A. L. Frapiccini

Explicit schemes for time propagating many-body wave functions

Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical ab initio solution of the time-dependent Schrodinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first-order differential equations that are characterized by a high degree of stiffness. In this contribution, we analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy, however, differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunlas or Arnoldis algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. In this contribution, we consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time-independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness which makes the time integration extremely difficult. In the case of the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.

Solving three-body-breakup problems with outgoing-flux asymptotic conditions

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.

Sturmian bases for two-electron systems in hyperspherical coordinates

We give a detailed account of an

Multiresolution schemes for time-scaled propagation of wave packets

\it{ab}

Double Photoionization of confined atoms in n-walled fullerenes

\it{initio}

Ground state for two-electron atoms in exponential-cosine-screened Coulomb potentials

spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron-electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present case, we use Coulomb sturmian functions of half integer angular momentum. We show that, in the case of H

Generating optimal Sturmian basis functions for atomic problems

^-

Discrete sets of Sturmian functions applied to two-electron atoms

, the accuracy of the energy and the width of the resonance states obtained through a single diagonalization of the Hamiltonian, is comparable to the values given by state-of-the-art methods while using a much smaller basis set. In addition, we show that precise values of the electric-dipole oscillator strengths for

Time scaling with efficient time-propagation techniques for atoms and molecules in pulsed radiation fields

S\rightarrow P