Functional integral formulation of Brueckner-Hartree-Fock theory

Constance J. Nelin, F. A. Matsen

D. S. Tang, F.A. Matsen

ROBERT K. NESBET

The method of superposition of configurations, which provides a general solution of the quantum-mechanical many-particle problem (for fermions), is reformulated so that equations may be compared with those used in the Brueckner theory. Important differences occur in application to finite or nonuniform systems for which the Hartree-Fock or Brueckner self-consistent orbitals are not plane waves. In such cases nonvanishing single-particle matrix elements occur which cannot be described by the Brueckner formalism based on a two-particle operator. Equations for an effective two-particle operator, equivalent to the variational equations of the method of superposition of configurations, are derived for a basis of Hartree-Fock orbitals. At the expense of making the orbital basis dependent upon the effective two-particle operator, the orbital basis can be determined by a condition which is essentially that of the Brueckner method. This condition removes a class of matrix elements which do not necessarily vanish in the Hartree-Fock basis although they would be neglected to second order in a perturbation calculation starting from the Hartree-Fock wave function. The equations for the effective two-particle operator are formally the same in both cases but lead to different operators because of the different choice of basis. In neither case can the equations be written in terms of products of such operators, a formalism assumed in the Brueckner theory. It is shown that the Brueckner condition is not equivalent to the condition which would determine the best possible orbital basis for the form of wave function implied by the use of an effective operator dependent on two particles only. The argument of the present paper is limited to systems with a finite number of particles, since the variational principle used here is not applicable without modification to systems with an infinite number of particles.

Stella M. Peltier, A. Piastino

P. Poschenrieder, M. K. Weigel

In this paper we present the theory of nuclear matter in the framework of relativistic nuclear field theory utilizing the technique of relativistic many-body Green's functions. The analytic properties of the Green's functions and related quantities are given and used to obtain the final set of equations for the nuclear matter problem. In detail, we have investigated theoretically and numerically the so-called ${\ensuremath{\Lambda}}^{00}$ and ${\ensuremath{\Lambda}}^{10}$ approximations. For comparison we also calculated the relativistic Hartree-Fock and the Brueckner-Hartree-Fock approximation, respectively. For masses and coupling strengths we used (phenomenological) parameter sets given by the Bonn and Groningen group. The results of the \ensuremath{\Lambda} approximations are similar to the relativistic Brueckner treatment.

DAVID J. ROWE