Progress of Theoretical Physics Supplement

Rocky Paths, Dead Ends and Smooth Paths towards a Theory of Nuclear Collective Motion

Felix M. H. Villars

Published Jan 1, 1983• 2 citations

Abstract

This report contains two main parts.The first part summarizes the well known construction based on TDHF of a collective Hamiltonian .!J((p, q) from an A-particle Hamiltonian fl.This construction is stated as a prescription, that may also be applied to any one particle operator 'Y, and its time derivative [iH, 'Y].The operators Q} (p, q) and ciJ (p, q) so obtained are required to obey ci}(p, q)=[i.!J((p, q), Q}(p, q)].It is shown that this consistency condition on collective dynamics can indeed be enforced, and leads to the same conditions as the TDHF-variational principle.The second part presents an alternative to TDHF, which is quantum mechanical.from the outset.Eigenfunctions of the collective "position" operator Q are constructed by projection.In the adiabatic limit, the results obtained by variationally optimizing the trial function for the system are in substantial agreement with quantized TDHF.Zero-point energy corrections are automatically included.

DOI: 10.1143/ptps.74.184

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