O. Chuluunbaatar

(e,2e) ionization of helium and the hydrogen molecule: signature of two-centre interference effects

Relative (e,2e) triply differential cross sections (TDCS) are measured for the ionization of the helium atom and the hydrogen molecule in coplanar asymmetric geometry at a scattered electron energy of 500 eV and ejected electron energies of 205, 74 and 37 eV. The He experimental results are found to be in very good agreement with convergent close-coupling calculations (CCC). The H2 experimental results are compared with two state-of-the-art available theoretical models for treating differential electron impact ionization of molecules. Both models yield an overall good agreement with experiments, except for some intensity deviations in the recoil region. Similar (e,2e) works were recently published on H2 with contrasted conclusions to the hypothesis that the two H nuclei could give rise to an interference pattern in the TDCS structure. Murray (2005 J. Phys. B: At. Mol. Opt. Phys. 38 1999) found no evidence for such an effect, whereas Milne-Brownlie et al (2006 Phys. Rev. Lett. 96 233201) reported its indirect observation. In this work, based on a direct comparison between experimental results for He and H2, we observe an oscillatory pattern due to these interference effects, and for the first time the destructive or constructive character of the interference is observed, depending on the de Broglie wavelength of the ejected electron wave. The experimental finding is in good agreement with the theoretical prediction by Stia et al (2003 J. Phys. B: At. Mol. Opt. Phys. 36 L257).

KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

A FORTRAN 77 program is presented which calculates energy values, reaction matrix and corresponding radial wave functions in a coupledchannel approximation of the hyperspherical adiabatic approach. In this approach, a multi-dimensional Schrodinger equation is reduced to a system of the coupled second-order ordinary differential equations on the finite interval with homogeneous boundary conditions of the third type. The resulting system of radial equations which contains the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite-element method. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials. Program summary

ODPEVP: A program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem ✩

article i nfo abstract A FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm- Liouville problem with the parametric third type boundary conditions on the finite interval. The program calculates also potential matrix elements - integrals of the eigenfunctions multiplied by their first derivatives with respect to the parameter. Eigenvalues and matrix elements computed by the ODPEVP program can be used for solving the bound state and multi-channel scattering problems for

POTHMF: A program for computing potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field☆

A FORTRAN 77 program is presented which calculates with the relative machine precision potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field. The potential curves are eigenvalues corresponding to the angular oblate spheroidal functions that compose adiabatic basis which depends on the radial variable as a parameter. The matrix elements of radial coupling are integrals in angular variables of the following two types: product of angular functions and the first derivative of angular functions in parameter, and product of the first derivatives of angular functions in parameter, respectively. The program calculates also the angular part of the dipole transition matrix elements (in the length form) expressed as integrals in angular variables involving product of a dipole operator and angular functions. Moreover, the program calculates asymptotic regular and irregular matrix solutions of the coupled adiabatic radial equations at the end of interval in radial variable needed for solving a multi-channel scattering problem by the generalized R-matrix method. Potential curves and radial matrix elements computed by the POTHMF program can be used for solving the bound state and multi-channel scattering problems. As a test desk, the program is applied to the calculation of the energy values, a short-range reaction matrix and corresponding wave functions with the help of the KANTBP program. Benchmark calculations for the known photoionization cross-sections are presented.

Triply differential (e,2e) cross sections for ionization of the nitrogen molecule at large energy transfer

Measurements of the (e,2e) triply differential cross sections (TDCS) are presented for the ionization of the nitrogen molecule in coplanar asymmetric geometry at an incident energy of about 600 eV and a large energy transfer to the target. The experimental results are compared with state-of-the-art available theoretical models for treating differential electron impact ionization of molecules. The experimental TDCS are characterized by a shift towards larger angles of the angular distribution with respect to the momentum transfer direction, and by a large intensity in the recoil region, especially for ionization of the ‘inner’ 2σ g molecular orbital. Such shifts and intensity enhancement are not predicted by the model calculations which rather yield a TDCS symmetrically distributed around the momentum transfer direction. (Some figures in this article are in colour only in the electronic version)

