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Microscopic description of monopole isovector collective excitations in /sup 40/Ca

B.I. Barts, Yu. L. Bolotin, Vsevolod Yu. Gonchar, Н.А. Чеканов

Published Oct 1, 1981• 0 citations
OpenAlex

Abstract

The time-dependent Hartree-Fock method is used for description of collective excitations in nuclei. With this formulation of the effective interaction of the nucleons in the nucleus, both the single-particle basis and the particle-hole Green's function characterizing the collective properties of the nucleus are determined. The technique of construction of the particle-hole Green's function is discussed in detail.

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The time-dependent Hartree-Fock method is used for description of collective excitations in nuclei. With this formulation of the effective interaction of the nucleons in the nucleus, both the single-particle basis and the particle-hole Green's function characterizing the collective properties of the nucleus are determined. The technique of construction of the particle-hole Green's function is discussed in detail.
General treatment of nuclear many-body problem will be given in terms of Green functions and the correlation property of nucleus will be exhibited by correlation factor. Effective interaction certifying the independent particle motion is introduced and proved to identify with Brueckner's K-matrix. And on the basis of this point, applying the method of the particle-hole pair to the system, a collective mode will be derived and the effective interaction contributing to collective motion will be studied. It will also be shown that this effective interaction has the property very different from electron plasma case.
The nuclear collective response at finite temperature is investigated for the first time in the quantum framework of the small amplitude limit of the extended time-dependent Hartree-Fock approach, including a non-Markovian collision term. It is shown that the collision width satisfies a secular equation. By employing a Skyrme force, the isoscalar monopole, isovector dipole, and isoscalar quadrupole excitations in 40Ca{}^{40}\mathrm{Ca}40Ca are calculated and important quantum features are pointed out. The collisional damping due to decay into incoherent two-particle--two-hole states is small at low temperatures but increases rapidly at higher temperatures.
We present an elementary and fairly detailed review of several Green’s function methods for treating nuclear and other many-body systems. We first treat the single-particle Green’s function, by way of which some details concerning linked diagram expansion, rules for evaluating Green’s function diagrams and solution of the Dyson’s integral equation for Green’s function are exhibited. The particle-particle hole-hole (pphh) Green’s function is then considered, and a specific time-blocking technique is discussed. This technique enables us to have a one-frequency Dyson’s equation for the pphh and similarly for other Green’s functions, thus considerably facilitating their calculation. A third type of Green’s function considered is the particle-hole Green’s function. RPA and high order RPA are treated, along with examples for setting up particle-hole RPA equations. A general method for deriving a model-space Dyson’s equation for Green’s functions is discussed. We also discuss a method for determining the normalization of Green’s function transition amplitudes based on its vertex function. Some applications of Green’s function methods to nuclear structure and recent deep inelastic lepton-nucleus scattering are addressed.
An equation set describtng single particle excitations for excitation energies which are small compared with the chemical potential of the system can be obtained by investigating the analytical properties of the Green's functions and taking into account pair correlation. The equations are valid for an arbitrary interaction law. Equations are derived which describe the excited states of a system with a finite number of particles with an accuracy to terms of the order of N/sup -//sup 1//sup ///sup 3/ It is indicated how the results can be applied to real nuclei. (auth)
We develop a time-dependent Hartree-Fock approximation that is appropriate for Bose-condensed systems. Defining a depletion Green's function allows the construction of condensate and depletion particle densities from eigenstates of a single time-dependent (oscillating) Hamiltonian, guaranteeing that our approach is a number-conserving approximation. The poles of this Green's function yield the energies of number-changing excitations for which the condensate particle number is held fixed, which we show has a gapped spectrum in the superfluid state. The linearized time-dependent version of this has poles at the collective frequencies of the system, yielding the expected zero sound mode for a uniform infinite system. We show how the approximations may be expressed in a general linear response formalism.
The problem of the microscopic description of excited states of the even-even open-shell atomic nuclei is considered. A model is formulated which allows one to go beyond the quasiparticle random phase approximation. The physical content of the model is determined by the quasiparticle time blocking approximation (QTBA) which enables one to include contributions of the two-quasiparticle and the two-phonon configurations, while excluding (blocking) more complicated intermediate states. In addition, the QTBA ensures consistent treatment of ground state correlations in the Fermi systems with pairing. The model is based on the generalized Green function formalism (GGFF) in which the normal and the anomalous Green functions are treated in a unified way in terms of the components of generalized Green functions in a space that is double the size of the usual single-particle space. Modification of the GGFF is considered in the case when the many-body nuclear Hamiltonian contains two-, three-, and other many-particle effective forces.