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We study the excited states of the pairing Hamiltonian providing an expansion for their energy in the strong coupling limit. To assess the role of the pairing interaction we apply the formalism to the case of a heavy atomic nucleus. We show that only a few statistical moments of the level distribution are sufficient to yield an accurate estimate of the energy for not too small values of the coupling $G$ and we give the analytic expressions of the first four terms of the series. Further, we discuss the convergence radius $G_{\rm sing}$ of the expansion showing that it strongly depends upon the details of the level distribution. Furthermore $G_{\rm sing}$ is not related to the critical values of the coupling $G_{\rm crit}$, which characterize the physics of the pairing Hamiltonian, since it can exist even in the absence of these critical points., Comment: 28 pages, 5 figures

We reexamine several issues related to the physics of scaling in electron scattering from nuclei. A basic model is presented in which an assumed form for the momentum distribution having both long- and short-range contributions is incorporated in the single-particle Green function. From this one can obtain saturation of nuclear matter for an NN interaction with medium-range attraction and short-range repulsion, and can obtain the density-density polarization propagator and hence the electromagnetic response and scaling function. For the latter, the shape of the scaling function and how it approaches scaling as a function of momentum transfer are both explored., Comment: 24 pages, 15 figures. A reference has been corrected and updated

The one- and the two-particle propagators for an infinite non-interacting Fermi system are studied as functions of space-time coordinates. Their behaviour at the origin and in the asymptotic region is discussed, as is their scaling in the Fermi momentum. Both propagators are shown to have a divergence at equal times. The impact of the interaction among the fermions on their momentum distribution, on their pair correlation function and, hence, on the Coulomb sum rule is explored using a phenomenological model. Finally the problem of how the confinement is reflected in the momentum distribution of the system's constituents is briefly addressed., Comment: 26 pages, 9 figures, accepted for publication on Phys. Rev. C

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, 2009

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, Bulgaria

Using ideas from BCS descriptions of systems of fermions, a covariant extension of the relativistic Fermi gas model is presented as a way to incorporate correlation effects in nuclei. The model is developed for the BCS nuclear ground state and for final states consisting of a single plane-wave nucleon plus a BCS recoiling daughter nucleus. The nuclear spectral function is obtained 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: 17 pages, 9 figures

We report results for the ground state energies and wave functions obtained by projecting spatially unrestricted Hartree Fock states to eigenstates of the total spin and the angular momentum for harmonic quantum dots with $N\leq 12$ interacting electrons including a magnetic field states with the correct spatial and spin symmetries have lower energies than those obtained by the unrestricted method. The chemical potential as a function of a perpendicular magnetic field is obtained. Signature of an intrinsic spin blockade effect is found., Comment: 12 pages, 5 tables, 10 figures, submitted to Phys. Rev. B

Ground state energies are obtained using the unrestricted Hartree Fock method for up to four interacting electrons parabolically confined in a quantum dot subject to a magnetic field. Restoring spin and rotational symmetries we recover Hund first rule. With increasing magnetic field, crossovers between ground states with different quantum numbers are found for fixed electron number that are not reproduced by the unrestricted Hartree Fock approximation. These are consistent with the ones obtained with more refined techniques. We confirm the presence of a spin blockade due to a spin mismatch in the ground states of three and four electrons., Comment: 16 Pages, 2 figures, accepted for publication on New Journal of Physics

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 figures

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 figures

We explore the possible occurrence of $\sigma$-$\omega$ condensation in the Quantum Hadro-Dynamics (QHD), namely the Serot and Walecka model, finding that at the mean field level it corresponds to a critical value of the coupling constant $g_\sigma=8.828$ and density $k_F=207.2$ MeV/c, significantly below the standard value of QHD., Comment: 14 pages, 4 figures

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 covariance

We present here analytic expressions for the generalised Lindhard function, also referred to as Fermi Gas polarisation propagator, in a relativistic kinematic framework and in the presence of various resonances and vertices. Particular attention is payed to its real part, since it gives rise to substantial difficulties in the definition of the currents entering the dynamics., Comment: 48 pages, 2 figures, to be published in EPJA

