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

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.

Lepton mass effects in the Bethe-Heitler process

We develop the full finite lepton mass formalism for the production of real photons via the Bethe-Heitler reaction of unpolarized leptons off unpolarized nucleons. Genuine lepton mass effects are described, in particular their dependence upon the lepton mass and the initial beam energy, as well as their sensitivity to the nucleon isospin. In the minimum momentum transfer region, these effects dominate the muon induced proton cross section and become significant for electron scattering at small $x_B$.Comment: Final version including errat

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