On the Accuracy of Hyperspherical Harmonics Approaches to Photonuclear Reactions

Using the Lorentz Integral Transform (LIT) method we compare the results for the triton total photodisintegration cross section obtained using the Correlated Hyperspherical Harmonics (CHH) and the Effective Interaction Hyperspherical Harmonics (EIHH) techniques. We show that these two approaches, while rather different both conceptually and computationally, lead to results which coincide within high accuracy. The calculations which include two- and three-body forces are of the same high quality in both cases. We also discuss the comparison of the two approaches in terms of computational efficiency. These results are of major importance in view of applications to the much debated case of the four-nucleon photoabsorption.Comment: 12 pages, 3 figure

On the control of a linear functional- differential equation with quadratic cost

Linear functional differential equations control with quadratic cos

The effective interaction hyperspherical harmonics method for non-local potentials

A different formulation of the effective interaction hyperspherical harmonics (EIHH) method, suitable for non-local potentials, is presented. The EIHH method for local interactions is first shortly reviewed to point out the problems of an extension to non-local potentials. A viable solution is proposed and, as an application, results on the ground-state properties of 4- and 6-nucleon systems are presented. One finds a substantial acceleration in the convergence rate of the hyperspherical harmonics series. Perspectives for an application to scattering cross sections, via the Lorentz transform method are discussed.Comment: 6 pages, 1 figure, to be published in the Proceedings of the International Nuclear Physics Conference, Vancouver, 201

Incorporation of three-nucleon force in the effective interaction hyperspherical harmonic approach

It is shown how a bare three-nucleon force is incorporated into the formalism of the effective interaction approach for hyperspherical harmonics. As a practical example we calculate the ground state properties of 3H and 3He using the Argonne V18 nucleon-nucleon potential and the Urbana IX three-nucleon force. A very good convergence of binding energies and matter radii is obtained. We also find a very good agreement of our results compared to other high precision calculations.Comment: 17 pages, 3 figure

Few body Calculation of Neutrino Neutral Inelastic scattering on 4He

The inelastic neutral reaction of neutrino on 4He is calculated using two modern nucleon--nucleon potentials. Full final state interaction among the four nucleons is considered, via the Lorentz integral transform (LIT) method. The effective interaction hyperspherical-harmonic (EIHH) approach is used to solve the resulting Schrodinger like equations. A detailed energy dependent calculation is given in the impulse approximation.Comment: 4 pages; talk at 18th International Conference on Few-Body Problems in Physics (FB18), Santos, SP, Brazil, August 200

On the structure of just infinite profinite groups

A profinite group $G$ is just infinite if every closed normal subgroup of $G$ is of finite index. We prove that an infinite profinite group is just infinite if and only if, for every open subgroup $H$ of $G$, there are only finitely many open normal subgroups of $G$ not contained in $H$. This extends a result recently established by Barnea, Gavioli, Jaikin-Zapirain, Monti and Scoppola, who proved the same characterisation in the case of pro-$p$ groups. We also use this result to establish a number of features of the general structure of profinite groups with regard to the just infinite property.Comment: 16 page

Neutrino Breakup of A=3 Nuclei in Supernovae

We extend the virial equation of state to include 3H and 3He nuclei, and predict significant mass-three fractions near the neutrinosphere in supernovae. While alpha particles are often more abundant, we demonstrate that energy transfer cross-sections for muon and tau neutrinos at low densities are dominated by breakup of the loosely-bound 3H and 3He nuclei. The virial coefficients involving A=3 nuclei are calculated directly from the corresponding nucleon-3H and nucleon-3He scattering phase shifts. For the neutral-current inelastic cross-sections and the energy transfer cross sections, we perform ab-initio calculations based on microscopic two- and three-nucleon interactions and meson-exchange currents.Comment: 6 pages, 2 figures, minor additions, to appear in Phys. Rev.

Are there compact heavy four-quark bound states?

We present an exact method to study four-quark systems based on the hyperspherical harmonics formalism. We apply it to several physical systems of interest containing two heavy and two light quarks using different quark-quark potentials. Our conclusions mark the boundaries for the possible existence of compact, non-molecular, four-quark bound states. While $QQ\bar n \bar n$ states may be stable in nature, the stability of $Q\bar Qn \bar n$ states would imply the existence of quark correlations not taken into account by simple quark dynamical modelsComment: 10 pages, 1 figure. Accepted for publication in Phys. Rev.