Relativistic Effects in Electroweak Nuclear Responses

The electroweak response functions for inclusive electron scattering are calculated in the Relativistic Fermi Gas model, both in the quasi-elastic and in the $\Delta$ peak regions. The impact of relativistic kinematics at high momentum transfer is investigated through an expansion in the initial nucleonic momentum, which is however exact in the four-momentum of the exchanged boson. The same expansion is applied to the meson exchange currents in the particle-hole sector: it is shown that the non-relativistic currents can be corrected by simple kinematical factors to account for relativity. The left-right asymmetry measured via polarized electron scattering is finally evaluated in the quasi-elastic and $\Delta$ peaks.Comment: 9 pages, 3 figures, to appear in "Proceedings of the VIII Convegno su Problemi di Fisica Nucleare Teorica, 18-20 October 2000", World Scientifi

Gauge and Lorentz invariant pionic correlations in quasi-elastic electron scattering

The role of the pion in the parity-conserving and parity-violating quasi-elastic nuclear response functions is analyzed within a relativistic model which fulfills gauge invariance.Comment: 14 pages, 4 figures, Proceedings of the Varenna School "From Nuclei and Thier Constituents to Stars", August 200

Relativistic effects in quasielastic electron scattering

The impact of pionic correlations and meson-exchange currents on the quasi-elastic electromagnetic response functions is studied in a fully relativistic framework.Comment: 6 pages, 5 figures, to appear in the Proceedings of "The Nuclear Many Body Problem 2001", NATO Science Series II - Mathematics, Physics and Chemistry, Kluwer Academic Publisher

The pairing Hamiltonian for one pair of identical nucleons bound in a potential well

The problem of one pair of identical nucleons sitting in ${\cal N}$ single particle levels of a potential well and interacting through the pairing force is treated introducing even Grassmann variables. The eigenvectors are analytically expressed solely in terms of these with coefficients fixed by the eigenvalues and the single particle energies. When the latter are those of an harmonic oscillator well an accurate expression is derived for both the collective eigenvalue and for those trapped in between the single particle levels, for any strength of the pairing interaction and for any number of levels. Notably the trapped solutions are labelled through an index upon which they depend parabolically.Comment: 5 pages, 1 postscript figur

The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single particle levels of a potential well (mean field) and interacting through a pairing force. The associated solutions of the Richardson's equations are classified in terms of a number $v_l$, which reduces to the seniority $v$ in the limit of large values of the pairing strength $G$ and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the $G\to\infty$ limit. We express analytically, through the moments of the single particle levels distribution, the collective mode energy and the two critical values $G_{\rm cr}^{+}$ and $G_{\rm cr}^{-}$ of the coupling which can exist on a single particle level with no pair degeneracy. Notably $G_{\rm cr}^{+}$ and $G_{\rm cr}^{-}$ merge when the number of single particle levels goes to infinity, where they coincide with the $G_{\rm cr}$ (when it exists) of a one pair system, not envisioned by the Richardson theory. In correspondence of $G_{\rm cr}$ the system undergoes a transition from a mean field to a pairing dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes finding out that the former, for $G>G_{\rm cr}^{-}$, come close to the BCS predictions, whereas the latter display a divergence at $G_{\rm cr}$, signaling the onset of a long range off-diagonal order in the system.Comment: 35 pages, 6 figures, 2 tables, to be published in EPJ

The Determination of the Star Formation Rate in Galaxies

A spectrophotometric model able to compute the integrated spectrum of a galaxy, including the contribution both of the stellar populations and of the ionized interstellar gas of the HII regions powered by young hot stars, has been used to study several spectral features and photometric quantities in order to derive calibrations of the star formation history of late type galaxies. Attention has been paid to analyze the emission of the Balmer lines and the [OII]$\lambda$3727 line to test their attitude at providing estimates of the present star formation rate in galaxies. Other features, like D$_{4000}$ and the equivalent width of the H$_{\delta}$ line, influenced by the presence of intermediate age stars, have been considered. Several ways of estimating the star formation rates in normal galaxies are discussed and some considerations concerning the applicability of the models are presented. Criteria have been also studied for ascertaining the presence of a burst, current or ended not long ago. Bursts usually hinder the determination of the past star formation rate.Comment: 21 pages, needs A&A l-aa.sty, accepted for publication in Astronomy & Astrophysic

On the analytic solution of the pairing problem: one pair in many levels

We search for approximate, but analytic solutions of the pairing problem for one pair of nucleons in many levels of a potential well. For the collective energy a general formula, independent of the details of the single particle spectrum, is given in both the strong and weak coupling regimes. Next the displacements of the solutions trapped in between the single particle levels with respect to the unperturbed energies are explored: their dependence upon a suitably defined quantum number is found to undergo a transition between two different regimes.Comment: 30 pages, AMS Latex, 8 figures. Submitted to Phys. Rev.

Nuclear effects in charged-current quasielastic neutrino-nucleus scattering

After a short review of the recent developments in studies of neutrino-nucleus interactions, the predictions for double-differential and integrated charged current-induced quasielastic cross sections are presented within two different relativistic approaches: one is the so-called SuSA method, based on the superscaling behavior exhibited by electron scattering data; the other is a microscopic model based on relativistic mean field theory, and incorporating final-state interactions. The role played by the meson-exchange currents in the two-particle two-hole sector is explored and the results are compared with the recent MiniBooNE data.Comment: 12 pages, 9 figures, to appear in the Proceedings of "XIII Convegno di Cortona su Problemi di Fisica Nucleare Teorica", Cortona (Italy), April 6-8, 201

A simple model for NN correlations in quasielastic lepton-nucleus scattering

We present a covariant extension of the relativistic Fermi gas model which incorporates correlation effects in nuclei. Within this model, inspired by the BCS descriptions of systems of fermions, we obtain the nuclear spectral function and from it the superscaling function for use in treating high-energy quasielastic electroweak processes. Interestingly, this model has the capability to yield the asymmetric tail seen in the experimental scaling function.Comment: 11 pages, 6 figures, Proceedings of the Twenty Seventh International Workshop on Nuclear Theory, June 23 - 28, 2008, Rila mountains, Bulgari