Short-range correlations in finite nuclear systems

Recent results concerning the use of the Correlated Basis Function to investigate the ground state properties of medium-heavy doubly magic nuclei with microscopic interactions are presented. The calculations have been done by considering a Short-Range Correlation between nucleons. The possibility of identifying effects produced by Short-Range Correlations in electromagnetically induced phenomena is discussed.Comment: 12 pages, 10 Postscript figures, Contribution to the International Workshop on Nuclear Theory, Rila Mountains, Bulgaria 10 to June 15, 200

Random Phase Approximation and neutrino-nucleus cross sections

The Random Phase Approximation theory is used to calculate the total cross sections of electron neutrinos on $^{12}$C nucleus. The role of the excitation of the discrete spectrum is discussed. A comparison with electron scattering and muon capture data is presented. The cross section of electron neutrinos coming from muon decay at rest is calculated.Comment: 6 pages, 5 eps figures, Presented at the XX Max Born Symposium, Wroclaw (Poland

Introducing the Random Phase Approximation Theory

Random Phase Approximation (RPA) is the theory most commonly used to describe the excitations of many-body systems. In this article, the secular equations of the theory are obtained by using three different approaches: the equation of motion method, the Green's function perturbation theory and the time-dependent Hartree--Fock theory. Each approach emphasizes specific aspects of the theory overlooked by the other methods. Extensions of the RPA secular equations to treat the continuum part of the excitation spectrum and also the pairing between the particles composing the system are presented. Theoretical approaches which overcome the intrinsic approximations of RPA are outlined.Comment: 57 pages, 6 figure

Two Proton Emission with Electromagnetic Probes

A model to study two-proton emission from nuclei induced by electromagnetic probes is developed. The process is due to one-body electromagnetic operators, acting together with short-range correlations, and two-body $\Delta$ currents. The model includes all the diagrams containing a single correlation function. The sensitivity of the cross section to the details of the correlation function is studied by using realistic and schematic correlations. Results for the $^{16}$O nucleus are presented.Comment: 9 pages, 8 figures, Contribution to the 6th. Workshop on "Electromagnetic Induced Two-Hadron Emission",Pavia, 200

Photo-emission of two protons from nuclei

The photo-emission of two protons from the $^{12}$C, $^{16}$O and $^{40}$Ca nuclei is investigated. Aim of the work is the study of the possibilities offered by this probe to obtain information about the characteristics of the short-range correlations. We have also evaluated the effects of the two-body $\Delta$-currents which, in this processes, compete with those produced by the short-range correlations. Our results show that ($\gamma$,pp) processes could be more useful than (e,e'pp) for the study of the short-range correlations.Comment: 21 pages, 15 figures, 3 table

Neutrino cross sections and nuclear structure

The effects of the theoretical uncertainties in the description of neutrino-nucleus cross sections for supernova neutrino energies are investigated.Comment: Contribution to NOW 2008, Conca Specchiulla (Otranto, Italy), September 6-13 200

Analytical and numerical analysis of the complete Lipkin-Meshkov-Glick Hamiltonian

The Lipkin-Meshkov-Glick is a simple, but not trivial, model of a quantum many-body system which allows us to solve the many-body Schr\"odinger equation without making any approximation. The model, which in its unperturbed case is composed only by two energy levels, includes two interacting terms. A first one, the $V$ interaction, which promotes or degrade pairs of particles, and a second one, the $W$ interaction, which scatters one particle in the upper and another in the lower energy level. In comparing this model with other approximation methods, the $W$ term interaction is often set to zero. In this paper, we show how the presence of this interaction changes the global structure of the system, generates degeneracies between the various eigenstates and modifies the energy eigenvalues structure. We present analytical solutions for systems of two and three particles and, for some specific cases, also for four, six and eight particles. The solutions for systems with more than eight particles are only numerical but their behaviour can be well understood by considering the extrapolations of the analytical results. Of particular interest it is the study of how the $W$ interaction affects the energy gap between the ground state and the first-excited state.Comment: 17 pages, 8 figure