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An effective interaction for nuclear Hartree-Fock calculations
ANNALS
OF PHYSICS:
Abstracts
28,
346348
(1964)
of Papers
to Appear
in Future
Issues
Theory of Transport Phenomena in an Electron-Phonon Gas. T. HOLSTEIN, Department of Physics, University of Pittsburgh, Pittsburgh 13, Pennsylvania. In this paper a quanta1 transport theory is developed for a model electron-phonon-gas, as described by the Frohlich Hamiltonian. The treatment is focussed specifically on the determination of the electrical conductivity, u(n, o), in the presence of an external field of arbitrary wave vector, 9, and frequency, W. The starting point is a generalized Kubo relationship between u(q, w) and an appropriately defined velocity-correlation function. The perturbation expansion of this function in powers of the electron-phonon interaction is analyzed with the aid of the so-called “temperature” diagram technique. The problem of computing the correlation function [and hence u(n, w)] is shown to be equivalent to that of solving two coupled linear integra1 equations. In the limit of zero external frequency (W = 0) these equations reduce to the standard linearized coupled Boltzmann equations for an electron-phonon gas. In the limit of high frequencies (ho > Debye energy) the explicit solution for u(n, w) coincides with the quanta1 version of the Drude-Lorentz formula (which had been obtained earlier by standard time-dependent perturbation theory). Estimates of various higher-order corrections indicate that the theory is valid to lowest order in the parameter h/rEF - c,/v~ (where E F = Fermi energy, UF = Fermi velocity, cs = velocity of sound, and 7 is the lifetime of an electron whose energy exceeds the Fermi energy by an amount of the order of the Debye energy). An Effective Interactionfor Nuclear Hartree-Fock Calculations. FRANK TABAKIN, Department of Physics, Columbia University, New York, New York. An effective potential is presented which matches S, P, and D-wave nucleon-nucleon phase parameters up to 320 MeV without generating the usual strong, short-range correlations. A suitably defined set of separable potentials, including a noncentral force and having small off-energy-shell matrix elements, is employed to produce smooth two-body wave functions. As a preliminary theoretical test of this effective interaction and of the applicability of perturbation theory, the average energy per particle, the single particle potential, and the symmetry energy of infinite nuclear matter have been computed. A saturation of nuclear matter is found in first order at a Fermi momentum of kF = 1.6f-1 with an average energy per particle of -8 MeV; second-order contributions move the minimum to kp = 1.8f-1 with an average energy per particle of -14.1 MeV. This saturation is characterized by significant P-wave contributions. A convergence of perturbation theory is indicated by a ratio of second to first order potential energy of
OF PHYSICS:
Abstracts
28,
346348
(1964)
of Papers
to Appear
in Future
Issues
Theory of Transport Phenomena in an Electron-Phonon Gas. T. HOLSTEIN, Department of Physics, University of Pittsburgh, Pittsburgh 13, Pennsylvania. In this paper a quanta1 transport theory is developed for a model electron-phonon-gas, as described by the Frohlich Hamiltonian. The treatment is focussed specifically on the determination of the electrical conductivity, u(n, o), in the presence of an external field of arbitrary wave vector, 9, and frequency, W. The starting point is a generalized Kubo relationship between u(q, w) and an appropriately defined velocity-correlation function. The perturbation expansion of this function in powers of the electron-phonon interaction is analyzed with the aid of the so-called “temperature” diagram technique. The problem of computing the correlation function [and hence u(n, w)] is shown to be equivalent to that of solving two coupled linear integra1 equations. In the limit of zero external frequency (W = 0) these equations reduce to the standard linearized coupled Boltzmann equations for an electron-phonon gas. In the limit of high frequencies (ho > Debye energy) the explicit solution for u(n, w) coincides with the quanta1 version of the Drude-Lorentz formula (which had been obtained earlier by standard time-dependent perturbation theory). Estimates of various higher-order corrections indicate that the theory is valid to lowest order in the parameter h/rEF - c,/v~ (where E F = Fermi energy, UF = Fermi velocity, cs = velocity of sound, and 7 is the lifetime of an electron whose energy exceeds the Fermi energy by an amount of the order of the Debye energy). An Effective Interactionfor Nuclear Hartree-Fock Calculations. FRANK TABAKIN, Department of Physics, Columbia University, New York, New York. An effective potential is presented which matches S, P, and D-wave nucleon-nucleon phase parameters up to 320 MeV without generating the usual strong, short-range correlations. A suitably defined set of separable potentials, including a noncentral force and having small off-energy-shell matrix elements, is employed to produce smooth two-body wave functions. As a preliminary theoretical test of this effective interaction and of the applicability of perturbation theory, the average energy per particle, the single particle potential, and the symmetry energy of infinite nuclear matter have been computed. A saturation of nuclear matter is found in first order at a Fermi momentum of kF = 1.6f-1 with an average energy per particle of -8 MeV; second-order contributions move the minimum to kp = 1.8f-1 with an average energy per particle of -14.1 MeV. This saturation is characterized by significant P-wave contributions. A convergence of perturbation theory is indicated by a ratio of second to first order potential energy of