Extended Shell Model Research Articles

Hypernuclear production spectroscopy with an extended shell model

The (e, e’K+) reaction experiments with several nuclear targets performed recently at the Jefferson laboratory have provided high-resolution spectroscopic data. Among others, the 10B(e, e’K+) 10ΛBe reaction data are particularly interesting due to new appearance of extra sub-peaks which seem difficult to be explained within the conventional model with the p-shell nuclear naturalparity configurations. To describe this novel hypernuclear structure, we have extended the model space by introducing the new configurations which include unnatural-parity nuclear core-excited states. This configuration mixing successfully explains the sub-peaks in the 10B(e, e’K+) reaction data. For adjacent hypernuclei with A = 9–11, we show the DWIA spectra of (K−, π−), (π+, K+) and (γ, K+) reactions that are calculated within the extended model in a consistent way. We discuss the theoretical spectra of 9,10ΛBe and 11ΛB production reactions.

Core-Polarization Effects on the Isoscalar and Isovector Transitions in 24Mg Using Extended Shell Model

Core-Polarization Effects on the Isoscalar and Isovector Transitions in ²⁴Mg Using Extended Shell Model

Study of the deformation-driving [formula omitted] orbital in 6728Ni39 using one-neutron transfer reactions

The νg9/2,d5/2,s1/2 orbitals are assumed to be responsible for the swift onset of collectivity observed in the region below 68Ni. Especially the single-particle energies and strengths of these orbitals are of importance. We studied such properties in the nearby 67Ni nucleus, by performing a (d,p)-experiment in inverse kinematics employing a post-accelerated radioactive ion beam (RIB) at the REX-ISOLDE facility. The experiment was performed at an energy of 2.95 MeV/u using a combination of the T-REX particle detectors, the Miniball γ-detection array and a newly-developed delayed-correlation technique as to investigate μs-isomers. Angular distributions of the ground state and multiple excited states in 67Ni were obtained and compared with DWBA cross-section calculations, leading to the identification of positive-parity states with substantial νg9/2 (1007 keV) and νd5/2 (2207 keV and 3277 keV) single-particle strengths up to an excitation energy of 5.8 MeV. 50% of the νd5/2 single-particle strength relative to the νg9/2-orbital is concentrated in and shared between the first two observed 5/2+ levels. A comparison with extended Shell Model calculations and equivalent (3He, d) studies in the region around 9040Zr50 highlights similarities for the strength of the negative-parity pf and positive-parity g9/2 state, but differences are observed for the d5/2 single-particle strength.

Binding energy of the sd shell nuclei in the supersymmetric model

The supersymmetric model within the interacting boson model IBM4 with spin and isospin quantum numbers has been applied in our previous papers to the interpretation of energy levels and electromagnetic E2 transitions. The application of the model supersymmetric Hamiltonian to the binding energy calculations leads to the approximate mass formula with a relatively small number of parameters. The results when compared with experimental data are quite satisfactory, although not so good as extended shell model results. There is, however, another aim of this paper, namely to present an additional argument for the main assumption: the supersymmetry of the sd shell nuclei.

Extended shell model calculation for even N = 82 isotones with a realistic effective interaction

The shell model within the 2s1d0g 7 2 0h 11 2 shell is applied to calculate nuclear structure properties of the even Z = 52−62, N = 82 isotones. The results are compared with experimental data and with the results of a quasiparticle random-phase approximation (QRPA) calculation. The interaction used in these calculations is a realistic two-body G-matrix interaction derived from modern meson-exchange potential models for the nucleon-nucleon interaction. For the shell model all the two-body matrix elements are renormalized by the Q -box method whereas for the QRPA the effective interaction is defined by the G-matrix.

Inelastic neutron scattering measurements on the transverse acoustic and lowest optic modes in doped with lithium

Two crystals of with 1% and 5% Li have been investigated by inelastic neutron scattering. The transverse acoustic and lowest optic modes have been measured in the [100] direction from room temperature down to 10 K. The wavevector dependences of the mode softening, damping and intensities are represented. The measured dispersions are analysed in the framework of an extended shell model assuming an anisotropic non-linear polarizability of the oxygen ion. On the basis of this model, structure factors are calculated and compared with measured phonon intensities. Conclusions on the influence of the lithium substitution on the non-linear character of the polarizability are discussed.

