Coupling of two quasiparticles to coherent cores in the Pt isotopes

A model for coupling the motion of particles to that of a quadrupole-collective core is proposed. The quadrupole vibrations and rotations of the core are described by angular momentum projected coherent states. The spherical shell model particles interact among themselves by pairing and surface delta interactions. The particles are coupled to the core through a multipole-multipole interaction. The method is applied to several even mass isotopes of Pt. The agreement with experimental data of the excitation energies, gyromagnetic factors andE2 probabilities is very good.     

Rare-earth nuclei and the pseudo-SU(3) model

An extended version of the pseudo-SU(3) model is used to describe low-energy positive-parity states of three rare-earth nuclei in a full proton-neutron formalism. Along with other residual interactions, the Hamiltonian includes the pairing which induces mixing between different representations of SU(3). Excitation energies, B(E2) values, B(M1) values, quadrupole moments, andg _R factors of¹³⁶Xe,¹³⁸Ba, and²⁰⁴Hg are calculated in a truncation free environment and the results are compared with the experimental data and other theories.     

Shape variables and the shell model

The irreducible representation labelsλ andμ of the SU(3) shell model are related to the shape variablesβ andγ of the collective model by invoking a linear mapping between eigenvalues of invariant operators of the two theories. All but one parameter of the theory is fixed if the shell-model result is required to reproduce the collective-model geometry. And for one special value of the remaining free parameter there is a simple linear relationship between the eigenvalues, λ_α, of the quadrupole matrix of the collective model and the SU(3) representation labels: $$\lambda _1 = ( - \lambda + \mu )/3, \lambda _2 = ( - \lambda + 2\mu + 3)/3, \lambda _3 = (2\lambda + \mu + 3)/3.$$ The correspondence between hamiltonians that describe rotations in each theory is also given. Results are shown for two cases,²⁴Mg and¹⁶⁸Er, to demonstrate that the simplest mapping yields excellent results for both energies and transition rates. For λ and/or μ large, the (β, γ)?(λ,μ) correspondence introduced here reduces to the symplectic shell-model result.     

High spin yrast states in even platinum isotopes

The high spin yrast states up toJ=20⁺ in^{184, 186}Pt and^{190, 192, 194}Pt are studied in a microscopic approach of variation with number-conserved projected states. The energy spectra, quadrupole moments andB(E2) values are calculated by employing the Hamiltonian with quadrupole plus pairing interactions. The results of the calculations are in fair agreement with the available experimental data.     

The quantum harmonic oscillator on the sphere and the hyperbolic plane

A nonlinear model of the quantum harmonic oscillator on two-dimensional space of constant curvature is exactly solved. This model depends on a parameter λ that is related with the curvature of the space. First, the relation with other approaches is discussed and then the classical system is quantized by analyzing the symmetries of the metric (Killing vectors), obtaining a λ-dependent invariant measure dμ_λ and expressing the Hamiltonian as a function of the Noether momenta. In the second part, the quantum superintegrability of the Hamiltonian and the multiple separability of the Schrödinger equation is studied. Two λ-dependent Sturm-Liouville problems, related with two different λ-deformations of the Hermite equation, are obtained. This leads to the study of two λ-dependent families of orthogonal polynomials both related with the Hermite polynomials. Finally the wave functions Ψ_m,n and the energies E_m,n of the bound states are exactly obtained in both the sphere S² and the hyperbolic plane H².     

Collinear laser spectroscopy on108g, 108m In using an ion source with bunched beam release

The hyperfine structure and isotope shift of^108gIn and^108mIn have been investigated by means of collinear fast-beam laser spectroscopy in the resonance line atλ=451 nm. The indium isotopes were prepared at the GSI on-line mass separator following a fusion evaporation reaction. For the first time, a FEBIAD ion source with bunched release of indium was used. Magnetic dipole moments, electric quadrupole moments and isotope shifts were determined. The present results lead us to assign the spinI=2 to the¹⁰⁸In (T _1/2=40 min) state. Spins and moments are discussed in the framework of thejj-coupling model.     

Description of low-lying vibrationalK π≠0+ states of deformed nuclei in the quasiparticle-phonon nuclear model

The QPNM equations are derived taking account of p-h and p-p interactions. The calculated quadrupole, octupole and hexadecapole vibrational states in¹⁶⁸Er,¹⁷²Yb and¹⁷⁸Hf are found to be in reasonable agreement with experimental data. It is shown that distribution of theEλ strength in some deformed nuclei differs from the standard one. There are cases when for a givenK ^π theEλ strength is concentrated not on the first but on higher-lying states. The assertion made earlier about the absence of collective two-phonon states in deformed nuclei is confirmed.     

Back-bending in182,184,186osmium

The high spin yrast states uptoJ=22⁺ in^182,184,186Os are studied in a microscopic variational approach with number-conserved projected states. The energy spectra, quadrupole, moments andB (E2) values are calculated by employing the Hamiltonian with quadrupole plus pairing interactions. The results of the calculations are in fair agreement with the available experimental data.     

Isotope shift of calcium isotopes withA=40, 42, 43, 44, 46 and 48 by laser spectroscopy

Isotope shifts of all the stable Ca isotopes in the intercombination lineλ=6573Å have been studied by laser spectroscopy. The nuclear volume effect for⁴³Ca and⁴⁶Ca could be evaluated from the measurements and the quadrupole moment of⁴³Ca was obtained.     

