On the basis of a microscopic model of self-consistent field, the thermodynamics of the many-particle Fermi system at finite temperatures with account of three-body interactions is built and the quasiparticle equations of motion are obtained.It is shown that the delta-like three-body interaction gives no contribution into the selfconsistent field, and the description of three-body forces requires their nonlocality to be taken into account.The spatially uniform system is considered in detail, and on the basis of the developed microscopic approach general formulas are derived for the fermion's effective mass and the system's equation of state with account of contribution from three-body forces.The effective mass and pressure are numerically calculated for the potential of "semi-transparent sphere" type at zero temperature.Expansions of the effective mass and pressure in powers of density are obtained.It is shown that, with account of only pair forces, the interaction of repulsive character reduces the quasiparticle effective mass relative to the mass of a free particle, and the attractive interaction raises the effective mass.The question of thermodynamic stability of the Fermi system is considered and the three-body repulsive interaction is shown to extend the region of stability of the system with the interparticle pair attraction.The quasiparticle energy spectrum is calculated with account of three-body forces.
The dependence upon momentum
k and upon energy
E of the self-energy of a dilute Fermi gas is studied up to terms of order
(kFc)2, where
kF denotes the Fermi momentum and
c is the positive scattering length. Algebraic expressions are derived for the imaginary part
W(k;E) of the self-energy in the whole (
k,
E) plane. They are compared with a conjecture recently made by Orland and Schaeffer in their analysis of single-particle states in nuclei. The contributions of core polarization and of ground state correlations to the real part
V(k;E) of the self-energy are calculated with the help of subtracted dispersion relations which connect them with $W(k;{E}^{\ensuremath{'}})$. Algebraic expressions are derived for the momentum distribution in the correlated ground state. It is shown that the effective mass of a quasiparticle with momentum
k is equal to the bare particle mass at
k=0 and reaches a local maximum for
k close to
kF. This maximum is ascribed to the dependence of
V(k;E) upon
E, which is described in terms of an
E mass. We compute the contributions of core polarization and of ground state correlations to this
E mass. The dependence of
V(k;E) upon
k reflects the nonlocality of the self-energy. It is characterized by a
k mass that we also calculate. These results shed light on some nuclear matter properties and on the meaningfulness and limitation of nuclear matter calculations that have recently been performed in the framework of the Brueckner-Hartree-Fock approximation.NUCLEAR STRUCTURE Effective mass near the Fermi surface in dilute Fermi gas model.
We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction in the presence of bare mass anisotropy (i.e., with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading-order dynamical self-energy approximation. Our theory is exact in the high-density limit. We find anisotropic features of quasiparticle properties that are not captured by the commonly used isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are as follows: (1) The many-body renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the interaction-induced inelastic-scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective-mass enhancement is larger (smaller) for the light (heavy) mass, showing that the anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system and inaccurate estimates of physical quantities of interest although the use of an equivalent isotropic approximation using the density-of-states effective mass as is commonly and uncritically performed in the literature, works as a reasonable approximation in many situations. In addition to the complete random phase approximation theory for the anisotropic quasiparticles, we also provide a theory using the simpler plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi-surface topology, finding that the elliptic shape of the bare Fermi surface is preserved with suppressed ellipticity in the interacting system to a high degree of accuracy except in the very strongly interacting limit (and for very high bare mass anisotropy). Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.
For calculating low-energy properties of a dilute gas of atoms interacting via a Feshbach resonance, we develop an effective theory in which the parameters that enter are an atom-molecule coupling strength and the magnetic moment of the molecular resonance. We demonstrate that, for resonances in the fermionic systems 6Li and 40K that are under experimental investigation, the coupling is so strong that many-body effects are appreciable even when the resonance lies at an energy large compared with the Fermi energy. We calculate a number of many-body effects, including the effective mass and the lifetime of atomic quasiparticles in the gas.
We present a quantitative study of the quasiparticle properties of a three-dimensional electron Fermi liquid. Our approach is based on the theory of the many-body local field factors which we use to include vertex corrections associated with charge and spin fluctuations. Extensive use is made of the results of recent quantum Monte Carlo calculations. Several models for the wave-vector dependence of the spin-antisymmetric many-body local field factor ${G}_{\ensuremath{-}}$, for which no numerical results are currently available, are discussed and compared. Both the real and imaginary parts of the self-energy as well as the quasiparticle renormalization constant and the enhancement of the effective mass are calculated in the experimentally accessible range of electron densities. The results obtained by means of the on-shell approximation are critically compared with those given by a self-consistent solution of the Dyson equation. An ultraviolet catastrophe in the Coulomb-hole part of the self-energy is identified and a satisfactory resolution of this impasse is presented. The same many-body local field factors are also used to obtain the Landau interaction function. This allows us to obtain both the spin susceptibility and the proper compressibility of the system.
We discuss high-order calculations in perturbative effective field theory for fermions at low energy scales. The Fermi-momentum or
kFas expansion for the ground-state energy of the dilute Fermi gas is calculated to fourth order, both in cutoff regularization and in dimensional regularization. For the case of spin one-half fermions we find from a Bayesian analysis that the expansion is well converged at this order for $|{k}_{\mathrm{F}}{a}_{s}|\ensuremath{\lesssim}0.5$. Furthermore, we show that Pad\'e-Borel resummations can improve the convergence for $|{k}_{\mathrm{F}}{a}_{s}|\ensuremath{\lesssim}1$. Our results provide important constraints for nonperturbative calculations of ultracold atoms and dilute neutron matter.