Integral representation of one dimensional three particle scattering for delta function interactions

The Schr\"{o}dinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The interactions are replaced by appropriate boundary conditions. This leads then to requiring the solution of a free-particle Schr\"{o}dinger equation subject to these boundary conditions. A generalized Kontorovich - Lebedev transformation is used to write this solution as an integral involving a product of Bessel functions and pseudo-Sturmian functions. The coefficient of the product is obtained from a three-term recurrence relation, derived from the boundary condition. The contours of the Kontorovich-Lebedev representation are fixed by the asymptotic conditions. The scattering matrix is then derived from the exact solution of the recurrence relation. The wavefunctions that are obtained are shown to be equivalent to those derived by McGuire. The method can clearly be applied to a larger number of particles and hopefully might be useful for unequal masses and potentials.Comment: 18 pages, 2 figures, to be published in J. Math. Phy

Intermanifold similarities in partial photoionization cross sections of helium

Using the eigenchannel R-matrix method we calculate partial photoionization cross sections from the ground state of the helium atom for incident photon energies up to the N=9 manifold. The wide energy range covered by our calculations permits a thorough investigation of general patterns in the cross sections which were first discussed by Menzel and co-workers [Phys. Rev. A {\bf 54}, 2080 (1996)]. The existence of these patterns can easily be understood in terms of propensity rules for autoionization. As the photon energy is increased the regular patterns are locally interrupted by perturber states until they fade out indicating the progressive break-down of the propensity rules and the underlying approximate quantum numbers. We demonstrate that the destructive influence of isolated perturbers can be compensated with an energy-dependent quantum defect.Comment: 10 pages, 10 figures, replacement with some typos correcte

Space Charge at Nanoscale: Probing Injection and Dynamic Phenomena Under Dark/Light Configurations by Using KPFM and C-AFM

International audienc

Étude théorique d’une série de dihalogénures du groupe II A par la méthode ESEMO

Les structures électroniques des molécules MX2 (M = Be, Mg et X = F, Cl) ont été étudiées théoriquement par la méthode des orbitales moléculaires ESEMO. Les énergies ont été calculées en fonction de l’angle de valence. En accord avec les données expérimentales et les résultats des calculs a priori, les molécules BeF2, BeCl2 et MgCl2 ont été trouvées linéaires. Par contre, pour la molécule MgF2 l’angle de valence obtenu (120°) ne concorde pas avec les prévisions des calculs a priori mais est au moins en accord qualitatif, avec les résultats expérimentaux (158° d’après l’analyse du spectre infrarouge de la molécule piégée en matrice de gaz rare). L’incidence des diverses approximations utilisées sur ces résultats sera discutée. Enfin la méthode ESEMO a été comparée aux méthodes a priori : pour un temps de calcul beaucoup plus court elle donne des résultats qui sont dans l’ensemble, proches de ceux des méthodes a priori

Matrix description of the anisotropy of the inter-sub-band transition of a quantum multi-pit structure

International audienc

Wavelength and temperature dispersion of refractive index of thin films

International audienc

Top-flat and top-patterned cone gratings for mid-infrared antireflective properties

International audienc