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

Angular response of grating-coupled quantum well infrared photodetectors: An experimental study

QWIPs are nowadays considered as rather good candidates for multispectral imaging. Indeed, their narrow spectral bandwidth can be tailored by band gap engineering, and they rely on the use of the mature GaAs technology. However, a light coupling scheme, such as 2D-grating for example, is required to obtain normal incidence absorption. The geometrical parameters of this 2D-grating (grating period, etch depth of the grating) need to be optimized. This optimization is particularly difficult for dual-band pixels, since a compromise is required between the two wavelengths. This paper deals with the influence of the etch depth of the grating on the angular response of quantum well infrared photodetectors. We will first present the experimental setup which was specifically developed at ONERA to perform angular response measurements on infrared photodetectors from different technologies. The results obtained on "low-noise" QWIP samples provided by Fraunhofer-IAF will be presented and analyzed, with emphasis on the effect of the etch depth of the grating on the angular response

Theoretical Study of Electronic Autoionization in CO: Vibrationally resolved results between 17 and 18.3 eV.

peer reviewedWe have theoretically studied the electronic autoionization between 17 and 18.3 eV of Rydberg series converging to the B 2Sigma+ state of CO+ (RB series). We have obtained partial and vibrationally resolved differential and total photoionization cross sections by combining ab initio electronic quantities with a variant of the two-step multichannel quantum defect theory (MQDT). The formalism of the Feshbach projection operators is used to separate the electronic quantities needed in the first and second steps of the MQDT. We have introduced the vibrational motion within the Condon approximation. Our results lead to new unambiguous assignments of the RB series. The vibrationally resolved cross sections, the associated branching ratios, and the background and resonant features are discussed in detail and compared with the available experimental data. There is an overall agreement between theory and experiement except for the angular distribution of photoelectrons