J. P. Draayer

Search for a coupling scheme in heavy deformed nuclei: the pseudo SU(3) model.

To test the possible usefulness of the pseudo SU(3) coupling scheme a few nuclear properties are examined which can be expected to be governed largely by the (lg

Generalized pseudo-SU(3) model and pairing☆

d~2d+3s+) part of the proton configuration for odd-2 nuclei and the (lh2fs2f*3p+3p+) part of the neutron configuration for odd-N nuclei. The equivalence between these configurations and pseudo oscillator shells (?

Wigner and Racah coefficients for SU3

&&) and (~

Towards a shell model description of the low-energy structure of deformed nuclei I. Even-even systems

+) is exploited to show that the low-lying natural-parity rotational bands in deformed nuclei can be described approximately by many- particle states which are coupled to leading pseudo SU(3) representation (maximum possible value of 2i+;) of these configurations. The simple model in which the natural-parity part of the proton and neutron configurations are coupled to leading pseudo SU(3) representation predicts ground state magnetic moments in remarkably good agreement with experiment. The strong hindrance factors observed in certain interband Ml transition probabilities are, however, not predicted by this model. The diagonalization of a simple effective interaction within the leading pseudo SU(3) representation leads to spectra with the experimentally observed ordering of the K-bands. (The case of the Eu and Tm isotopes has been examined in some detail since these are expected to have leading pseudo SU(3) representations with the same quantum numbers (&) but with quite different ordering of the K-bands.)

Strength distributions and statistical spectroscopy. I. General theory

The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The pairing interaction, which couples different irreducible representations of SU(3), is expressed in terms of pseudo-space tensors and a general result is given for calculating its matrix elements. The importance of pairing correlations in pseudo-SU(3) model calculations is demonstrated by examining the dependence of wavefunctions, low-energy collective excitation spectra, and moments of inertia on the strength of the pairing interaction.Abstract The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The pairing interaction, which couples different irreducible representations of SU(3), is expressed in terms of pseudo-space tensors and a general result is given for calculating its matrix elements. The importance of pairing correlations in pseudo-SU(3) model calculations is demonstrated by examining the dependence of wavefunctions, low-energy collective excitation spectra, and moments of inertia on the strength of the pairing interaction.

New algebraic solutions for SO(6) ↔ U(5) transitional nuclei in the interacting boson model

A general yet simple and hence practical algorithm for calculating SU3⊃SU2×U1 Wigner coefficients is formulated. The resolution of the outer multiplicity follows the prescription given by Biedenharn and Louck. It is shown that SU3 Racah coefficients can be obtained as a solution to a set of simultaneous equations with unknown coefficients given as a by‐product of the initial steps in the SU3⊃SU2×U1 Wigner coefficient construction algorithm. A general expression for evaluating SU3⊃R3 Wigner coefficients as a sum over a simple subset of the corresponding SU3⊃SU2×U1 Wigner coefficients is also presented. State conjugation properties are discussed and symmetry relations for both the SU3⊃SU2×U1 and SU3⊃R3 Wigner coefficients are given. Machine codes based on the results are available.

On the validity of the pseudo-spin concept for axially symmetric deformed nuclei

Method of solution A build-up process based on the Biedenharn-Louck prescription for specifying the outer multiplicity is employed to generate SU 3 D SU2 X U t Wigner coefficients [ 1 ]. SU 3 Racah coefficients follow through standard recoupling formulae [2]. SU3 ~ R3 Wigner coefficients are obtained from the corresponding SU 3 D SU 2 X U 1 Wigner coefficients via unitary transformation coefficients relating SU3 3 SU2 X Ul and SU 3 D R 3 basis states [3].

Alpha-particle spectroscopic amplitudes for sd shell nuclei

Abstract Localized patterns and nonlinear oscillation formations on the bounded free surface of an ideal incompressible liquid are investigated. Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are discussed. A finite-difference differential generalized Korteweg-de Vries (KdV) equation is shown to describe the three-dimensional motion of the fluid surface, and in the limit of long and shallow channels one recovers the well-known KdV equation. A tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial conditions is introduced. The model is useful in multilayer fluid dynamics, cluster formation, and nuclear physics since, up to an overall scale, these systems display a free liquid surface behavior.