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

Parity-violating longitudinal response

The longitudinal quasielastic parity-violating electron scattering response is explored within the context of a model that builds antisymmetrized RPA-HF correlations on a relativistic Fermi gas basis. The large sensitivity to nuclear dynamics of this observable, found in previous studies where only pionic correlations were included, is shown to survive in the present model where the effects from pion, rho, sigma and omega exchange in a version of the Bonn potential are incorporated. Through an intricate diagrammatic cancellation/filtration mechanism the longitudinal parity-violating response turns out to be close to the one obtained in first-order perturbation theory with the pion alone. Finally, in accord with our previous work, the parity-violating response is seen to display appreciable sensitivity to the electric strangeness content of the nucleon, especially at high momentum transfer.Comment: 13 pages, uses REVTeX and epsfig, 10 postscript figures; a postscript version of the paper is available by anonymous ftp at ftp://carmen.to.infn.it/pub/barbaro/papers/951

Influence of nucleonic motion in Relativistic Fermi Gas inclusive responses

Impulsive hadronic descriptions of electroweak processes in nuclei involve two distinctly different elements: one stems from the nuclear many-body physics --- the medium --- which is rather similar for the various inclusive response functions, and the other embodies the responses of the hadrons themselves to the electroweak probe and varies with the channel selected. In this letter we investigate within the context of the relativistic Fermi gas in both the quasi-elastic and $N\to\Delta$ regimes the interplay between these two elements. Specifically, we focus on expansions in the one small parameter in the problem, namely, the momentum of a nucleon in the initial wave function compared with the hadronic scale, the nucleon mass. Both parity-conserving and -violating inclusive responses are studied and the interplay between longitudinal ($L$) and transverse ($T$ and $T'$) contributions is highlighted.Comment: 11 pages, 1 figur

The multilevel pairing Hamiltonian versus the degenerate case

We study the pairing Hamiltonian in a set of non degenerate levels. First, we review in the path integral framework the spontaneous breaking of the U(1) symmetry occurring in such a system for the degenerate situation. Then the behaviors with the coupling constant of the ground state energy in the multilevel and in the degenerate case are compared. Next we discuss, in the multilevel case, an exact strong coupling expansion for the ground state energy which introduces the moments of the single particle level distribution. The domain of validity of the expansion, which is known in the macroscopic limit, is explored for finite systems and its implications for the energy of the latter is discussed. Finally the seniority and Gaudin excitations of the pairing Hamiltonian are addressed and shown to display the same gap in leading order.Comment: 20 pages, 4 figure

Superscaling and Charge-changing Neutrino Cross Sections

The superscaling function extracted from inclusive electron scattering data is used to predict high energy charge-changing neutrino cross sections in the quasi-elastic and $\Delta$ regions.Comment: 3 pages, 2 figures, to appear in the Proceedings of the 7th International Workshop on Neutrino Factories and Superbeams, Laboratori Nazionali di Frascati, Frascati (Rome), June 21 - 26, 200

Skewed recoil polarization in (e,e'p) reactions from polarized nuclei

The general formalism describing $\vec{A}(\vec{e},e'\vec{p})B$ reactions, involving polarization of the electron beam, target and ejected proton, is presented within the framework of the relativistic plane wave impulse approximation for medium and heavy nuclei. It is shown that the simultaneous measurement of the target and ejected proton polarization can provide new information which is not contained in the separate analysis of the $\vec{A}(\vec{e},e'p)B$ and $A(\vec{e},e'\vec{p})B$ reactions. The polarization transfer mechanism in which the electron interacts with the initial nucleon carrying the target polarization, making the proton exit with a fractional polarization in a different direction, is referred to here as ``skewed polarization''. The new observables characterizing the process are identified, and written in terms of polarized response functions and asymmetries which are of tensor nature. The corresponding half-off-shell single-nucleon responses are analyzed using different prescriptions for the electromagnetic vertex and for different kinematics. Numerical predictions are presented for selected perpendicular and parallel kinematics in the case of $^{39}$K as polarized target.Comment: 30 pages, 8 figure

Bosonization and even Grassmann variables

A new approach to bosonization in relativistic field theories and many-body systems, based on the use of fermionic composites as integration variables in the Berezin integral defining the partition function of the system, is tested. The method is applied to the study of a simplified version of the BCS model.Comment: 20 pages, LaTe

Scaling and isospin effects in quasielastic lepton-nucleus scattering in the Relativistic Mean Field Approach

The role of isospin in quasielastic electron scattering and charge-changing neutrino reactions is investigated in the relativistic impulse approximation. We analyze proton and neutron scaling functions making use of various theoretical descriptions for the final-state interactions, focusing on the effects introduced by the presence of strong scalar and vector terms in the relativistic mean field approach. An explanation for the differences observed in the scaling functions evaluated from $(e,e')$ and $(\nu,\mu)$ reactions is provided by invoking the differences in isoscalar and isovector contributions.Comment: 10 pages, 5 figures, submitted to Phys. Lett.

Relativistic pionic effects in quasielastic electron scattering

The impact of relativistic pionic correlations and meson-exchange currents on the response functions for electromagnetic quasielastic electron scattering from nuclei is studied in detail. Results in first-order perturbation theory are obtained for one-particle emission electronuclear reactions within the context of the relativistic Fermi gas model. Improving upon previous analyses where non-relativistic reductions of the currents were performed, here a fully relativistic analysis in which both forces and currents are treated consistently is presented. Lorentz covariance is shown to play a crucial role in enforcing the gauge invariance of the theory. Effects stemming uniquely from relativity in the pionic correlations are identified and, in particular, a comprehensive study of the self-energy contributions and of the currents associated with the pion is presented. First- and second-kind scaling for high momentum transfer is investigated.Comment: 43 pages, 21 figure

Strange form factors of the proton: a new analysis of the neutrino (antineutrino) data of the BNL-734 experiment

We consider ratios of elastic neutrino(antineutrino)-proton cross sections measured by the Brookhaven BNL-734 experiment and use them to obtain the neutral current (NC) over charged current (CC) neutrino-antineutrino asymmetry. We discuss the sensitivity of these ratios and of the asymmetry to the electric, magnetic and axial strange form factors of the nucleon and to the axial cutoff mass M_A. We show that the effects of the nuclear structure and interactions on the asymmetry and, in general, on ratios of cross sections are negligible. We find some restrictions on the possible values of the parameters characterizing the strange form factors. We show that a precise measurement of the neutrino-antineutrino asymmetry would allow the extraction of the axial and vector magnetic strange form factors in a model independent way. The neutrino-antineutrino asymmetry turns out to be almost independent on the electric strange form factor and on the axial cutoff mass.Comment: 12 page