Static properties of nuclear matter within the Boson Loop Expansion

The use of the Boson Loop Expansion is proposed for investigating the static properties of nuclear matter. We explicitly consider a schematic dynamical model in which nucleons interact with the scalar-isoscalar sigma meson. The suggested approximation scheme is examined in detail at the mean field level and at the one- and two-loop orders. The relevant formulas are provided to derive the binding energy per nucleon, the pressure and the compressibility of nuclear matter. Numerical results of the binding energy at the one-loop order are presented for Walecka's sigma-omega model in order to discuss the degree of convergence of the Boson Loop Expansion.Comment: 40 pages, 13 figure

Collective Modes in a Slab of Interacting Nuclear Matter: The effects of finite range interactions

We consider a slab of nuclear matter and investigate the collective excitations, which develop in the response function of the system. We introduce a finite-range realistic interaction among the nucleons, which reproduces the full G-matrix by a linear combination of gaussian potentials in the various spin-isospin channels. We then analyze the collective modes of the slab in the S=T=1 channel: for moderate momenta hard and soft zero-sound modes are found, which exhaust most of the excitation strength. At variance with the results obtained with a zero range force, new "massive" excitations are found for the vector-isovector channel .Comment: 14 pages, TeX, 5 figures (separate uuencoded and tar-compressed postscript files), Torino preprint DFTT 6/9

The longitudinal and transverse responses in the inclusive electron scattering: a functional approach

The splitting between the charge-longitudinal and spin-transverse responses is explained in a model whose inputs are the effective interactions in the particle-hole channels in the frame of the first order boson loop expansion. It is shown that the interplay between $\omega$-meson exchange and box diagrams (two-meson exchange with simultaneous excitation of one or two nucleons to $\Delta$'s) mainly rules the longitudinal response, while in the transverse one the direct $\Delta$ excitations almost cancel the one-loop correction and the response is mainly governed by the $\rho$-meson rescattering inside the nucleus. It is also shown that a small variation in the nuclear densities may explain the observed discrepancies between different nuclei.Comment: LaTex2e file with 53 .ps figures; submitted to Nucl. Phys

Functional approach to the non-mesonic decay of Lambda-hypernuclei

We present an evaluation of the non-mesonic decay widths for Lambda-hypernuclei (Lambda N --> NN, Lambda NN --> NNN) within the framework of the polarization propagator method. The full Lambda self-energy is evaluated microscopically in nuclear matter by using the functional approach, which supplies a theoretically well grounded approximation scheme for the classification of the relevant diagrams, according to the prescriptions of the bosonic loop expansion. We employ average Fermi momenta, suitably adapted to different mass number regions (medium-light, medium and heavy hypernuclei). Moreover, we study the dependence of the decay rates on the NN and Lambda-N short range correlations. With a proper choice of the parameters which control these correlations in the new approximation scheme, it is possible to reproduce the experimental decay widths for A > 10 hypernuclei.Comment: 25 pages, 8 figure

On the Relativistic Description of the Nucleus

We present here a formalism able to generalise to a relativistically covariant scheme the standard nuclear shell model. We show that, using some generalised nuclear Green's functions and their Lehmann representation we can define the relativistic equivalent of the non relativistic single particle wave function (not loosing, however, the physical contribution of other degrees of freedom, like mesons and antinucleons). It is shown that the mass operator associated to the nuclear Green's function can be approximated with the equivalent of a shell-model potential and that the corresponding ``single particle wave functions'' can be easily derived in a specified frame of reference and then boosted to any other system, thus fully restoring the Lorentz covarianc

A statistical theory of the mean field

A statistical theory of the mean field is developed. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction, obtained after the average interaction is removed, are random with the average value of zero. With these two assumptions one obtains explicit expressions for the mean field and the fluctuation away from the average. The fluctuation is expanded in terms of more and more complex excitations. Using the randomness of the matrix elements one can then obtain formulas for the contribution to the error from each class of complex excitations and a general condition for the convergence of the expansion is derived. It is to be emphasized that no conditions on the nature of the system being studied are made. Making some simplifying assumptions a schematic model is developed. This model is applied to the problem of nuclear matter. The model yields a measure of the strength of the effective interaction. It turns out to be three orders of magnitude less than that calculated using a potential which gives a binding energy of about -7 MeV/nucleon demonstrating the strong damping of the interaction strength induced by the averaging process.Comment: 25 pages, REVTeX, 4 eps figure

Quasielastic Electron Scattering from Nuclei: Random-Phase vs. Ring Approximations

We investigate the extent to which the nuclear transverse response to electron scattering in the quasielastic region, evaluated in the random-phase approximation can be described by ring approximation calculations. Different effective interactions based on a standard model of the type g'+V_pi+V_rho are employed. For each momentum transfer, we have obtained the value of g'_0 permitting the ring response to match the position of the peak and/or the non-energy weighted sum rule provided by the random-phase approach has been obtained. It is found that, in general, it is not possible to reproduce both magnitudes simultaneously for a given g'_0 value.Comment: 7 pages, 4 Postscript figures, to appear in Physical Review

Variational Methods for Nuclear Systems with Dynamical Mesons

We derive a model Hamiltonian whose ground state expectation value of any two-body operator coincides with that obtained with the Jastrow correlated wave function of the many-body Fermi system. Using this Hamiltonian we show that the variational principle can be extended to treat systems with dynamical mesons, even if in this case the concept of wave function looses its meaning