A Unified Theory of Nuclear Reactions, II

Publisher Summary: This chapter discusses two major developments that have taken place over the past decade. First is the enormous wealth of energy band calculations that have had tremendous success in explaining the properties of specific solids, but in which the connection with first principles is not always apparent. Second is the spectacular progress of many-body theory applied to the solid state that has given a number of new results, although often of a rather general and formal nature, such as to provide the justification and a formal basis for a one-electron theory. The electron gas problem is treated in some detail here. The problem of the crystal potential is given due attention. It discusses the potential from the ion cores as well as from the valence electrons, and suggests schemes that incorporate essential exchange and correlation effects for the valence electrons. An energy band calculation that properly includes the effects of exchange and correlation describes the elementary excitations called quasi particles. Quasi-particle properties are usually discussed using the remarkable Landau theory of the Fermi liquid. This chapter gives a brief presentation of the theory and reviews the present status of calculations of the Fermi liquid parameters and how they are determined from experiments. (Less)

Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids

Many Body Theory of Nuclear Matter

The spectral properties of Hamilton operators perturbed by a complex absorbing potential (CAP) are studied. For a wide class of CAPS proper eigenvalues of the perturbed Hamilton operator converge to Siegert resonance eigenvalues of the unperturbed Hamiltonian with decreasing CAP strength. The errors in the calculation of complex resonance energies caused by the additional CAP and by finite basis set representation are examined. In order to minimize these errors a scheme of approximations is provided. The application of this method allows for the use of real L2 basis sets. The feasibility and accuracy of the proposed method is demonstrated by calculations of resonance energies of a model potential and of the 2 Pi g shape resonance of N2.

https://iopscience.iop.org/article/10.1088/0953-4075/26/23/021/pdf

Calculation of resonance energies and widths using the complex absorbing potential method

Causality and the threshold anomaly of the nucleus-nucleus potential

A construction is given of an equivalent one-body pocomplex target. The case of incident and target particles being identical nonrelativistic fermions, and allowing fully for antisymmetry, is considered explicitly. (A.C.)

J. S. Bell

Papers

A formal optical model