Perturbation theory of nuclear matter and finite nuclei

Abstract

This dissertation investigates several related topics in the theory and application of perturbation methods to nuclear matter and finite nuclei. (l) Theoretical discussions include the concise rederivation of many basic equations describing the properties of many fermion systems. The techniques thus developed are then employed, with a "change of parameter" procedure, to derive an approximate expansion for the energy of the "normal" state. In this expansion, the momentum density occurs in place of the Fermi functions and the "self-energy" terms are absent. Also discussed is a new method for including the "core volume energy" in the K-matrix approximation. A later discussion includes a study of other nuclear matter theories, and discloses a previously unreported second order difference between an expansion of the equations of the Puff theory and the Brueckner-Goldstone expansion. (2) A simplified version of the Brueckner-Gammel K-matrix approximation is then presented, and employed to show that the variation of many-body properties with choice of phenomenological potentials is quite large: the saturation values for the ground state energy vary from -8.3 MeV at an equilibrium spacing of 1.28 Fermis for the Breit potential to -22.3 MeV at 0-9 Fermi for one Gammel Thaler potential, a result that implies that comparison of results with extrapolated experimental values is not at present an accurate test of a nuclear matter theory. The simplified approximation is also used to obtain estimates of the attractive contributions of many perturbation diagrams , leading to the conclusion that calcula tions with hard core potentials must be carried to the equivalent of the third Born approximation (on the attractive part of the potential) and that the self-consistent energy denominators must be computed with at least "first iteration" reaction matrices for quantitative (± 2 MeV) results. (3) The approximation for finite nuclei is also extended with a semi -independent verification of previous calculations, an evaluation of a new rearrangement energy approximation (which gives a more accurate energy spectrum but only slightly better average properties than previous calculations), and the calculation of the pr perties of Pb . The latter yielded a mean energy of -6.86 MeV and mean rms proton radius of 4.63 Fermi s, compared to experimental values of -7.8? MeV and (5-^3 ± 0.07) Fermis. These results are slightly better than the results for the smaller nuclei, indicating that some of the errors in the theory arise from inadequacies in the treatment of the nuclear surface. (h) In addition to the theoretical discussion of other nuclear matter approximations, this dissertation features quantitative analyses of the Moszkowski -Scott separation method and the Mohling and Puff approximations. In a computationally feasible form for hard core local potentials, the Puff and Mohling approximations are the same, and are shown to give mean energy and equilibrium spacing which are 10$ more negative and smaller respectively than more accurate K-matrix results. The Bethe reference spectrum method is briefly discussed, and a supplementary calculation presented. (5) Finally, an approximation is developed which is computationally simpler than previous approximations for hard core potentials. For the potential employed in the calculation of Brueckner and Gammel, the mean energy with the new approximation is -14.0 MeV at 1.04 Fermis, compared to their -15.2 MeV at 1.02 Fermis.