The three-photon detachment cross sections of the ions F-, Br-and Iare measured, using the fundamental 1064.2 nm wavelength of a single-mode Nd:YAG laser. The detachment signal is measured by detecting the neutral atoms produced from an ionic beam of kinetic energy 1.2 keV. The data analysis takes into account the laser pulse time profile, the actual spatial profile of the laser beam in the interaction region, and the fast motion of the ions through the laser beam during the laser pulse. Saturation of the threephoton process is observed and used to normalise the detachment signal. We obtain u(F-) = 6.1' ::8 x s2 m6. These measured cross sections are compared with theoretical predictions. The result obtained for Fagrees with a very recent measurement performed with a different technique. s2 m6, u(Br-) = 1.6' ;:: x s2 m6 and u(I-) = 3.3:;:: x i. This work was supported by the DRET office (Direction des Recherches, Etudes et Techniques) under contract No 84/079.

Abstract. The stability of the Majorana modes in the presence of a repulsive interaction is studied in the standard semiconductor wire -metallic superconductor configuration. The effects of short-range Coulomb interaction, which is incorporated using a purely repulsive δ-function to model the strong screening effect due to the presence of the superconductor, are determined within a Hartree-Fock approximation of the effective Bogoliubov-De Gennes Hamiltonian that describes the low-energy physics of the wire. Through a numerical diagonalization procedure we obtain interaction corrections to the single particle eigenstates and calculate the extended topological phase diagram in terms of the chemical potential and the Zeeman energy. We find that, for a fixed Zeeman energy, the interaction shifts the phase boundaries to a higher chemical potential, whereas for a fixed chemical potential this shift can occur either to lower or to higher Zeeman energies. This effects can be interpreted as a renormalization of the g-factor due to the interaction. The minimum Zeeman energy needed to realize Majorana fermions decreases with increasing the strength of the Coulomb repulsion. Furthermore, we find that in wires with multi-band occupancy this effect can be enhanced by increasing the chemical potential, i. e. by occupying higher energy bands.

Charge and spin density distributions are studied within a nano-ring structure endowed with Rashba and Dresselhaus spin orbit coupling (SOI). For a small number of interacting electrons, in the presence of an external magnetic field, the energy spectrum of the system is calculated through an exact numerical diagonalization procedure. The eigenstates thus determined are used to estimate the charge and spin densities around the ring. We find that when more than two electrons are considered, the charge-density deformations induced by SOI are dramatically flattened by the Coulomb repulsion, while the spin density ones are amplified.