57 research outputs found
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
"Special section on: Next Generation Solar Cells", Solar Energy Materials and Solar Cells
International audienc
Photonic crystals for imporving light absorption in organic solar cells
International audienc
"Special section on: Next Generation Solar Cells", Solar Energy Materials and Solar Cells
International audienc
Collection and conversion of light into electricity using rectenna technology.
International audienc
Matrix description of the anisotropy of the inter-sub-band transition of a quantum multi-pit structure
International audienc
Description matricielle de l'anisotropie de la transition inter-sous-bande d'une structure Ă multi-puits quantiques
Dans un puits quantique, les transitions radiatives
inter-sous-bande sont telles que seule la composante du champ
électrique parallèle à l'axe de croissance est
affectĂ©e. Cette spĂ©cificitĂ© confère Ă
l'absorption un caractère foncièrement anisotrope. Nous
Ă©tablissons la matrice de transfert d'une structure Ă
multi-puits quantiques en assimilant chaque puits Ă une
couche mince anisotrope uniaxe. À l'anisotropie
intrinsèque (règles de sélection) se superpose une
anisotropie structurelle (biréfringence de forme). Les
symétries du système permettent néanmoins de
découpler les états de polarisation () et ()
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