The formalism based on Correlated Basis Functions (CBF) and the cluster-expansion technique has been recently employed to derive an effective interaction from a realistic nuclear Hamiltonian. One of the main objectives of the work described in this Thesis is establishing the accuracy of this novel approach--that allows to combine the flexibility of perturbation theory in the basis of eigenstates of the noninteracting system with a realistic description of short-range correlations in coordinate space--by focusing on the hard-sphere fermion system. As a first application of the formalism, the quasiparticle properties of hard spheres of degeneracy four have been determined from the two-point Green's function. The calculation has been performed carrying out a perturbative expansion of the self-energy, up to the second order in the CBF effective interaction. The main results of this study are the momentum distributions, the quasiparticle spectra and their description in terms of effective mass. The investigation of the hard-sphere fermion fluid has been extended to study the shear viscosity and thermal conductivity coefficients of the system with degeneracy two, that can be regarded as a model of pure neutron matter. The resulting transport coefficients show a strong sensitivity to the quasiparticle effective mass, reflecting the effect of second order contributions to the self-energy which are not taken into account in nuclear matter studies available in the literature. The difference between first and second order results is likely to play an important role in astrophysical applications and needs to be carefully investigated extending our analysis to nuclear matter.The formalism based on Correlated Basis Functions (CBF) and the cluster-expansion technique has been recently employed to derive an effective interaction from a realistic nuclear Hamiltonian. One of the main objectives of the work described in this Thesis is establishing the accuracy of this novel approach--that allows to combine the flexibility of perturbation theory in the basis of eigenstates of the noninteracting system with a realistic description of short-range correlations in coordinate space--by focusing on the hard-sphere fermion system. As a first application of the formalism, the quasiparticle properties of hard spheres of degeneracy four have been determined from the two-point Green's function. The calculation has been performed carrying out a perturbative expansion of the self-energy, up to the second order in the CBF effective interaction. The main results of this study are the momentum distributions, the quasiparticle spectra and their description in terms of effective mass. The investigation of the hard-sphere fermion fluid has been extended to study the shear viscosity and thermal conductivity coefficients of the system with degeneracy two, that can be regarded as a model of pure neutron matter. The resulting transport coefficients show a strong sensitivity to the quasiparticle effective mass, reflecting the effect of second order contributions to the self-energy which are not taken into account in nuclear matter studies available in the literature. The difference between first and second order results is likely to play an important role in astrophysical applications and needs to be carefully investigated extending our analysis to nuclear matter.

arXiv:1603.02077Mar 7, 20160 citations

Quasiparticle Interactions in Many-Body Systems

J. Ruvalds

Springer eBooksJan 1, 19760 citations

Retarded Interactions in Fermi Systems. II. Quasiparticle Lifetimes

C. B. Dover, Richard H. Lemmer

Properties of the inverse lifetime $\frac{1}{\ensuremath{\tau}}$ of quasiparticles in an infinite system of nucleons ("nuclear matter") interacting via the exchange of a neutral scalar boson are studied in the dielectric formulation of the many-body problem. It is shown that the polarization of the nuclear medium plays an essential role in determining $\frac{1}{\ensuremath{\tau}}$. The presence of the medium mediates the interaction between two nucleons in it through the introduction of an effective "dielectric constant" for nuclear matter. The interaction becomes "dressed" in a fashion analogous to, but different in its details from, the screening of the Coulomb interaction between electrons in metals. Calculations of $\frac{1}{\ensuremath{\tau}}$ are made for nuclear matter both in second-order perturbation theory, and using the fully dressed interaction calculated in the random-phase approximation (RPA). The RPA estimate is lower by about a factor of 3 over a wide range of momenta and is in good agreement with empirical optical-model estimates of $\frac{1}{\ensuremath{\tau}}$. The second-order perturbation estimate is by contrast entirely inadequate, emphasizing the importance of taking the polarization effects into account for scattering processes at actual nuclear densities. The use of a dielectric constant for the medium also introduces another feature into the properties of $\frac{1}{\ensuremath{\tau}}$. The behavior of $\frac{1}{\ensuremath{\tau}}$ near the Fermi surface now becomes sensitive to whether or not the interacting ground state is unstable with respect to a permanent density fluctuation. If it is, then $\frac{1}{\ensuremath{\tau}}$ behaves like ($p\ensuremath{-}{p}_{F}$) instead of ${(p\ensuremath{-}{p}_{F})}^{2}$ near the Fermi surface ( ${p}_{F}$ is the Fermi momentum). This is not a new physical result, but rather a reflection of the inadequacy of the RPA if the system becomes unstable. It is shown that as the momentum increases the effect of such an instability, if present, decreases, and becomes entirely negligible when $p\ensuremath{\gtrsim}\sqrt{2}{p}_{F}$.Properties of the inverse lifetime $\frac{1}{\ensuremath{\tau}}$ of quasiparticles in an infinite system of nucleons ("nuclear matter") interacting via the exchange of a neutral scalar boson are studied in the dielectric formulation of the many-body problem. It is shown that the polarization of the nuclear medium plays an essential role in determining $\frac{1}{\ensuremath{\tau}}$. The presence of the medium mediates the interaction between two nucleons in it through the introduction of an effective "dielectric constant" for nuclear matter. The interaction becomes "dressed" in a fashion analogous to, but different in its details from, the screening of the Coulomb interaction between electrons in metals. Calculations of $\frac{1}{\ensuremath{\tau}}$ are made for nuclear matter both in second-order perturbation theory, and using the fully dressed interaction calculated in the random-phase approximation (RPA). The RPA estimate is lower by about a factor of 3 over a wide range of momenta and is in good agreement with empirical optical-model estimates of $\frac{1}{\ensuremath{\tau}}$. The second-order perturbation estimate is by contrast entirely inadequate, emphasizing the importance of taking the polarization effects into account for scattering processes at actual nuclear densities. The use of a dielectric constant for the medium also introduces another feature into the properties of $\frac{1}{\ensuremath{\tau}}$. The behavior of $\frac{1}{\ensuremath{\tau}}$ near the Fermi surface now becomes sensitive to whether or not the interacting ground state is unstable with respect to a permanent density fluctuation. If it is, then $\frac{1}{\ensuremath{\tau}}$ behaves like ($p\ensuremath{-}{p}_{F}$) instead of ${(p\ensuremath{-}{p}_{F})}^{2}$ near the Fermi surface (${p}_{F}$ is the Fermi momentum). This is not a new physical result, but rather a reflection of the inadequacy of the RPA if the system becomes unstable. It is shown that as the momentum increases the effect of such an instability, if present, decreases, and becomes entirely negligible when $p\ensuremath{\gtrsim}\sqrt{2}{p}_{F}$.

Physical ReviewJul 20, 196914 citations

{p}_{F}

is the Fermi momentum). This is not a new physical result, but rather a reflection of the inadequacy of the RPA if the system becomes unstable. It is shown that as the momentum increases the effect of such an instability, if present, decreases, and becomes entirely negligible when $p\ensuremath{\gtrsim}\sqrt{2}{p}_{F}$.