An analytically solvable three-body collision system ($s$ wave) model is used to test two different theoretical methods. The first one is a configuration interaction expansion of the scattering wave function using a basis set of Generalized Sturmian Functions (GSF) with purely outgoing flux (CISF), introduced recently in A. L. Frapicinni, J. M. Randazzo, G. Gasaneo, and F. D. Colavecchia [J. Phys. B: At. Mol. Opt. Phys. 43, 101001 (2010)]. The second one is a finite element method (FEM) calculation performed with a commercial code. Both methods are employed to analyze different ways of modeling the asymptotic behavior of the wave function in finite computational domains. The asymptotes can be simulated very accurately by choosing hyperspherical or rectangular contours with the FEM software. In contrast, the CISF method can be defined both in an infinite domain or within a confined region in space. We found that the hyperspherical (rectangular) FEM calculation and the infinite domain (confined) CISF evaluation are equivalent. Finally, we apply these models to the Temkin-Poet approach of hydrogen ionization. DOI: http://dx.doi.org/10.1103/PhysRevA.84.052715 ©2011 American Physical Society

We describe astra (attosecond transitions), a close-coupling approach to molecular ionization that uses many-body transition-density matrices between ionic states with arbitrary spin and symmetry, in combination with hybrid integrals between Gaussian and numerical orbitals, to efficiently evaluate photoionization observables. Within the transition-density-matrix approach, the evaluation of interchannel coupling is exact and does not depend on the size of the configuration-interaction space of the ions. Thanks to these two crucial features, astra opens the way to studying highly correlated and comparatively large targets at a manageable computational cost. Here, astra is used to predict the parameters of bound and autoionizing states of the boron atom and of the ${\mathrm{N}}_2$ molecule, as well as the total photoionization cross section of boron, the nitrogen molecule $\left({\mathrm{N}}_2\right)$, and formaldehyde $\left({\mathrm{H}}_2\mathrm{CO}\right)$. Our results are in excellent agreement with theoretical and experimental values from the literature.

The photodouble ionization of the water molecule is studied at 20 eV excess energy in a combined experimental and theoretical investigation. In the experiments, two photoelectrons of equal kinetic energy are detected in coincidence after energy and angular selection. On the theoretical side, a generalized Sturmian function approach is implemented to describe accurately the correlated two-electron continuum, while separable products of Moccia orbitals [ J. Chem. Phys. 40, 2164 (1964)] are used for the initial electronic state of the water molecule. The theoretical triple-differential cross sections (TDCSs) are averaged over all possible molecular orientations in order to be compared with the experiments. The measured TDCSs display rich angular distributions that are in large part well reproduced by the adopted first-order treatment of the interaction with a two-active-electron target.

We studied the hydrogen atom as a system of two quantum particles in different confinement conditions; a spherical-impenetrable-wall cavity and a fullerene molecule cage. The motion refers to the center of spherical cavities and the Schrödinger equation is solved by means of a generalized Sturmian function expansion in spherical coordinates. The solutions present different properties from the ones described by the many models found in the literature, where the proton is fixed in space and only the electron is considered as a quantum particle. Our results show that the position of the proton (i.e. the center of mass of the H atom) is very sensitive to the confinement condition, and could vary substantially from one state to another, from being sharply centered to being localized outside the fullerene molecule. Interchange of the localization characteristics between the states when varying the strength of the fullerene cage and mass occurred through crossing phenomena.