Xiaoxu Guan

Complete Breakup of the Helium Atom by Proton and Antiproton Impact

We present a fully ab initio, nonperturbative, time-dependent approach to describe single and double ionization of helium by proton and antiproton impact. The problem is discretized by a flexible finite-element discrete-variable representation on the radial grid. Good agreement with the most recent experimental data for absolute angle-integrated cross sections is obtained for projectile energies between 3 keV and 6 MeV. Also, angle-differential cross sections for two-electron ejection are predicted for a proton impact energy of 6 MeV. The time evaluation of the ionization process is portrayed by displaying the electron density as a function of the projectile location.

General approach to few-cycle intense laser interactions with complex atoms

A general ab initio and nonperturbative method to solve the time-dependent Schroedinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom, i.e., beyond the models of quasi-one-electron or quasi-two-electron targets, is described. The field-free Hamiltonian and the dipole matrices are generated using a flexible B-spline R-matrix method. This numerical implementation enables us to construct term-dependent, nonorthogonal sets of one-electron orbitals for the bound and continuum electrons. The solution of the TDSE is propagated in time using the Arnoldi-Lanczos method, which does not require the diagonalization of any large matrices. The method is illustrated by an application to the multiphoton excitation and ionization of Ne atoms. Good agreement with R-matrix Floquet calculations for the generalized cross sections for two-photon ionization is achieved.

A time-dependent B-spline R-matrix approach to double ionization of atoms by XUV laser pulses

We present an ab initio and non-perturbative time-dependent approach to the problem of double ionization of a general atom driven by intense XUV laser pulses. After using a highly flexible B-spline R-matrix method to generate field-free Hamiltonian and electric dipole matrices, the initial state is propagated in time using an efficient Arnoldi–Lanczos scheme. Test calculations for double ionization of He by a single laser pulse yield good agreement with benchmark results obtained with other methods. The method is then applied to two-colour pump–probe processes, for which momentum and energy distributions of the two outgoing electrons are presented.

ALTDSE: An Arnoldi–Lanczos program to solve the time-dependent Schrödinger equation

Abstract We describe a general ab initio and non-perturbative method to solve the time-dependent Schrodinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom. While the field-free Hamiltonian and the dipole matrices may be generated using an arbitrary primitive basis, they are assumed to have been transformed to the eigenbasis of the problem before the solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. Probabilities for survival of the ground state, excitation, and single ionization can be extracted from the propagated wavefunction. Program summary Program title: ALTDSE Catalogue identifier: AEDM_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEDM_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2154 No. of bytes in distributed program, including test data, etc.: 30 827 Distribution format: tar.gz Programming language: Fortran 95. [A Fortran 2003 call to “flush” is used to simplify monitoring the output file during execution. If this function is not available, these statements should be commented out.]. Computer: Shared-memory machines Operating system: Linux, OpenMP Has the code been vectorized or parallelized?: Yes RAM: Several Gb, depending on matrix size and number of processors Supplementary material: To facilitate the execution of the program, Hamiltonian field-free and dipole matrix files are provided. Classification: 2.5 External routines: LAPACK, BLAS Nature of problem: We describe a computer program for a general ab initio and non-perturbative method to solve the time-dependent Schrodinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom [1,2]. The probabilities for survival of the initial state, excitation of discrete states, and single ionization due to multi-photon processes can be obtained. Solution method: The solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. The field-free Hamiltonian and the dipole matrices, originally generated in an arbitrary basis (e.g., the flexible B -spline R -matrix (BSR) method with non-orthogonal orbitals [3]), must be provided in the eigenbasis of the problem as input. Restrictions: The present program is restricted to a 1 S e initial state and linearly polarized light. This is the most common situation experimentally, but a generalization is straightforward. Running time: Several hours, depending on the number of threads used. References: [1] X. Guan, O. Zatsarinny, K. Bartschat, B.I. Schneider, J. Feist, C.J. Noble, Phys. Rev. A 76 (2007) 053411. [2] X. Guan, C.J. Noble, O. Zatsarinny, K. Bartschat, B.I. Schneider, Phys. Rev. A 78 (2008) 053402. [3] O. Zatsarinny, Comput. Phys. Comm. 174 (2006) 273.

Two-photon double ionization ofH2in intense femtosecond laser pulses

Triple-differential cross sections for two-photon double ionization of molecular hydrogen are presented for a central photon energy of 30 eV. The calculations are based on a fully {\it ab initio}, nonperturbative, approach to the time-dependent Schroedinger equation in prolate spheroidal coordinates, discretized by a finite-element discrete-variable-representation. The wave function is propagated in time for a few femtoseconds using the short, iterative Lanczos method to study the correlated response of the two photoelectrons to short, intense laser radiation. The current results often lie in between those of Colgan {\it et al} [J. Phys. B {\bf 41} (2008) 121002] and Morales {\it et al} [J. Phys. B {\bf 41} (2009) 134013]. However, we argue that these individual predictions should not be compared directly to each other, but preferably to experimental data generated under well-defined conditions.

