On the valence model for radiative capture

ANNALS

OF PHYSICS

93, 402403

Abstracts

(1975)

of Papers

to Appear

Modelfor Radiative Capture. J. CUGNON. de Physique Thtorique, 91406 Orsay, France AND C. of Liege at Sart Tilman, 4000 Liege 1, Belgium.

in Future

On the Valence

Issues

Institut de Physique NuclCaire, Division Theoretical Physics, University

MAHAUX.

We give several parametrizations for the elastic scattering and radiative capture cross sections for low neutron bombarding energy and discuss the relationship between the corresponding resonance parameters. We then perform an extensive investigation of the valence radiative capture model of Lane and Lynn. This model is formulated here in the frame of the shell-model approach. We exhibit the similarities and differences between our results and those derived from the R-matrix approach by Lane and Lynn on the one hand and from the optical-model approach by Lane and Mughabghab on the other hand. Particular attention is paid to the choice of the average potential well in the shell-model approach, in relation to the proper way to identify theoretical quantities and phenomenological parameters. We show that practically equivalent results can be obtained from a complex average potential well and from a suitably chosen real potential well, respectively. The following topics are investigated formally and numerically: dependence of the various theoretical expressions on the choice of the (real or complex) average potential well; relative importance of external and internal capture; dependence of photon widths and background cross section on mass number (for thermal energy and for E = 100 keV); dependence of the resonance parameters and background cross sections on energy, for A = 60; comparison between experimental data and theoretical values for radiative capture on saFe and @Ni. We discuss the conditions of validity of the valence capture model. In particular, we investigate the role of the giant dipole resonance and of the closed channels. We argue that the success of the valence capture model is intimately related to the importance of external capture. The contribution of the low-lying excited target states is investigated formally and numerically; it increases with mass number and tends to diminish the correlation between neutron and photon widths, which is implied by the valence capture model.

Renormaliration I. Intrinsic

for Frame

Collective Motion within in a Schematic Model.

Chalk River Nuclear Laboratories,

a Truncated

Space

of the Spherical

Shell

Model

M. HARVEY. Atomic Energy of Canada Limited, Chalk River, Ontario, Canada KOJ 1JO.

Using schematic Hamiltonians in the ZONeexample, the series of perturbation terms for effective interactions and operators in a truncated space of a spherical shell model is found that, when summed, yields the results for intrinsic moments and energy of the unrestricted deformed HartreeFock state. Black-box and random phase approximation diagrams are shown to be important as is another (little used and to be called IBG) diagram and the ladder diagrams. A black-dot vertex renormalization is introduced corresponding to consistent renormalization of every transformation within the model space. The black-dot corresponds exactly to the self consistency of deformed Hartree-Fock.

402 Copyright 0 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.