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.

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

Neutral current (anti)neutrino scattering: relativistic mean field and superscaling predictions

We evaluate the neutral current quasi-elastic neutrino cross section within two nuclear models: the SuSA model, based on the superscaling behavior of electron scattering data, and the RMF model, based on relativistic mean field theory. We also estimate the ratio $(\nu p \to \nu p)/(\nu N \to \nu N)$ and compare with the MiniBooNE experimental data, performing a fit of the parameters $M_A$ and $g_A^{(s)}$ within the two models. Finally, we present our predictions for antineutrino scattering.Comment: 15 pages, 4 figure

Extensions of Superscaling from Relativistic Mean Field Theory: the SuSAv2 Model

We present a systematic analysis of the quasielastic scaling functions computed within the Relativistic Mean Field (RMF) Theory and we propose an extension of the SuperScaling Approach (SuSA) model based on these results. The main aim of this work is to develop a realistic and accurate phenomenological model (SuSAv2), which incorporates the different RMF effects in the longitudinal and transverse nuclear responses, as well as in the isovector and isoscalar channels. This provides a complete set of reference scaling functions to describe in a consistent way both $(e, e')$ processes and the neutrino/antineutrino-nucleus reactions in the quasielastic region. A comparison of the model predictions with electron and neutrino scattering data is presented.Comment: 19 pages, 24 figure

Off-shell effects in the relativistic mean field model and their role in CC (anti)neutrino scattering at MiniBooNE kinematics

The relativistic mean field (RMF) model is used to describe nucleons in the nucleus and thereby to evaluate the effects of having dynamically off-shell spinors. Compared with free, on-shell nucleons as employed in some other models, within the RMF nucleons are described by relativistic spinors with strongly enhanced lower components. In this work it is seen that for MiniBooNE kinematics, neutrino charged-current quasielastic cross sections show some sensitivity to these off-shell effects, while for the antineutrino-nucleus case the total cross sections are seen to be essentially independent of the enhancement of the lower components. As was found to be the case when comparing the RMF results with the neutrino-nucleus data, the present impulse approximation predictions within the RMF also fall short of the MiniBooNE antineutrino-nucleus data.Comment: 19 pages, 7 figures, submitted to Physics Letters

Semi-relativistic description of quasielastic neutrino reactions and superscaling in a continuum shell model

The so-called semi-relativistic expansion of the weak charged current in powers of the initial nucleon momentum is performed to describe charge-changing, quasielastic neutrino reactions $(\nu_\mu,\mu^-)$ at intermediate energies. The quality of the expansion is tested by comparing with the relativistic Fermi gas model using several choices of kinematics of interest for ongoing neutrino oscillation experiments. The new current is then implemented in a continuum shell model together with relativistic kinematics to investigate the scaling properties of $(e,e')$ and $(\nu_\mu,\mu^-)$ cross sections.Comment: 33 pages, 10 figures, to appear in PR

Nuclear effects in neutrino and antineutrino CCQE scattering at MINERvA kinematics

We compare the charged-current quasielastic neutrino and antineutrino observables obtained in two different nuclear models, the phenomenological SuperScaling Approximation and the Relativistic Mean Field approach, with the recent data published by the MINERvA Collaboration. Both models provide a good description of the data without the need of an ad hoc increase in the mass parameter in the axial-vector dipole form factor. Comparisons are also made with the MiniBooNE results where different conclusions are reached.Comment: 6 pages, 7 figures, Accepted for publication in Physical Review

Charged-current inclusive neutrino cross sections in the SuperScaling model including quasielastic, pion production and meson-exchange contributions

Charged current inclusive neutrino-nucleus cross sections are evaluated using the superscaling model for quasielastic scattering and its extension to the pion production region. The contribution of two-particle-two-hole vector meson-exchange current excitations is also considered within a fully relativistic model tested against electron scattering data. The results are compared with the inclusive neutrino-nucleus data from the T2K and SciBooNE experiments. For experiments where $\langle E_\nu \rangle \sim 0.8$ GeV, the three mechanisms considered in this work provide good agreement with the data. However, when the neutrino energy is larger, effects from beyond the $\Delta$ also appear to be playing a role. The results show that processes induced by two-body currents play a minor role at the kinematics considered.Comment: 10 pages, 7 figure

Nuclear effects in electron reactions and their impact on neutrino processes

We suggest that superscaling in electroweak interactions with nuclei, namely the observation that the reduced electron-nucleus cross sections are to a large degree independent of the momentum transfer and of the nuclear species, can be used as a tool to obtain precise predictions for neutrino-nucleus cross sections in both charged and neutral current-induced processes.Comment: 11 pages, 7 figures, proceedings of NUINT09, 6th International Workshop of Neutrino-Nucleus Interactions in the Few-Gev Region, Sitges (Spain), May 18-22, 200