Effect of inclusion of 1g orbits on the Gamow-Teller strengths for the capture rates of solar neutrinos in Ga detectors

Neutrino capture rates for Ga detectors are calculated using a simple model for the Gamow-Teller strength distribution in an extended shell model space consisting of (1f2p1g) orbits and compared to the values obtained in the (1f2p) model space. It is seen that though the Gamow-Teller strength functions for the two model spaces differ at energies greater than the neutron emission threshold of 71Ge, the difference is small below this energy. This results in a vanishingly small change in the neutrino capture cross section and consequently the actual capture rate.

Enhancement of symmetry violation in a chaotic system

Enhancement of parity violation effects are calculated in an extended shell model space. Strong enhancements in the longitudinal asymmetry are found when the nucleus is in a regime of large density of states and when nuclear states are very complicated exhibiting features of complete mixing characteristic of the chaotic stage. The nature and mechanism of the enhancement are discussed and compared with parity violation effects found at the single-particle stage. The universality of this effect for a wider class of symmetries and symmetry breakings as well as for a large class of complex systems is mentioned.

The magnetoacoustic cyclotron instability of an extended shell distribution of energetic ions

The magnetoacoustic cyclotron instability is a mechanism by which waves on the perpendicular fast Alfvén-ion Bernstein branch can be excited through cyclotron resonance with an energetic ion population. It is a candidate emission mechanism for the superthermal ion cyclotron radiation, apparently associated with the products of fusion reactions, that has been observed from tokamak plasmas. In the present paper, an extended shell model is adopted for the energetic ion distribution function, fα(v)∼nα exp[−(v−v0)2/vT2]. An analytical formulation of the dispersion relation is obtained, whose numerical solution yields quantitative information on the role of vT in stabilizing wave growth at ion cyclotron harmonics. The results show that, for typical plasma parameters of interest, the degree of instability is significantly depressed, relative to its level for vT=0, once vT/v0≂0.1. Gaps appear in typical multiple cyclotron harmonic excitation patterns for 0.1≤vT/v0≤0.2, and most harmonics are stable for vT/v0≥0.25. Thus the energetic ion shell-driven magnetoacoustic cyclotron instability typically occurs only when the shell is relatively narrow in velocity space.

The Two-Phonon Raman Spectra of AgBr at LHeT

The two-phonon Raman spectra have been measured for an AgBr single crystal at LHeT, by using a time correlated single photon counting method. The results are compared with the two-phonon density of states based on the extended shell model.

Experimental and theoretical study of the Raman spectrum in KTa1-xNbxO3 solid solutions.

The three symmetry components of the Raman spectra in paraelectric ${\mathrm{KTa}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Nb}}_{\mathrm{x}}$${\mathrm{O}}_{3}$ (KTN) mixed crystals have been measured as a function of temperature (${T}_{c}$800 K) and for several niobium concentrations (x=0.008, x=0.012, x=0.02, x=0.09, x=0.21, and x=0.36). The results are analyzed in the framework of an extended shell model by assuming an anisotropic and nonlinear polarizability of the oxygen ion. This intraionic anharmonicity is indicated to be primarily responsible for the strong second-order Raman effect. Conclusions on the leading mechanism of the phase transitions in the KTN system are discussed.

Extended shell model calculation of the T=0 natural parity spectrum of 4He

The ground state and the first excited state of 4He are calculated in a complete 10ħω shell model basis using the potentials of Volkov and Brink and Boeker. The 1 −, 2 + and 4 + T=0 states are also investigated, respectively, up to 9, 8 and 6ħω. It is fou und that the agreement with experiment is significantly improved when the model space is enlarged.

The effect of proton correlations in the M1 scattering strengths of even calcium isotopes

The proton correlations are evaluated in Ca isotopes using the wave functions obtained in an extended shell model calculation in the [ 1 d 3 2 , 1 f 7 2 , 1 f 5 2 ] valence space. The inclusion of 2p-2h correlations in M1 scattering strengths and magnetic moments improves the agreement with the experimental data. The M1 strength in 40Ca is correctly reproduced.

Lattice dynamics of SnSe2

Neutron inelastic scattering measurements of the phonon dispersion curves of Sn${\mathrm{Se}}_{2}$ have been analyzed in terms of an extended shell model including static dipoles and van der Waals forces between anions. The model provides a good fit to the experimental dispersion curves. Inclusion of the static dipoles is essential to understand the anisotropy of the LO-TO splittings of the infrared-active modes at $\ensuremath{\Gamma}$ and the Se ions are found to have a static dipole of $\ensuremath{-}0.67 e$ \AA{}. The inclusion of van der Waals forces is necessary to fit correctly the LA mode at the zone-boundary point $A$. The layer character of Sn${\mathrm{Se}}_{2}$ is exemplified by the weak Se-Se short-range interlayer interaction.

