Relativistic electronic dressing

We study the effects of the relativistic electronic dressing in laser-assisted electron-hydrogen atom elastic collisions. We begin by considering the case when no radiation is present. This is necessary in order to check the consistency of our calculations and we then carry out the calculations using the relativistic Dirac-Volkov states. It turns out that a simple formal analogy links the analytical expressions of the differential cross section without laser and the differential cross section in presence of a laser field.Comment: 11 pages, 18 figures, Late

R-matrix Floquet theory for laser-assisted electron-atom scattering

A new version of the R-matrix Floquet theory for laser-assisted electron-atom scattering is presented. The theory is non-perturbative and applicable to a non-relativistic many-electron atom or ion in a homogeneous linearly polarized field. It is based on the use of channel functions built from field-dressed target states, which greatly simplifies the general formalism.Comment: 18 pages, LaTeX2e, submitted to J.Phys.

Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory

\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation which uses as input data not only the elements of a sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates $\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit incorporation of the information contained in the truncation error estimates makes this and related transformations potentially much more powerful than for instance Pad\'{e} approximants. Special cases of the new transformation are sequence transformations introduced by Levin [Int. J. Comput. Math. B \textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189 - 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A \textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations - explicit expressions, recurrence formulas, explicit expressions in the case of special remainder estimates, and asymptotic order estimates satisfied by rational approximants to power series - is formulated in terms of hitherto unknown mathematical properties of the new transformation introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of Mathematical Physic

NONCOPLANAR (E,2E) REACTIONS

JETZKE S, Faisal F. NONCOPLANAR (E,2E) REACTIONS. JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS. 1992;25(11):L269-L274.Using a two-electron wavefunction satisfying the exact asymptotic boundary conditions together with a recently discussed model, based on the multiple scattering approach, we investigate the electron impact ionization of atomic hydrogen in a non-coplanar scattering geometry. We show that the magnitude as well as the structure of the triple differential cross sections change significantly when the momentum of one of the outgoing electrons is rotated out of the plane spanned by the incoming and the second outgoing momentum. The non-coplanar angular correlations are found to exhibit two general symmetry properties

COULOMB CORRELATIONS IN ELECTRON AND POSITRON IMPACT IONIZATION OF HYDROGEN AT INTERMEDIATE AND HIGHER ENERGIES

JETZKE S, Faisal F. COULOMB CORRELATIONS IN ELECTRON AND POSITRON IMPACT IONIZATION OF HYDROGEN AT INTERMEDIATE AND HIGHER ENERGIES. JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS. 1992;25(7):1543-1558.Investigating the relation between the asymptotic condition and the dynamic Coulomb correlation for single and multiple ionization we discuss a complete set of spatially separable N-electron final-state wavefunctions, satisfying multiple ionization boundary conditions. We apply these results to electron and positron impact ionization of atomic hydrogen in the energy range 54.4 and 250 eV on the basis of a parameter-free model formulated within the scope of the multiple scattering approach. A comparison between our results and available experimental data and alternative theoretical calculations are made and discussed. The role of exchange is also investigated. The contribution of exchange in the triple differential cross section is found to be virtually negligible whereas the asymmetry parameter A is significantly affected

ABOVE-THRESHOLD ELECTRON EJECTION SPECTRA

CHEN B, Faisal F, JETZKE S, Lutz HO, SCANZANO P. ABOVE-THRESHOLD ELECTRON EJECTION SPECTRA. PHYSICAL REVIEW A. 1987;36(8):4091-4094

ROLE OF FINAL-STATE CORRELATIONS IN ELECTRON AND POSITRON-IMPACT IONIZATION OF H AND HE

BECKER A, JETZKE S, Faisal F. ROLE OF FINAL-STATE CORRELATIONS IN ELECTRON AND POSITRON-IMPACT IONIZATION OF H AND HE. In: Hyperfine Interactions. HYPERFINE INTERACTIONS. Vol 89. BALTZER SCI PUBL BV; 1994: 83-93.Single ionization of H and double ionization of He are investigated using a multiple scattering approach and a correlated final state wavefunction, which satisfies the correct asymptotic condition for the electron and positron impact ionization of atoms. Analyses presented here show the influence of the Coulomb correlations in the final state on the three- and fivefold differential cross sections. Situations are discussed in which consideration of every pair of electron-electron and/or electron-positron correlation in the final state becomes important for physically satisfactory results

ELECTRON-IMPACT IONIZATION OF ATOMIC-HYDROGEN

JETZKE S, ZAREMBA J, Faisal F. ELECTRON-IMPACT IONIZATION OF ATOMIC-HYDROGEN. ZEITSCHRIFT FUR PHYSIK D-ATOMS MOLECULES AND CLUSTERS. 1989;11(1):63-69

SIMULTANEOUS ELECTRON PHOTON EXCITATION OF HYDROGEN AND HELIUM

JETZKE S, Faisal F, HIPPLER R, Lutz HO. SIMULTANEOUS ELECTRON PHOTON EXCITATION OF HYDROGEN AND HELIUM. ZEITSCHRIFT FUR PHYSIK A-HADRONS AND NUCLEI. 1984;315(3):271-276