Calculation of a hydrogen atom photoionization in a strong magnetic field by using the angular oblate spheroidal functions

A new efficient method for calculating the photoionization of a hydrogen atom in a strong magnetic field is developed based on the Kantorovich approach to the parametric boundary problems in spherical coordinates using the orthogonal basis set of angular oblate spheroidal functions. The progress as compared with our previous paper (Dimova M G, Kaschiev M S and Vinitsky S I 2005 J. Phys. B: At. Mol. Opt. Phys. 38 2337–52) consists of the development of the Kantorovich method for calculating the wavefunctions of a continuous spectrum, including the quasi-stationary states imbedded in the continuum. Resonance transmission and total reflection effects for scattering processes of electrons on protons in a homogenous magnetic field are manifested. The photoionization cross sections found for the ground and excited states are in good agreement with the calculations by other authors and demonstrate correct threshold behavior. The estimates using the calculated photoionization cross section show that due to the quasi-stationary states the laser-stimulated recombination may be enhanced by choosing the optimal laser frequency.

Channeling problem for charged particles produced by confining environment

Channeling problem produced by confining environment that leads to resonance scattering of charged particles via quasistationary states imbedded in the continuum is examined. Nonmonotonic dependence of physical parameters on collision energy and/or confining environment due to resonance transmission and total reflection effects is confirmed that can increase the rate of recombination processes. The reduction of the model for two identical charged ions to a boundary problem is considered together with the asymptotic behavior of the solution in the vicinity of pair-collision point and the results of R-matrix calculations. Tentative estimations of the enhancement factor and the total reflection effect are discussed.

Symbolic-numerical algorithms to solve the quantum tunneling problem for a coupled pair of ions

Symbolic-numerical algorithms for solving a boundary value problem (BVP) for the 2D Schrodinger equation with homogeneous third type boundary conditions to study the quantum tunneling model of a coupled pair of nonidentical ions are described. The Kantorovich reduction of the above problem with non-symmetric long-range potentials to the BVPs for sets of the second order ordinary differential equations (ODEs) is given by expanding solution over the one-parametric set of basis functions. Symbolic algorithms for evaluation of asymptotics of the basis functions, effective potentials, and linear independent solutions of the ODEs in the form of inverse power series of independent variable at large values are given by using appropriate etalon equations. Benchmark calculation of quantum tunneling problem of coupled pair of identical ions through Coulomb-like barrier is presented.

Uncoupled correlated calculations of helium isoelectronic bound states

An uncoupled correlated variational method for the calculation of helium isoelectronic bound states is proposed. New projective coordinates s = r1 + r2, v = (r12) / (r1 + r2), w = (r1-r2) / (r12) are introduced instead of the conventional ones s = r1 + r2, t = r1-r2, u = r12. All matrix elements of the total Hamiltonian and the weight function are expressed as simple products of three one-dimensional integrals. The variational basis is formed by a set of Laguerre polynomials with a single nonlinear parameter and two sets of Jacobi polynomials for the projective coordinates s,v,w, respectively. It provides a reasonable rate of convergence of the energy, E = E(N), with respect to a number N of the basis components of the eigenvector. The proposed method yields the best available energies for the isoelectronic ground states of the helium atom. New estimations of the isotope helium ground states are also presented.

The application of adiabatic method for the description of impurity states in quantum nanostructures

In the framework of effective mass approximation the application of adiabatic method for the description of impurity states in quantum dots, wires and wells with parabolic confinement potential as well as rectangular infinitely-high potential is presented. A rate of convergence of the method and efficiency of the proposed program complex for solving a boundary value problem, realized by the finite element method, is demonstrated on examples of calculation of spectral and optical characteristics of the considered quantum nanostructures.