Occupation numbers in Self Consistent RPA

A method is proposed which allows to calculate within the SCRPA theory the occupation numbers via the single particle Green function. This scheme complies with the Hugenholtz van Hove theorem. In an application to the Lipkin model it is found that this prescription gives consistently better results than two other commonly used approximations: lowest order boson expansion and the number operator method.Comment: 25 pages, 10 figures, submitted to Nucl. Phys.

The Linear Sigma-Model in the 1/N-Expansion via Dynamical Boson Mappings and Applications to ππ\pi\pi-Scattering

We present a non-perturbative method for the study of the O(N+1)-version of the linear sigma-model. Using boson-mapping techniques, in close analogy to those well-known for fermionic systems, we obtain a systematic 1/N-expansion for the Hamiltonian which is symmetry-conserving order by order. The leading order for the Hamiltonian is evaluated explicitly and we apply the method to $\pi\pi$-scattering, in deriving the T-matrix to leading order.Comment: 28 pages, Latex, (with minor corrections to some misprints in the appendix of the old version

Two-particle spatial correlations in superfluid nuclei

We discuss the effect of pairing on two-neutron space correlations in deformed nuclei. The spatial correlations are described by the pairing tensor in coordinate space calculated in the HFB approach. The calculations are done using the D1S Gogny force. We show that the pairing tensor has a rather small extension in the relative coordinate, a feature observed earlier in spherical nuclei. It is pointed out that in deformed nuclei the coherence length corresponding to the pairing tensor has a pattern similar to what we have found previously in spherical nuclei, i.e., it is maximal in the interior of the nucleus and then it is decreasing rather fast in the surface region where it reaches a minimal value of about 2 fm. This minimal value of the coherence length in the surface is essentially determined by the finite size properties of single-particle states in the vicinity of the chemical potential and has little to do with enhanced pairing correlations in the nuclear surface. It is shown that in nuclei the coherence length is not a good indicator of the intensity of pairing correlations. This feature is contrasted with the situation in infinite matter.Comment: 14 pages, 17 figures, submitted to PR

Fermion Condensation and Non Fermi Liquid Behavior in a Model with Long Range Forces

The phenomenon of the so called Fermion condensation, a phase transition analogous to Bose condensation but for Fermions, postulated in the past to occur in systems with strong momentum dependent forces, is reanalysed in a model with infinite range interactions. The strongly non Fermi Liquid behavior of this system is demonstrated analytically at $T=0$ and at $T\neq 0$ in the superconducting and normal phases. The validity of the quasiparticle picture is investigated and seems to hold true for temperatures less than the characteristic temperature $T_f$ of the Fermion condensation.Comment: 22 LaTeX pages, 6 figures can be obtained from [email protected]

Generalized Second-Order Thomas-Fermi Method for Superfluid Fermi Systems

Using the $\hbar$-expansion of the Green's function of the Hartree-Fock-Bogoliubov equation, we extend the second-order Thomas-Fermi approximation to generalized superfluid Fermi systems by including the density-dependent effective mass and the spin-orbit potential. We first implement and examine the full correction terms over different energy intervals of the quasiparticle spectra in calculations of finite nuclei. Final applications of this generalized Thomas-Fermi method are intended for various inhomogeneous superfluid Fermi systems.Comment: 8 pages, 10 figures, PR

Nuclear Pairing in the T=0 channel revisited

Recent published data on the isoscalar gap in symmetric nuclear matter using the Paris force and the corresponding BHF single particle dispersion are corrected leading to an extremely high proton-neutron gap of $\Delta \sim 8$ MeV at $\rho \sim 0.5\rho_0$. Arguments whether this value can be reduced due to screening effects are discussed. A density dependent delta interaction with cut off is adjusted so as to approximately reproduce the nuclear matter values with the Paris force.Comment: 4 pages, 4 figure

Fission from saddle to exit : influence of curvature and compression energies

We investigate the influence of terms beyond the standard Liquid Drop Model on the slope of the fission valley. An important reduction of the slope is obtained when using values of the curvature energy calculated from effective forces currently in use, thus corroborating a recent microscopic calculation by Berger et al

Boson-Fermion pairing in a Boson-Fermion environment

Propagation of a Boson-Fermion (B-F) pair in a B-F environment is considered. The possibility of formation of stable strongly correlated B-F pairs, embedded in the continuum, is pointed out. The new Fermi gas of correlated B-F pairs shows a strongly modified Fermi surface. The interaction between like particles is neglected in this exploratory study. Various physical situations where our new pairing mechanism could be of importance are invoked.Comment: 8 pages, 8 figers, to be published in Phys. Rev.

Dynamics of a trapped Fermi gas in the BCS phase

We derive semiclassical transport equations for a trapped atomic Fermi gas in the BCS phase at temperatures between zero and the superfluid transition temperature. These equations interpolate between the two well-known limiting cases of superfluid hydrodynamics at zero temperature and the Vlasov equation at the critical one. The linearized version of these equations, valid for small deviations from equilibrium, is worked out and applied to two simple examples where analytical solutions can be found: a sound wave in a uniform medium and the quadrupole excitation in a spherical harmonic trap. In spite of some simplifying approximations, the main qualitative results of quantum mechanical calculations are reproduced, which are the different frequencies of the quadrupole mode at zero and the critical temperature and strong Landau damping at intermediate temperatures. In addition we suggest a numerical method for solving the semiclassical equations without further approximations.Comment: 15 pages, 4 figures; v2: discussion and references adde