the competition among shell effect, pairing interaction, blocking effect on pairing, and Coriolis antipairing interaction, where a strict and consistent treatment of blocking effect plays a crucial role.

Shell model study of backbending phenomena in Xe isotopes

Xe isotopes near mass $A\ensuremath{\sim}130$ region, which exhibit features of O(6) symmetry at low energy and the backbending at high spins, are studied in the shell model framework. The monopole and quadrupole pairing plus quadrupole-quadrupole interaction is employed as an effective interaction. As for single-particle levels, the ${1d}_{3/2},$ ${0h}_{11/2},$ ${2s}_{1/2}$ orbitals are taken into account for neutrons and the ${1d}_{5/2},$ ${0g}_{7/2}$ orbitals for protons under the assumption of $N=Z=64$ subshell closure. The calculation reproduces the experimental energy levels of high-spin states as well as low-lying states well. This is the first successful microscopic description of the backbending in this mass region. The shell model states are examined in pair-truncated models. The analysis shows the alignment of two ${0h}_{11/2}$ neutrons at high spins.

Blocking effect and the moments of inertia of high-Kmultiquasiparticle bands in172,173,174,175Hf

The series of high-$K$ multiquasiparticle bands in ${}^{172,173,174,175}\mathrm{Hf}$ are investigated using the particle-number-conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. The experimental results, including the moments of inertia and angular momentum alignments relative to the ground state band ${}^{172}\mathrm{Hf}(\mathrm{g}.\mathrm{s}.\mathrm{b}.)$ are reproduced quite well by the PNC calculation, in which no free parameter is involved. The difference in the $\ensuremath{\omega}$ variation of the moments of inertia between the high-$K$ multiquasiparticle bands and ${}^{172}\mathrm{Hf}(\mathrm{g}.\mathrm{s}.\mathrm{b}.)$ is mainly due to the blocking effects of high j intruder orbitals near the Fermi surface. The $\ensuremath{\omega}$ variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each major shell and from each cranked orbital are investigated.

Signature inversion in the yrast band of164Ta

Excited states in Ta-164 were populated in the Nd-142(Al-27,5n)Ta-164 reaction and investigated using the AFRODITE spectrometer Arran. The yrast rotational decay sequence Lip to spin 21(-) is identified for the first time and assigned to the pi[514]9/2(-) x nu[660]1/2(+) configuration. A less intense. excited hand is also identified. Low-spin signature inversion is observed in the yrast band, and is compared with the extended total Routhian surface calculations. It is likely that quadrupole pairing plays a role in generating the anomalous signature splitting, but an additional mechanism apart front the assumed mean field and quadrupole pairing interaction may be required to account for the experimental data.

Reflection Asymmetric Shell Model for the Description ofOctupole Rotational Bands

The reflection asymmetric shell model hasbeen formulated to describe the high spin states of octupole-deformednuclei. The long-range separable forces of quadrupole, octupole andhexadecapole, as well as monopole and quadrupole pairing, are included inthe Hamiltonian. The bases, on which the Hamiltonian is diagonalized, arethe eigenstates of angular momentum and parity obtained by projecting theoctupole-deformed multi-quasiparticle states onto good angular momentumand good parity. The general features of rotational octupole bands ineven-even nuclei can be reproduced by the model and the calculated resultis in good agreement with experiment.

Quadrupole pairing and downturn of moment of inertia for the superdeformed band194Hg(1)

Quadrupole pairing and downturn of moment of inertia for the superdeformed band194Hg(1)

Relationship between the fermion dynamical symmetric model Hamiltonian and nuclear collective motion

In this paper we investigate the role of single-particle energies on the low-lying states of ${}^{132}\mathrm{Ba},$ a typical O(6) nucleus in the IBM and the fermion dynamical symmetric model (FDSM). It is found that one can reproduce the physical quantities of a realistic system with nondegenerate single-particle energies using degenerate single-particle levels and a slightly different parametrization of the two-body interaction. However, if the single-particle splittings are enlarged by a factor of 1.5, the O(6)-like behavior of the nucleus is lost and a model that assumes degenerate levels cannot describe its collective structure. Contributions from interactions other than monopole and quadrupole pairing and a quadrupole-quadrupole force are found to be unimportant. Although the role of the abnormal-parity level depends on the details of the single-particle structure, its effects can be ``compensated'' by using different Hamiltonian parameters and degenerate single-particle levels in a FDSM treatment.