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 EPJA

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. C

Several perspectives that can be opened by studying the electroexcitation of the delta via parity-violating electron scattering from nuclei are examined, working within the context of the relativistic Fermi gas model. A strong enhancement of the left-right asymmetry in the delta sector compared with that in the quasi-elastic regime is found and the potential to find clear signatures for the axial-vector contributions of the nucleon-to-delta transition to the asymmetry identified at specific low momentum transfer kinematics. Possibilities of probing the deformation of the delta are also explored, and using both the proton and nuclei as targets, the abilitiy to study the asymmetry on neutrons is studied., Comment: 26 pages, 20 figures

The presence of a resonant structure corresponding to the $\Delta$ excitation in the longitudinal response to an e.m. probe is investigated. It is shown that many-body effects could significantly increase the relativistic contribution suggested by M.Ericson and coworkers, Comment: Accepted by Nuovo Ciment A

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 figures

In this paper dividing factors GL and GT are constructed for the longitudinal and transverse responses of the relativistic Fermi gas in such a way that the reduced responses so obtained scale. These factors parallel another dividing factor studied previously, HL, that yields a (different) reduced response which fulfills the Coulomb sum rule. GL, GT and HL are all found to be only very weakly model-dependent, thus providing essentially universal dividing factors. To explore the residual degree of dependence which remains, the scaling and sum rule properties of several specific models have been considered. It is seen that the relativistic Fermi gas (by construction) and also typical shell-model reduced responses successfully scale and satisfy the Coulomb sum rule, as do experimental results at medium to high momentum transfers. On the other hand, it is observed that the quantum hadrodynamic model does so only if interaction effects become weaker with increasing momentum transfer, as predicted in the most recent versions of that model., Comment: 29 pages, 11 figures; typeset using REVTEX

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 A

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 first order boson loop expansion. The interplay between $\omega$-meson exchange and box diagrams mainly governs the longitudinal response, while in the transverse one the direct $\Delta$ excitations almost cancel the one-loop correction and the response is ruled by the $\rho$-meson rescattering., Comment: LaTex file with 25 .ps figures, to appear on Proc. of XIII ISHEPP seminars - Dubna 1996

The separated electromagnetic responses $R_L(q,\omega)$ and $R_T(q,\omega)$ for inclusive electron scattering off nuclei are studied within a functional scheme., Comment: 13 pages, ReVTeX, with figures included as epsfiles

Two different methods for establishing a space-like Coulomb sum rule for the relativistic Fermi gas are compared. Both of them divide the charge response by a normalizing factor such that the reduced response thus obtained fulfills the sum rule at large momentum transfer. To determine the factor, in the first approach one exploits the scaling property of the longitudinal response function, while in the second one enforces the completeness of the states in the space-like domain via the Foldy-Wouthuysen transformation. The energy-weighted and the squared-energy-weighted sum rules for the reduced responses are explored as well and the extension to momentum distributions that are more general than a step-function is also considered. The two methods yield reduced responses and Coulomb sum rules that saturate in the non-Pauli-blocked region, which can hardly be distinguished for Fermi momenta appropriate to atomic nuclei. Notably the sum rule obtained in the Foldy-Wouthuysen approach coincides with the well known non-relativistic one. Only at quite large momentum transfers (say 1 GeV/c) does a modest softening of the Foldy-Wouthuysen reduced response with respect to that obtained in the scaling framework show up. The two responses have the same half-width to second order in the Fermi momentum expansion. However, when distributions extending to momenta larger than that at the Fermi surface are employed, then in both methods the Coulomb sum rule saturates only if the normalizing factors are appropriately modified to account for the high momentum components of the nucleons., Comment: LaTex file with 8 .ps figures

