M. Harvey

Effective nuclear forces in the quark model with Delta and hidden color channel coupling

Adiabatic potentials are calculated in a six-quark cluster model corresponding to having NN, ΔΔ and CC (hidden color) channel coupling. Color-dependent quark interactions are used that yield the N and Δ positive- and negative-parity resonances up to 2 GeV. Channel coupling is found to be large (especially with the CC state) and yields an effective NN potential having none of the characteristics of phenomenological potentials extracted from phase shifts.

Analogue symmetry breaking in superallowed fermi β-decay

Abstract The change in the Fermi matrix element due to deviations from perfect analogue symmetry has been estimated in a single-particle model with both harmonic oscillator and Saxon-Woods radial wave functions. A limitation of earlier calculations, in which the ground state of the A − 1 nucleus was taken as the unique parent, is removed to allow the whole spectrum of parent states to be operative. This improvement leads to slightly larger analogue symmetry breaking effects.

Nucleon-nucleon scattering in the quark-cluster model

Abstract Results of calculations of nucleon-nucleon scattering phase shifts (S-, P- and D-wave) and delta-production cross sections are presented for a quark potential model with channel coupling in both generator-coordinate and resonating-group formalisms. The dependence of the results on various input assumptions is shown. The interpretation in terms of a local potential is discussed, as are the extensions to the calculation necessary for agreement with experiment.

Effective operators in the nuclear shell model: (I). General theory

Abstract A general formalism for defining an effective operator (≅ t ) in a truncated Hubert space is presented and is shown to depend on the operator v 21 which connects the included and the excluded Hilbert space. The projection operator technique is used. The usual method of calculating the effective interaction in a restricted Hilbert space is a special case of this formalism. Details for an effective electromagnetic transition operator are given and it is shown that the effective electromagnetic operator has one-, two-, three- and four-body parts if the usual assumption that v 21 is a two-body operator is made. Connection of the present formulation with some earlier calculation of the effective charge for E2 transitions is discussed.

The structure of 8Be and its relevance to the fission problem

Abstract The structure of 8 Be is examined in the spherical shell model, the deformed shell model, the cluster model and the cluster model with the one- and three-dimensional generator coordinate techniques. The increase in binding energy with each sophistication is discussed. The collectivity of each model is demonstrated through the B ( E 2) in the projected states. A new method of generating clusters is presented which could have relevance for the fission problem.

EFFECTIVE OPERATORS IN THE NUCLEAR SHELL MODEL. II. PHENOMENOLOGY OF E2 OPERATORS.

Abstract The coupling operator discussed in paper I is defined in terms of a buffer space and parameterized to fit the observed E2 effective charge in the oxygen region. Variations in the exchange character of the coupling operator resulting from changes in the assumed effective charges are studied. The effect on the E3 effective charge and the magnitude of the two-body E2 operator are discussed.

Distribution of dipole and spin-dipole strength in nuclei

Abstract The schematic model of Goswami and Pal is applied to heavy nuclei and the dipole strength is shown to reside in just four non-degenerate levels. The collection of all the strength into a single level is discussed. The distribution of strength due to non-constancy of radial integrals and non-degeneracy of unperturbed particle-hole orbits is demonstrated in “realistic” calculations for 208 Pb, 132 Sn, 90 Zr and 56 Ni. The collection of low energy dipole strength into “mini-resonances” is shown to be sensitive to the mean energy difference between neutron and proton particle-hole states.

Generalised quartet model for particle-hole excitations across major shells

Abstract The schematic quartet model of Arima et al. is generalised to include any number of particle-hole excitations. The assumption of constancy of particle-hole matrix elements with mass number is examined in the deformed-oscillator model and shown to be poor in certain cases. A revised picture for particle-hole excitations shows smoother trends than with the schematic model. Comparison with the Zamick model yields greater insight into the structure of two-particle excited states.

Effective operators for the nuclear shell model: (III). E2 effective charge with realistic reaction matrices

Abstract The structure of effective operators is determined in time-dependent perturbation theory and compared with the approach using Bloch-Horowitz theory discussed in paper I. The E2 effective charges in the spherical shell model arising from the core polarisation in the oxygen and calcium regions are calculated with the G-matrices of Kahana et al.

The anatomy of the Hartree-Fock procedure in a simple model

Abstract The Hartree-Fock procedure is examined in detail for the simple problem of two particles in a four-dimensional function space for which the exact solution can be found. Conditions are determined for the stability of the iterative procedure used to solve the Hartree-Fock set of equations. The problem of drawing the energy surface using the constrained Hartree-Fock method is discussed.