A new Fortran 90 program to compute regular and irregular associated Legendre functions

Abstract We present a modern Fortran 90 code to compute the regular P l m ( x ) and irregular Q l m ( x ) associated Legendre functions for all x ∈ ( − 1 , + 1 ) (on the cut) and | x | > 1 and integer degree (l) and order (m). The code applies either forward or backward recursion in (l) and (m) in the stable direction, starting with analytically known values for forward recursion and considering both a Wronskian based and a modified Millers method for backward recursion. While some Fortran 77 codes existed for computing the functions off the cut, no Fortran 90 code was available for accurately computing the functions for all real values of x different from x = ± 1 where the irregular functions are not defined. Program summary Program title: Associated Legendre Functions Catalogue identifier: AEHE_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHE_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 6722 No. of bytes in distributed program, including test data, etc.: 310 210 Distribution format: tar.gz Programming language: Fortran 90 Computer: Linux systems Operating system: Linux RAM: bytes Classification: 4.7 Nature of problem: Compute the regular and irregular associated Legendre functions for integer values of the degree and order and for all real arguments. The computation of the interaction of two electrons, 1 / | r 1 − r 2 | , in prolate spheroidal coordinates is used as one example where these functions are required for all values of the argument and we are able to easily compare the series expansion in associated Legendre functions and the exact value. Solution method: The code evaluates the regular and irregular associated Legendre functions using forward recursion when | x | 1 starting the recursion with the analytically known values of the first two members of the sequence. For values of the argument | x | 1 , the upward recursion over the degree for the regular functions is numerically stable. For the irregular functions, backward recursion must be applied and a suitable method of starting the recursion is required. The program has two options; a modified version of Millers algorithm and the use of the Wronskian relation between the regular and irregular functions, which was the method considered in [1]. Both approaches require the computation of a continued fraction to begin the recursion. The Wronskian method (which can also be described as a modified Millers method) is a convenient method of computations when both the regular and irregular functions are needed. Running time: The example tests provided take a few seconds to run. References: [1] A. Gil, J. Segura, A code to evaluate prolate and oblate spheroidal harmonics, Comput. Phys. Commun. 108 (1998) 267–278.

Alignment effects in two-photon double ionization of H2in femtosecond xuv laser pulses

Triple-differential cross sections for two-photon double ionization of the aligned hydrogen molecule at the equilibrium distance are presented for a central photon energy of 30 eV. The temporal response of the laser-driven molecule is investigated by solving the time-dependent Schroedinger equation in full dimensionality using two-center elliptical coordinates and a finite-element discrete-variable-representation approach. The molecular orientation is found to have a strong effect on the emission modes of the two correlated photoelectrons. This molecular effect is most noticeable when the molecular axis and the laser polarization vector are oriented parallel to each other. For intermediate cases between the parallel and perpendicular geometries, the dominant emission modes for two-electron ejection oscillate between those for the two extreme cases. The contributions from different ionization channels are also analyzed in detail. Depending on the emission direction of the reference electron, the interference contributions from the various channels can be constructive or destructive at small alignment angles, while they always contribute constructively to the triple-differential cross sections near the perpendicular geometry.

Time-dependent B-spline R-matrix approach to double ionization of atoms by XUV laser pulses

We present an ab initio and non-perturbative time-dependent approach to the problem of double ionization of a general atom driven by intense XUV laser pulses. After using a highly flexible B-spline R-matrix method to generate field-free Hamiltonian and electric dipole matrices, the initial state is propagated in time using an efficient Arnoldi-Lanczos scheme. Example results for momentum and energy distributions of the two outgoing electrons in two-color pump-probe processes of He are presented.

Electron-impact ionization of magnesium

A distorted-wave method as well as a hybrid approach, in which the description of the ejected-electron–residual-ion interaction is improved through a close-coupling expansion, has been applied to calculate electron-impact ionization of magnesium atoms. For comparison with currently available experimental and theoretical data for this process, we show that only a few partial waves need to be calculated by sophisticated methods, even if a large number of partial waves are required for convergence. Suggestions are made for additional experiments, which should provide even more sensitive tests of the computational models.

Photoionization of H+2 by intense elliptically polarized radiation

We analyze the photoionization of the H+2 ion by elliptically polarized laser light as a function of the pulse duration. Angular distributions of the ejected electron for a variety of laser parameters are presented.