Connections are explored between exclusive and inclusive electron scattering within the framework of the relativistic plane-wave impulse approximation, beginning with an analysis of the model-independent kinematical constraints to be found in the missing energy--missing momentum plane. From the interplay between these constraints and the spectral function basic features of the exclusive and inclusive nuclear responses are seen to arise. In particular, the responses of the relativistic Fermi gas and of a specific hybrid model with confined nucleons in the initial state are compared in this work. As expected, the exclusive responses are significantly different in the two models, whereas the inclusive ones are rather similar. By extending previous work on the relativistic Fermi gas, a reduced response is introduced for the hybrid model such that it fulfills the Coulomb and the higher-power energy-weighted sum rules. While incorporating specific classes of off-shellness for the struck nucleons, it is found that the reducing factor required is largely model-independent and, as such, yields a reduced response that is useful for extracting the Coulomb sum rule from experimental data. Finally, guided by the difference between the energy-weighted sum rules of the two models, a version of the relativistic Fermi gas is devised which has the 0$^{\rm th}$, 1$^{\rm st}$ and 2$^{\rm nd}$ moments of the charge response which agree rather well with those of the hybrid model: this version thus incorporates {\em a priori} the binding and confinement effects of the stuck nucleons while retaining the simplicity of the original Fermi gas., Comment: LaTex file with 15 .ps figures

We introduce a new approach to highly correlated systems which generalizes the Fermi Hypernetted Chain and Correlated Basis Function techniques. While the latter approaches can only be applied to systems for which a nonrelativistic wave function can be defined, the new approach is based on the variation of a trial hamiltonian within a path integral framework and thus can also be applied to relativistic and field theoretical problems. We derive a diagrammatic scheme for the new approach and show how a particular choice of the trial hamiltonian corresponds exactly to the use of a Jastrow correlated ansatz for the wave function in the Fermi Hypernetted Chain approach. We show how our new approach can be used to find upper bounds to ground state energies in systems which the FHNC cannot handle, including those described by an energy-dependent effective hamiltonian. We demonstrate our approach by applying it to a quantum field theoretical system of interacting pions and nucleons., Comment: 35 RevTeX pages, 7 separated ps figures available on request

The nuclear response is evaluated in the frame of the bosonic loop expansion in a purely nucleonic dynamical scheme, which seems to be reliable in handling those channels where a direct excitation of a $\Delta$-resonance is not allowed. It is shown that the response strongly depends upon the effective interaction in the spin-transverse isovector channel. New experiments at CEBAF on parity-violating electron scattering could further constrain the form of the effective interaction., Comment: to appear in Journ. Phys. G

The results of an experiment on inclusive electron scattering from an oxygen jet target, performed in a wide range of energy and momentum transfer covering both quasi-elastic and $\Delta$(1232) resonance regions, are reported. In the former region the theoretical predictions, obtained including effects of nucleon-nucleon correlations in both initial and final states, give a good description of the experimental data. In the inelastic region a broadening as well as a damping of the resonant part of the cross section with respect to the free nucleon case is observed. The need of more detailed calculations including nuclear structure effects on the electroproduction cross section of nucleon resonances is highlighted., Comment: to appear in Nucl. Phys. A

In this paper we address the (charge) longitudinal electromagnetic response for a homogeneous system of nucleons interacting via meson exchanges in the functional framework. This approach warrants consistency if the calculation is carried on order-by-order in the mesonic loop expansion with RPA-dressed mesonic propagators. At the 1-loop order and considering pion, rho and omega exchanges we obtain a quenching of the response, in line with the experimental results., Comment: RevTeX, 18 figures available upon request - to be published in Physical Review C

A scaling variable for electron scattering off nuclei in the Delta-region is shown to exist. A scaling law for a large variety of scattering data with different kinematics is found. This property turns out to be very sensitive to the reaction mechanism. We will show that this outcome follows from drastic medium induced modifications on the momentum and energy dependence of the Delta width., Comment: 18 pages, LaTeX, figures not included, available upon request To be published in "Journal of Physics G"

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.

We discuss a relativistic theory of the atomic nuclei in the framework of the hamiltonian formalism and of the mesonic model of the nucleus. Attention is paid to the translational invariance of the theory. Our approach is centered on the concept of spectral amplitude, a function in the Dirac spinor space. We derive a Lorentz covariant equation for the latter, which requires as an input the baryon self-energy. For this we either postulate the most general Lorentz-Poincar\'e invariant expression or perform a calculation via a Bethe-Salpeter equation starting from a nucleon-nucleus interaction. We discuss the features of the nuclear spectrum obtained in the first instance. Finally the general constraints the self-energy should satisfy because of analyticity and Poincar\'e covariance are discussed.