Electron recombination with multicharged ions via chaotic many-electron states

We show that a dense spectrum of chaotic multiply excited eigenstates can play a major role in collision processes involving many-electron multicharged ions. A statistical theory based on chaotic properties of the eigenstates enables one to obtain relevant energy-averaged cross sections in terms of sums over single-electron orbitals. Our calculation of low-energy electron recombination of Au25+ shows that the resonant process is 200 times more intense than direct radiative recombination, which explains the recent experimental results of Hoffknecht [J. Phys. B 31, 2415 (1998)].

Many-body theory of positron-atom interactions

A many-body theory approach is developed for the problem of positron-atom scattering and annihilation. Strong electron- positron correlations are included nonperturbatively through the calculation of the electron-positron vertex function. It corresponds to the sum of an infinite series of ladder diagrams, and describes the physical effect of virtual positronium formation. The vertex function is used to calculate the positron-atom correlation potential and nonlocal corrections to the electron-positron annihilation vertex. Numerically, we make use of B-spline basis sets, which ensures rapid convergence of the sums over intermediate states. We have also devised an extrapolation procedure that allows one to achieve convergence with respect to the number of intermediate- state orbital angular momenta included in the calculations. As a test, the present formalism is applied to positron scattering and annihilation on hydrogen, where it is exact. Our results agree with those of accurate variational calculations. We also examine in detail the properties of the large correlation corrections to the annihilation vertex.

Secondary threshold laws for multiple ionization of atoms

We propose a physical mechanism that leads to the emergence of secondary threshold laws in processes of multiple ionization of atoms. We argue that the removal of n electrons (n>2) from a many-electron atom may proceed via intermediate resonant states of the corresponding doubly charged ion. For atoms such as rare gases, the density of such resonances in the vicinity of subsequent ionization thresholds is high. As a result, the appearance energies for multiply charged ions are close to these thresholds, while the effective power indices mu in the near-threshold energy dependence of the cross section, sigmaproportional toE(mu), are lower compared to those from the Wannier theory. This provides a possible explanation of the recent experimental results of B. Gstir [Nucl. Instrum. Methods Phys. Res. B 205, 413 (2003)].

Ionization energies of beryllium in strong magnetic fields: a frozen core approximation

An effective frozen core approximation has been developed and applied to the calculation of energy levels and ionization energies of the beryllium atom in magnetic field strengths up to 2.35 x 10(5) T. Systematic improvement over the existing results for the beryllium ground and low-lying states has been accomplished by taking into account most of the correlation effects in the four-electron system. To our knowledge, this is the first calculation of the electronic properties of the beryllium atom in a strong magnetic field carried out using a configuration interaction approximation and thus allowing a treatment beyond that of Hartree-Fock. Differing roles played by strong magnetic fields in intrashell correlation within different states are observed. In addition, possible ways to gain further improvement in the energies of the states of interest are proposed and discussed briefly.

Dissociative ionization of molecules in intense laser fields

Accurate and efficient grid based techniques for the solution of the time-dependent Schrodinger equation for few-electron diatomic molecules irradiated by intense, ultrashort laser pulses are described. These are based on hybrid finite-difference, Lagrange mesh techniques. The methods are applied in three scenarios, namely H-2(+) with fixed internuclear separation, H-2(+) with vibrating nuclei and H-2 with fixed internuclear separation and illustrative results presented.

Accurate computational methods for two-electron atom-laser interactions

We discuss the application of quantitatively accurate computational methods to the study of laser-driven two-electron atoms in short intense laser pulses. The fundamental importance of such calculations to the subject area is emphasized. Calculations of single- and double-electron ionization rates at 390 nm are presented. (C) 2001 Optical Society of America.

