[en] In the first order approximation the nucleons are moving into a collective well extracted from the two-body N-N interaction. The nuclear shell model is explained by the structure of the first order solution of the Schroedinger equation. In the next step the two-body correlations generated by the N-N potential are introduced in the wave function

[en] Various properties of the hyperspherical potential basis are investigated. The expansion of any two body function, in particular the two body potential, is given. The matrix elements with two and three potential harmonics needed for the construction of the potential matrix are calculated. Useful recurrence formulae are derived. The concept of potential basis is extended to systems with any number of fermions. A method for inproving the accuracy in the expansion of the wave-function in taking more than the two body correlations is suggested

[en] A theoretical analysis by a two parameter formula of the experimental cross sections for ionization of inner-shell electrons by electrons shows that the data for all the elements might be fitted with a single value for each of the parameters

[en] Exact solutions of the harmonic-oscillator and infinite hyperspherical well are given for the ground state of a infinitely heavy (N=Z) nucleus. The density of matter is a steadily decreasing function. The kinetic energy per particle is 12% smaller than the one predicted by the Fermi sea

[en] One shows in an application of the hyperspherical Lsub(m) approximation to ⁶Li with soft core two body potentials that for nuclei A>4 it is necessary to replace the Schroedinger equation by at least two coupled equations in order to treat correctly an interaction including a Majorana exchange operator. Binding energies for ⁶Li even parity states are calculated

[en] A method for solving the Schroedinger equation for the ground state of any number of bosons or for the trinucleon system or -particle is formulated in the framework of the hyperspherical harmonic expansion method. It is applied to the trinucleon system for nucleons interacting through realistic soft core potentials. The convergence of the method is carefully studied. Binding energies, electric form factors, one body densities, two body correlation functions and two body photodesintegration are calculated for various potentials

[en] The effect of the three body force, generated by two pions exchange with an intermediate Δ, on the trinucleon system is investigated

[en] In the framework of the hyperspherical formalism, we present a study of the Coupled Adiabatic Approximation (CAA) for the case of three nucleons interacting via central spin-dependent two-body potentials. We analyse the convergence of the ground state eigenvalues versus the grand orbital quantum number (2K) and compare the results to that of the Coupled Equations (CE). We also compare with two simpler but less accurate approximations: the Uncoupled Adiabatic Approximation (UAA) and the Extreme Adiabatic Approximation (EAA). The former provides an upper and the latter provides a lower bound to the ground state energy

[en] A procedure for introducing the two-body correlations in the solution of the Schrodinger equation is described. The N-body Schrodinger equation for nucleons subject to two-(or many)-body N-N interaction has never been solved with accuracy except for few-body systems. Indeed it is difficult to take the two-body correlations generated by the interaction into account in the wave function

[en] A solution of the Schoedinger equation including the two body correlations is proposed. This equation is transformed into an infinite set of coupled differential equations which can be truncated for the sake of computation