Lattice dynamics of layered transition-metal dihalides

We present an extended-shell-model (ESM) calculation of the dispersion relations and of the phonon density of crystals with either Cd${\mathrm{I}}_{2}$ or Cd${\mathrm{Cl}}_{2}$ structure, namely, of V, Mn, Fe, Co, and Ni dichlorides and dibromides. The dynamical matrix, including the Coulomb and short-range contributions originating from the anion static dipoles, is constructed from model interionic potentials. While anion-anion Born-Mayer repulsion and van der Waals interactions are taken as in alkali halides, the parameters of metal-halogen short-range potential are obtained from equilibrium nearest-neighbor distance and cohesive energy. To this purpose we have derived an expression for the cohesive energy suitable to crystals with reduced ionicity and open $d$-shell configurations. A transverse metal-metal force constant and a correction to the transverse anion-anion interlayer force constant are added in order to fulfill the rotational invariance conditions. The three electrostatic parameters, net charge $Z$, anion shell charge $Y$, and anion shell-core displacement ${w}_{0}$, are adjustable and are best-fitted to the experimental Raman and far-infrared data. A reliable scale of ionicities ranging from $Z=0.71$ of Ni${\mathrm{Br}}_{2}$ to 0.91 of Mn${\mathrm{Cl}}_{2}$ is obtained, and the theoretical dynamical charges and elastic constants are reported. The calculated dispersion curves are in good agreement with the few available neutron data. For Mn${\mathrm{Cl}}_{2}$, where a complete comparison with neutron data is possible, we show how the various ESM contributions influence the dynamical anisotropy and the lattice stability. Finally, we discuss the role of central metal-metal interaction, three-body forces, monopolar and quadrupolar metal-ion breathing (all neglected in the calculations) in order to explain the residual discrepancies.

Lattice dynamics and ionic charge of VI 2

We present an Extended Shell Model calculation of the phonon dispersion curves in VI 2. The dynamical matrix is derived from interionic potentials including Coulomb monopole and dipole, van der Waals, nearest-neighbor and next-nearest-neighbor Born-Mayer repulsive interactions. The potential parameters are either known in literature or derived from lattice constants and cohesive energy. A suitable choice of only three adjustable parameters (net charge Z, shell charge and shell-core displacement) yields an excellent fit of the five optical frequencies and of the anion static dipole. The resulting ionic charge Z = 0.75 is very well consistent with the recent neutron data on transferred hyperfine interaction.

Influence of static dipole moments on the lattice dynamics of PbI 2

We propose an extended shell model for ionic layer compounds which includes both static and dynamically induced electronic dipoles. The model is applied to PbI 2. In particular we find that the static dipoles at the iodine ions are important for the E uA 2u splitting at the zone center, the anomalously large and anisotropic effective charges, the electronic susceptibility σ ∞, the Davydov splitting in the polytypes, and the behavior of transverse dispersion curves throughout the Brillouin zone.

Neutron scattering study of the lattice dynamics of AgBr at 4.4 K

The phonon dispersion relations of AgBr at 4.4 K have been measured in the three principal symmetry directions using the triple-axis neutron scattering technique. The data have been fitted by the extended shell model developed by Cochran et al. and the one-phonon density of states has been calculated. Near the zone boundary in the [111] direction ($L$ point), high-resolution measurements of the TA and TO phonon intensities have been carried out. The character inversion between these two modes at $L$ originally predicted by Fischer et al. is clearly evidenced from the observed intensities. The present model fit can also reproduce this character inversion. Infrared absorption and luminescence spectra of AgBr have been remeasured at 2 K with high resolution and low concentration of impurities. The observed spectral shape of the one-phonon sidebands can be successfully analyzed using the one-phonon density of states obtained at 4.4 K in the present study.

Lattice Dynamics and Anharmonic Effects in AgCl

AbstractThe lattice vibrations of AgCl are calculated from an extended shell model where the shell of the Ag‐ion has a quadrupolar and a rotational degree of freedom. The model parameters are discussed in connection with the electronic 4d‐shell of the Ag‐ion. Thermal expansion, infrared reflection, and anharmonic frequency shift are calculated from a simple extension of the harmonic model, and are found to be in good agreement with experimental data. The anharmonic effects are comparable to those of the alkali halides.

Shell model calculations on the positive parity states in 20Ne

The results of an extended shell model calculation in the space spanned by the 0 p 1 2 orbital and the whole of the sd-shell for the nucleus 20Ne are presented. The positions of the (4p-0h), (6p-2h) and (8p-4h) bands are located and the results are compared with recent experiments.