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Theories for multiple resonances

Dietrich Klakow, M. Weber, P.‐G. Reinhard

Published Jan 1, 1995• 4 citations
OpenAlex

Abstract

Two microscopic theories for multiple resonances in nuclei are compared, n-particle-hole RPA and quantized Time-Dependent Hartree-Fock (TDHF). The Lipkin-Meshkov-Glick model is used as test case. We find that quantized TDHF is superior in many respects, except for very small systems. 1

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Physical Review C•Jun 1, 1978•10 citations
The time-dependent Hartree-Fock solutions of the two-level Lipkin-Meshkov-Glick model are studied by transforming the time-dependent Hartree-Fock equations into Hamilton's canonical form and analyzing the qualitative structure of the Hartree-Fock energy surface in the phase space. It is shown that as the interaction strength increases these time-dependent Hartree-Fock solutions undergo a qualitative change associated with the ground state phase transition previously studied in terms of coherent states. For twobody interactions stronger than the critical value, two types of time-dependent Hartree-Fock solutions (the "librations" and "rotations" in Hamilton's mechanics) exist simultaneously, while for weaker interactions only the rotations persist. It is also shown that the coherent states with the maximum total pseudospin value are determinants, so that time-dependent Hartree-Fock analysis is equivalent to the coherent state method.NUCLEAR STRUCTURE Lipkin-Meshkov-Glick model, TDHF, transformation of TDHF equations to Hamilton's canonical form, coherent states, ground state phase transition.
According to a theory of H. Spohn, the time-dependent Hartree (TDH) equation governs the 1-particle state in N -particle systems whose dynamics are prescribed by a non-relativistic Schrödinger equation with 2-particle interactions, in the limit N tends to infinity while the strength of the 2-particle interaction potential is scaled by 1/N .In previous work we have considered the same mean field scaling for systems of fermions, and established that the error of the time-dependent Hartree-Fock (TDHF) approximation tends to 0 as N tends to infinity.In this article we extend our results to systems of fermions with m-particle interactions (m > 2).