Collective Vector method in nuclear and atomic physics.

摘要

We present a brief review of the method of the Collective Vector (CV) and its use in conjunction with the Lanczos algorithm (LA). The combination of these two ideas produces a method for contracting super-large hamiltonians (up to 10(sup 6) (times) 10(sup 6)) by factors of 1000 or more. The contracted hamiltonians, which we call quasi-hamiltonians, typically have dimensions of the order of 10(sup 2) (times) 10(sup 2) and produce corresponding quasi-spectra with associated quasi-eigenfunctions which reproduce the features of the full microscopic spectrum thru the conservation of the spectral moments. Examples of applications to both nuclear and atomic physics are given demonstrating the convergence properties of the method. The application of the LA/CV approach to the problem of modelling nuclear level densities is described and finally we discuss the possibility of conjoining new collective models of nuclear structure with the LA/CV method. 13 refs., 4 figs.