Discrete Dirac system: rectangular Weyl functions, direct and inverse problems

A transfer matrix function representation of the fundamental solution of the general-type discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szeg\"o recurrence, Schur coefficients and structured matrices are treated. Borg-Marchenko-type uniqueness theorem is derived. Inverse problems on the interval and semiaxis are solved.Comment: Section 2 is improved in the second version: some new results on Halmos extension are added and arguments are simplifie

Scattering of twisted relativistic electrons by atoms

The Mott scattering of high-energetic twisted electrons by atoms is investigated within the framework of the first Born approximation and Dirac's relativistic equation. Special emphasis is placed on the angular distribution and longitudinal polarization of the scattered electrons. In order to evaluate these angular and polarization properties we consider two experimental setups in which the twisted electron beam collides with either a single well-localized atom or macroscopic atomic target. Detailed relativistic calculations have been performed for both setups and for the electrons with kinetic energy from 10 keV to 1000 keV. The results of these calculations indicate that the emission pattern and polarization of outgoing electrons differ significantly from the scattering of plane-wave electrons and can be very sensitive to the parameters of the incident twisted beam. In particular, it is shown that the angular- and polarization-sensitive Mott measurements may reveal valuable information about, both the transverse and longitudinal components of the linear momentum and the projection of the total angular momentum of twisted electron states. Thus, the Mott scattering emerges as a diagnostic tool for the relativistic vortex beams.Comment: 12 pages, 4 figure

Electron-ion recombination of Si IV forming Si III: Storage-ring measurement and multiconfiguration Dirac-Fock calculations

The electron-ion recombination rate coefficient for Si IV forming Si III was measured at the heavy-ion storage-ring TSR. The experimental electron-ion collision energy range of 0-186 eV encompassed the 2p(6) nl n'l' dielectronic recombination (DR) resonances associated with 3s to nl core excitations, 2s 2p(6) 3s nl n'l' resonances associated with 2s to nl (n=3,4) core excitations, and 2p(5) 3s nl n'l' resonances associated with 2p to nl (n=3,...,infinity) core excitations. The experimental DR results are compared with theoretical calculations using the multiconfiguration Dirac-Fock (MCDF) method for DR via the 3s to 3p n'l' and 3s to 3d n'l' (both n'=3,...,6) and 2p(5) 3s 3l n'l' (n'=3,4) capture channels. Finally, the experimental and theoretical plasma DR rate coefficients for Si IV forming Si III are derived and compared with previously available results.Comment: 13 pages, 9 figures, 3 tables. Accepted for publication in Physical Review

Post-Wick theorems for symbolic manipulation of second-quantized expressions in atomic many-body perturbation theory

Manipulating expressions in many-body perturbation theory becomes unwieldily with increasing order of the perturbation theory. Here I derive a set of theorems for efficient simplification of such expressions. The derived rules are specifically designed for implementing with symbolic algebra tools. As an illustration, we count the numbers of Brueckner-Goldstone diagrams in the first several orders of many-body perturbation theory for matrix elements between two states of a mono-valent system.Comment: J. Phys. B. (in press); Mathematica packages available from http://wolfweb.unr.edu/homepage/andrei/WWW-tap/mathematica.htm

Semiseparable integral operators and explicit solution of an inverse problem for the skew-self-adjoint Dirac-type system

Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in terms of the Weyl function and a procedure to solve the inverse problem is given. The case of the generalized Weyl functions of the form $\phi(\lambda)\exp\{-2i\lambda D\}$, where $\phi$ is a strictly proper rational matrix function and $D=D^* \geq 0$ is a diagonal matrix, is treated in greater detail. Explicit formulas for the inversion of the corresponding semiseparable integral operators and recovery of the Dirac-type system are obtained for this case