Coupling of one and three quasiparticles to a collective core projected from quadrupole coherent states

The excitation energies and the electromagnetic properties of some odd-mass isotopes of Pt are treated in the framework of a particle-core coupling model. The collective motion of the core is treated by the coherent state model (CSM). A system of interacting shell model nucleons is coupled to the core through aλ-pole-λ-pole term withλ=0, 2, 4. The coupled system is treated alternatively in the strong and weak coupling limit. Numerical applications to the isotopes^189,191,193Pt show a good agreement with the available data. The backbending of the yrast band is interpreted as being caused by the intersection of the one and three quasiparticle bands.     

Calculations of the energy spectra of Zn,Ga, and Ge isotopes by the shell model

The effective Hamiltonian which was determined empirically by Koops and Glaudemans is tested in shell model calculations for the^65–68Zn,^67–69Ga, and^68–70Ge nuclei in the full (1p _3/2,0f _5/2,1p _1/2) ⁿ space. The resulting energy spectra are compared with the experimental spectra and results of previous calculations. The overall agreement with experiment is as satisfactory for these nuclei as for the Ni and Cu isotopes, by which the Hamiltonian was determined. It is noticed that the spectra of⁶⁷Zn and^67,69Ga calculated in this work are similar to those provided by the Alaga model.     

Geometric shapes withg- bosons in the interacting boson model

Geometric aspects of the extended interacting boson model (gIBM) withs, d andg bosons are studied using coherent states. Algebraic expressions for the coherent state expectation values of various terms in the general gIBM Hamiltonian are derived in terms of the quadrupole and hexadecupole deformation variablesβ ₂ andβ ₄ and the asymmetry angleγ. These in turn are used to determine the equilibrium shape parameters (β ₂ ⁰ ,β ₄ ⁰ ,γ ⁰) in the seven dynamical symmetry limits of gIBM.     

Proton-neutron interactions in nuclei withA∼90

An extension of the cluster-(quadrupole-octupole) phonon model is proposed for nuclei withA～90 to describe simultaneously positive- and negative-parity states, in which quadrupole as well as octupole vibrations of the⁸⁸Sr core are allowed. The cluster states include particle and particle-hole core excitations. The residual interaction is a delta-function force with spin-spin exchange plus a quadrupole-quadrupole force. The model is applied to⁸⁷Sr,⁸⁹Sr,⁸⁸Y, and⁹⁰Y nuclei. For each case, energy levels, spectroscopic factors, and electromagnetic properties are calculated and compared with experiment.     

Structure calculations for 25Mg-25Al

The results of a shell model calculation for ²⁵Mg-²⁵Al are presented in which the Hamiltonian for the system was taken to be that of an inert ¹⁶O core plus nine s-d shell particles interacting through the usual one-body l² and l · s terms plus general two-body residual interactions of the Kuo-Brown type. The basis was truncated to include nine favored representations of SU(3) in each of the two leading spatial symmetries ([441]: (66), (93), (74), (82)², (55)², (28), (90); [432]: (10,1), (74), (82)², (55)², (28), (47), (90)). It is found that a (λμ)-dependent renormalization of the type proposed by Harvey but empirically modified for axially asymmetric shape distributions is required to reproduce the experimentally observed ordering of the three lowest rotational bands. The goodness of K_J as a band label for the calculated eigenstates is investigated by comparing calculated quadrupole moments with simple rotational model predictions. Calculated B(E2) and B (M1) rates are compared with the available data. Results for relative spectroscopic factors from (d, p) stripping on the ground state of ²⁴Mg are also presented.     

Laserspectroscopic studies of collective properties of neutron deficient Ba Nuclei

Isotope shifts and hyperfine structure of the BaI resonance-line (λ=553.6 nm) have been measured by dye laser induced resonance fluorescence on an atomic beam for^{135m, 129g, 129m, 126}Ba thus extending previous high resolution measurements of neutron deficient Ba nuclides (N<82). The experimental results, now available for 16Ba isotopes and isomers withA=140?126, are used to deduce differences of rms charge radii, magnetic dipole and electric quadrupole moments. While the groundstates display a pronounced odd-even staggering the h 11/2^? isomers^135mBa and^133mBa show a decreased staggering. Conspicuously the isomer shift of theg 7/2⁺ isomer^129m Ba proves to be negative. The nuclear structure information is discussed in the context of gammaspectroscopic studies of transitional nuclei with 50<N,Z<82 and on the basis of a quasi-particle-plus-triaxial rotor model. The isotope shift discrepancy observed is fairly well described by the droplet model.     

On the Yrast levels of106–108Sn

The isotope shift in the Ca-intercombination line withλ=6,573 Å was measured for all isotopes between⁴⁰Ca and⁴⁸Ca with the only exception of 47Ca. The combination of the results with muonic x-ray data yields highly accurate values for the changes of the mean square nuclear charge radii. In addition, the nuclear quadrupole moments of the three isotopes⁴¹Ca,⁴³Ca and⁴⁵Ca have been determined from the hyperfine structure splitting of the 4s 4p ³ P ₁ state.     

Boson description of nuclear collective motion

Nuclear system with octupole-octupole interaction is studied by means of the boson expansion method. Expressions of the fourth-order collective Hamiltonian and third-order octupole moment operator are derived. For¹¹²Cd and¹⁴⁸Sm, characteristics of octupole vibrational spectra are discussed in comparison with the quadrupole vibration.