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Physical Review C

Response function of nuclear matter

A. Dellafiore, F. Matera

Published Sep 1, 1988• 1 citation
Publisher

Abstract

We propose a new method to calculate the particle-hole Green's function for an infinite system of fermions in the long-wavelength limit of the random-phase approximation. Contrary to the standard approach the present method does not require approximating the residual particle-hole interaction by a sum of separable terms. The method can also be applied to the Landau theory of Fermi liquids. We illustrate the method by evaluating the response function of nuclear matter in the long-wavelength limit for two different isospin channels.

DOI
10.1103/physrevc.38.1494

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We propose a new method to calculate the particle-hole Green's function for an infinite system of fermions in the long-wavelength limit of the random-phase approximation. Contrary to the standard approach the present method does not require approximating the residual particle-hole interaction by a sum of separable terms. The method can also be applied to the Landau theory of Fermi liquids. We illustrate the method by evaluating the response function of nuclear matter in the long-wavelength limit for two different isospin channels.
We treat short-range correlations in nuclear matter, induced by the repulsive core of the nucleon-nucleon potential, within the framework of a self-consistent Green's function theory. The effective in-medium interaction sums the ladder diagrams of both the particle-particle and hole-hole type. The demand of self-consistency results in a set of nonlinear equations which must be solved by iteration. We explore the possibility of approximating the single-particle Green's function by a limited number of poles and residues.
We analyze the long-wavelength response of a normal Fermi liquid using Landau theory. We consider contributions from intermediate states containing one additional quasiparticle-quasihole pair as well as those from states containing two or more additional quasiparticle-quasihole pairs. For the response of an operator corresponding to a conserved quantity, we show that the behavior of matrix elements to states with more than one additional quasiparticle-quasihole pair at low excitation energies $\ensuremath{\omega}$ varies as $1/\ensuremath{\omega}$. It is shown how rates of processes involving transitions to two quasiparticle-quasihole states may be calculated in terms of the collision integral in the Landau transport equation for quasiparticles.
The set of equations for the two-particle Green's functions in a nonequilibrium medium is derived in the diffusive approximation. Both the two- and single-particle Green's functions are calculated when matter is in the ground state. It is shown that the Landau Fermi-liquid consideration is correct when the interaction between particles in matter is rather weak or when matter is not too dense. In the opposite cases the energy spectrum of the particles is rearranged so that the step in the momentum distribution of the particles disappears. The applicability of the Landau Fermi-liquid theory is established in the general case.
An expression for the response of the system, valid up to the second order in the general potential, has been derived by developing the Green function by an equation-of-motion method. In the long-wavelength limit, contact with other theories can be made in a transparent manner. The expression for the width contains contributions from direct and exchange processes, the latter contribution being exactly half of the former. The decay of zero sound into two-particle-two-hole pair excitations is found to vary as q 2 . The dispersion relation up to the second order in the potential is an upward parabola.
We review self-consistent spectral methods for nuclear matter calculations. The in-medium T −matrix approach is conserving and thermodynamically consistent. It gives both the global and the single-particle properties the system. The T −matrix approximation allows to address the pairing phenomenon in cold nuclear matter. A generalization of nuclear matter calculations to the superfluid phase is discussed and numerical results are presented for this case. The linear response of a correlated system going beyond the Hartree-Fock+ Random-Phase-Approximation (RPA) scheme is studied. The polarization is obtained by solving a consistent Bethe-Salpeter (BS) equation for the coupling of dressed nucleons to an external field. We find that multipair contributions are important for the spin(isospin) response when the interaction is spin(isospin) dependent. 1
We review self-consistent spectral methods for nuclear matter calculations. The in-medium T -matrix approach is conserving and thermodynamically consistent. It gives both the global and the single-particle properties the system. The T -matrix approximation allows to address the pairing phenomenon in cold nuclear matter. A generalization of nuclear matter calculations to the super.uid phase is discussed and numerical results are presented for this case. The linear response of a correlated system going beyond the Hartree-Fock+ Random-Phase-Approximation (RPA) scheme is studied. The polarization is obtained by solving a consistent Bethe-Salpeter (BS) equation for the coupling of dressed nucleons to an external field. We find that multipair contributions are important for the spin(isospin) response when the interaction is spin(isospin) dependent.