Paul Goldhammer

WAVE FUNCTIONS IN 1p-SHELL NUCLEI.

Abstract Static magnetic moments, M1 transition rates, spectroscopic factors for (d, p), (p, 3 He) and (p, 3 H) reactions and Gamow-Teller transitions are calculated for 1p shell nuclei using wave functions derived by Goldhammer, Hill and Nachamkin. Results are compared with experiment and with the shell-model calculations of Cohen and Kurath. The general trend of agreement is found to be consistent with a gradual increase in configuration mixing throughout the shell. It is found that this mixing implies a channel coupling of 3 S 1 and 3 D 1 partial waves beyond the 1p shell, whose magnitude is approximately 9% in 6 Li and 20% in 14 N.

Realistic and effective interactions in light nuclei: (I). Effective interaction parameters of the 1p shell

Abstract An intensive study is made of the shell-model effective interaction in the 1p shell, with particular emphasis on determining the importance of high-order G -matrix diagrams. Forty-nine levels, with principal configuration (1s) 4 (1p) A−4 , are used to fit the interaction parameters. Feingolds three-body vector interaction, arising from second-order effects of the tensor force, is verified to be manifestly important in this fit. A simple four-body interaction, designed to simulate α-clustering, is also tested. The best fit obtained yields an rms deviation from experiment of 270 keV.

G-MATRIX INTERACTION IN THE NUCLEAR 1p SHELL.

Abstract A G-matrix interaction applicable to nuclear states of the configuration (1s)4(1p)A−4 is obtained by fitting the position of energy levels in the 1p shell. In addition to a simple two-body potential the three-body vector force previously shown to arise from second-order effects of the tensor force is included. A total of 18 potential parameters are fitted to 34 low-lying energy levels to an rms deviation of 0.381 MeV. An additional twelve known levels are predicted to an rms deviation of 0.402 MeV. The only well established levels for which a reasonable fit is not obtained are the strong α-emitting states in 8Be and 12C. It is concluded that α-clustering makes a significant contribution to the energy of these α-decaying states.

Reaction matrix calculation of /sup 4/He with three- and four-particle correlations

The Brueckner-Bethe-Goldstone-Faddeev formalism is employed to calculate the binding energy of /sup 4/He with the Reid soft-core potential. The propagator in the reaction matrix is modified to account for translational invariance, and antisymmetrization of the wave function. Convergence of the method is tested by introducing a variable energy shift in the excited-state spectrum. (AIP)

Properties of 1s shell nuclei with momentum dependent interactions

Abstract The Bolsterli-Feenberg perturbation procedure is applied to the momentum-dependent potentials of Nestor et al. Binding energies, rms radii, and percentage D-states are calculated for 2H, 3H and 4He, in addition to the Coulomb energies of 3He and 4He. A modified version of the separation method for solving the Bethe-Goldstone equation is also employed. This separation method is found to badly overestimate the binding energy, due to the explicit momentum dependence of the potentials. Second-order perturbation theory proves to yield results which are both quite accurate mathematically and in good agreement with experiment.

Solution of the Bethe-Goldstone equation with the Sussex interaction

An estimate of the possible error made by using second order perturbation theory with the Sussex interaction is obtained through solution of the Bethe-Goldstone equation. The correction is on the order of 1 MeV in the /sup 3/S/sub 1/ state. A much more modest correction is found for other partial waves. Particular attention must be paid to the method by which one includes the single particle insertions for the particle states in higher order. (AIP)

Deformed binding fields: (II). Deformed wave functions in 6Li arising from the tensor force

Abstract A Hill-Wheeler representation is used to provide variational wave functions in a calculation of the T = 0 levels of 6 Li. The model Hamiltonian contains a harmonic central force as well as a tensor interaction. It is found that the lowest levels with J = 1, 2 and 3 may be generated from a single intrinsic function with approximately the same stationary values of the variational parameters for each level and thus form a kind of collective band. The level scheme indicates that the vector effects of the tensor force have been taken into account. It appears that the α-particle core is soft towards deformation caused by the 1p nucleons.