Lepton-nucleus scattering in the impulse approximation regime

We discuss theoretical calculations of electron- and neutrino-nucleus scattering, carried out using realistic nuclear spectral functions and including the effect of final state interactions. Comparison between electron scattering data and the calculated inclusive cross sections off oxygen shows that the Fermi gas model fails to provide a satisfactory description of the measured cross sections, and inclusion of nuclear dynamics is needed. The role of Pauli blocking in charged-current neutrino induced reactions at low $Q^2$ is also analyzed.Comment: To be published in the Proceedings of NUFACT05 (Nucl. Phys. B, Proceedings Supplements

Final-state interactions in the response of nuclear matter

Final-state interactions in the response of a many-body system to an external probe delivering large momentum are normally described using the eikonal approximation, for the trajectory of the struck particle, and the frozen approximation, for the positions of the spectators. We propose a generalization of this scheme, in which the initial momentum of the struck particle is explicitly taken into account. Numerical calculations of the nuclear matter response at 1 $< |{\bf q}| <$ 2 GeV/c show that the inclusion of this momentum dependence leads to a sizable effect in the low energy tail. Possible implications for the analysis of existing electron-nucleus scattering data are discussed.Comment: 21 pages, 4 figure

Interpretation of y-scaling of the nuclear response

The behavior of the nuclear matter response in the region of large momentum transfer, in which plane wave impulse approximation predicts the onset of y-scaling, is discussed. The theoretical analysis shows that scaling violations produced by final state interactions are driven by the momentum dependence of the nucleon-nucleon scattering cross section. Their study may provide valuable information on possible modifications of nucleon-nucleon scattering in the nuclear medium.Comment: 4 pages with 3 figures. To appear in Physical Review Letter

A statistical theory of the mean field

A statistical theory of the mean field is developed. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction, obtained after the average interaction is removed, are random with the average value of zero. With these two assumptions one obtains explicit expressions for the mean field and the fluctuation away from the average. The fluctuation is expanded in terms of more and more complex excitations. Using the randomness of the matrix elements one can then obtain formulas for the contribution to the error from each class of complex excitations and a general condition for the convergence of the expansion is derived. It is to be emphasized that no conditions on the nature of the system being studied are made. Making some simplifying assumptions a schematic model is developed. This model is applied to the problem of nuclear matter. The model yields a measure of the strength of the effective interaction. It turns out to be three orders of magnitude less than that calculated using a potential which gives a binding energy of about -7 MeV/nucleon demonstrating the strong damping of the interaction strength induced by the averaging process.Comment: 25 pages, REVTeX, 4 eps figure

Short-Range Correlations and the One-Body Density Matrix in Finite Nuclei

The effects of short-range correlations derived from a realistic meson-exchange potential on the single-particle density matrix in finite nuclei are investigated by analyzing the one-body density in terms of the natural orbits. Basic features of these natural orbits and their spectral distributions are discussed. For many observables it seems to be sufficient to approximate the one-body density matrix in terms of those natural orbits, which exhibit the largest occupation probabilities. For the investigation of the high-momentum components in the single-particle density, however, it is important to take into account natural orbits with small occupation probabilities, originating from the single-particle Green function at large negative energies.Comment: 13 pages, RevTeX, 5 figures adde

Momentum Distribution in Nuclear Matter and Finite Nuclei

A simple method is presented to evaluate the effects of short-range correlations on the momentum distribution of nucleons in nuclear matter within the framework of the Green's function approach. The method provides a very efficient representation of the single-particle Green's function for a correlated system. The reliability of this method is established by comparing its results to those obtained in more elaborate calculations. The sensitivity of the momentum distribution on the nucleon-nucleon interaction and the nuclear density is studied. The momentum distributions of nucleons in finite nuclei are derived from those in nuclear matter using a local-density approximation. These results are compared to those obtained directly for light nuclei like $^{16}O$.Comment: 17 pages REVTeX, 10 figures ps files adde

Scaling in many-body systems and proton structure function

The observation of scaling in processes in which a weakly interacting probe delivers large momentum ${\bf q}$ to a many-body system simply reflects the dominance of incoherent scattering off target constituents. While a suitably defined scaling function may provide rich information on the internal dynamics of the target, in general its extraction from the measured cross section requires careful consideration of the nature of the interaction driving the scattering process. The analysis of deep inelastic electron-proton scattering in the target rest frame within standard many-body theory naturally leads to the emergence of a scaling function that, unlike the commonly used structure functions $F_1$ and $F_2$, can be directly identified with the intrinsic proton response.Comment: 11 pages, 4 figures. Proceedings of the 11th Conference on Recent Progress in Many-Body Theories, Manchester, UK, July 9-13 200

Momentum and Energy Distributions of Nucleons in Finite Nuclei due to Short-Range Correlations

The influence of short-range correlations on the momentum and energy distribution of nucleons in nuclei is evaluated assuming a realistic meson-exchange potential for the nucleon-nucleon interaction. Using the Green-function approach the calculations are performed directly for the finite nucleus $^{16}$O avoiding the local density approximation and its reference to studies of infinite nuclear matter. The nucleon-nucleon correlations induced by the short-range and tensor components of the interaction yield an enhancement of the momentum distribution at high momenta as compared to the Hartree-Fock description. These high-momentum components should be observed mainly in nucleon knockout reactions like $(e,e'p)$ leaving the final nucleus in a state of high excitation energy. Our analysis also demonstrates that non-negligible contributions to the momentum distribution should be found in partial waves which are unoccupied in the simple shell-model. The treatment of correlations beyond the Brueckner-Hartree-Fock approximation also yields an improvement for the calculated ground-state properties.Comment: 12 pages RevTeX, 7 figures postscript files appende

The Single-Particle Spectral Function of 16O^{16}{\rm O}

The influence of short-range correlations on the $p$-wave single-particle spectral function in $^{16}{\rm O}$ is studied as a function of energy. This influence, which is represented by the admixture of high-momentum components, is found to be small in the $p$-shell quasihole wave functions. It is therefore unlikely that studies of quasihole momentum distributions using the $(e,e'p)$ reaction will reveal a significant contribution of high momentum components. Instead, high-momentum components become increasingly more dominant at higher excitation energy. The above observations are consistent with the energy distribution of high-momentum components in nuclear matter.Comment: 5 pages, RevTeX, 3 figure

A linked cluster expansion for the calculation of the semi-inclusive A(e,e'p)X processes using correlated Glauber wave functions

The distorted one-body mixed density matrix, which is the basic nuclear quantity appearing in the definition of the cross section for the semi-inclusive A(e,e'p)X processes, is calculated within a linked-cluster expansion based upon correlated wave functions and the Glauber multiple scattering theory to take into account the final state interaction of the ejected nucleon. The nuclear transparency for 16O and 40Ca is calculated using realistic central and non-central correlations and the important role played by the latter is illustrated.Comment: 18 pages, RevTeX, 3 ps figures. Final version, to appear in Phys. Rev.