Quantum manifestations of scattering orbits in the scaled spectrum of a non-hydrogenic atom in crossed fields

Evidence for scattering closed orbits for the Rydberg electron of the singly excited helium atom in crossed electric and magnetic fields at constant scaled energy and constant scaled electric field strength has been found through a quantum calculation of the photo-excitation spectrum. A particular 3D scattering orbit in a mixed regular and chaotic region has been investigated and the hydrogenic 3D closed orbits composing it identified. To the best of our knowledge, this letter reports the first quantum calculation of the scaled spectrum of a non- hydrogenic atom in crossed fields.

Quantum manifestations of closed orbits in the photoexcitation scaled spectrum of the hydrogen atom in crossed fields

The scaled photoexcitation spectrum of the hydrogen atom in crossed electric and magnetic fields has been obtained by means of accurate quantum mechanical calculation using a new algorithm. Closed orbits in the corresponding classical system have also been obtained, using a new, efficient and practical searching procedure. Two new classes of closed orbit have been identified. Fourier transforming each photoexcitation quantum spectrum to yield a plot against scaled action has allowed direct comparison between peaks in such plots and the scaled action values of closed orbits, Excellent agreement has been found with all peaks assigned.

Multi-state CDW approximation to electron capture during slow p-H collisions

The first complete multi-state CDW close coupling calculations which use a fully normalized basis set are performed. The results obtained at impact energies in the region of 10 keV for total and n = 2 capture cross sections are in reasonably good accord with experiment despite the fact that only the ground states of both species and the n = 2 states of the projectile are incorporated into the model. The theory has significant advantages over other atomic and molecular expansions which may require extensive bases to obtain similar accuracy.

Ionization from the outer shell of Ar by proton impact

Recent results for proton-argon total ionization cross sections [Kirchner Phys. Rev. Lett. 79, 1658 (1997)] show large disagreement between theory and experiment for energies below 80 keV. To address this problem we have employed a recently developed theoretical method with a more pragmatic approach to the charge screening both in the initial and final channels. The target is considered as a one-electron atom and the interactions between this active electron and remaining target electrons are treated by a model potential including both short- and long-range effects. In the final channel the usual product of two continuum distorted wave functions each associated with a distinct electron-nucleus interaction is used. New results in the present calculation show good agreement in total cross sections for the energy range 10-300 keV with the measurement of Rudd [Rev. Mod. Phys. 57, 965 (1985)].

Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.

Semiclassical-quantal approach to the near-threshold ionization of hydrogen

A recent improved version of the semiclassical-quantal approach has been applied to the e(-)-H near-threshold ionization for theta (12) = 180 degrees geometry. It is found, that unlike other sophisticated theoretical methods such as distorted wave theory or convergent close-coupling calculation, the present relatively simpler approach produces correct behavior and numerical values for the triple-differential cross sections. We compare our results with recent absolute measurements and accurate numerical calculations at 2 eV and 4 eV above the threshold at constant theta (12) geometry.

Electron impact ionization of He above the threshold

Near-threshold ionization of He has been studied by using a uniform semiclassical wavefunction for the two outgoing electrons in the final channel. The quantum mechanical transition amplitude for the direct and exchange scattering derived earlier by using the Kohn variational principle has been used to calculate the triple differential cross sections. Contributions from singlets and triplets are critically examined near the threshold for coplanar asymmetric geometry with equal energy sharing by the two outgoing electrons. It is found that in general the tripler contribution is much smaller compared to its singlet counterpart. However, at unequal scattering angles such as theta (1) = 60 degrees, theta (2) = 120 degrees the smaller peaks in the triplet contribution enhance both primary and secondary TDCS peaks. Significant improvements of the primary peak in the TDCS are obtained for the singlet results both in symmetric and asymmetric geometry indicating the need to treat the classical action variables without any approximation. Convergence of these cross sections are also achieved against the higher partial waves. Present results are compared with absolute and relative measurements of Rosel et al (1992 Phys. Rev. A 46 2539) and Selles et al (1987 J. Phys. B. At. Mel. Phys. 20 5195) respectively.