3,721 research outputs found
Reductions of integrable equations on A.III-type symmetric spaces
We study a class of integrable non-linear differential equations related to
the A.III-type symmetric spaces. These spaces are realized as factor groups of
the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to
this symmetric space as an element of the reduction group and restrict generic
Lax operators to this symmetric space. The symmetries of the Lax operator are
inherited by the fundamental analytic solutions and give a characterization of
the corresponding Riemann-Hilbert data.Comment: 14 pages, 1 figure, LaTeX iopart styl
Asymptotic behavior of photoionization cross section in a central field
We demonstrate that the high energy nonrelativistic asymptotic for the
photoionization cross section in a central field can be expressed in
terms of the asymptotic of the Fourier transform of the field. We show
that the cross sections drop in the same way for the fields with the Coulomb
short distance behavior. The character of the cross sections energy behavior is
related to the analytical properties of the function . The cross sections
exhibit power drop for the potentials which have singularities an the real
axis. They suffer the exponential drop if has singularities in the
complex plane.Comment: 11 page
Asymptotic behavior of photoionization cross section in a central field. Ionization of the states
We continue our studies of the high energy nonrelativistic asymptotics for
the photoionization cross section of the systems bound by a central field
. We consider the bound states with the orbital momentum . We
show, that as well as for the states the asymptotics can be obtained
without solving of the wave equations for the bound and outgoing electrons. The
asymptotics of the cross sections is expressed in terms of the asymptotics of
the Fourier transform of the field and its derivative by
employing the Lippmann--Schwinger equation. The shape of the energy dependence
of the cross sections is determined by the analytical properties of the
potential . The cross sections exhibit power drop with the increase of
the photon energy for the potentials which have singularities on the
real axis. They experience exponential drop if has poles in the complex
plane. We trace the energy dependence of the ratios of the photoionization
cross sections for and electrons from the states with the same
principle quantum number. We apply the results to the physics of fullerenes.Comment: 14 page
Perturbative Symmetry Approach
Perturbative Symmetry Approach is formulated in symbolic representation.
Easily verifiable integrability conditions of a given equation are constructed
in the frame of the approach. Generalisation for the case of non-local and
non-evolution equations is disscused. Application of the theory to the
Benjamin-Ono and Camassa-Holm type equations is considered.Comment: 16 page
Photoionization of helium-like ions in asymptotic nonrelativistic region
The cross section for single K-shell ionization by a high-energy photon is
evaluated in the next-to-leading order of the nonrelativistic perturbation
theory with respect to the electron-electron interaction. The screening
corrections are of particular importance for light helium-like ions. Even in
the case of neutral He atom, our analytical predictions turn out to be in good
agreement with the numerical calculations performed with the use of the
sophisticated wave functions. The universal high-energy behavior is studied for
the ratio of double-to-single photoionization cross sections. We also discuss
the fast convergence of the perturbation theory over the reversed nuclear
charge number 1/Z.Comment: 12 pages, 1 figure. to be published in Physics Letters
About universal scalings in double K-shell photoionization
We discuss the problem of the universal scalings in the double ionization of
atomic K-shell electrons caused by absorption of a single photon. In
particular, we envisage the following questions: Under which conditions and up
to which accuracy the universal scalings are realized? Does it make sense to
talk about different physical mechanisms in the double-ionization process?
Finally, we present also the theoretical analysis of recent experimental
measurements performed on neutral atoms. As a testing ground, QED perturbation
theory is employed.Comment: 5 pages, 4 figure
X-Ray Fluorescence Determination of Trace Gold in an Ion-Exchange Resin
The use of portable X ray optics with a secondary radiator in the determination of trace gold in an ion exchange resin within the mass fraction range of 1–50 ppm is described. It is shown that the secondary radiator design with primary radiation filtering allows one to determine trace gold in an ion exchange resin when the mass fraction of gold is lower than 1 ppm
High-energy two-electron capture with emission of a single photon
We investigate the two-electron capture with emission of a single photon to the ground state in the Coulomb field of a heavy nucleus in its collision with a light atom. Describing electron-electron interactions in the bound state perturbatively, we obtained an analytical formula for the high-energy limit of the cross section. In combination with previous results obtained in the same approach we calculated the cross section in a broad interval of energies of the collision. We show that the amplitude of the process at high energy depends on the behavior of the bound state wave function near the triple coalescence point. We analyze the properties of the approximate wave functions which are necessary for the description of the high-energy limit
Microwave-induced magnetotransport phenomena in two-dimensional electron systems: Importance of electrodynamic effects
We discuss possible origins of recently discovered microwave induced
photoresistance oscillations in very-high-electron-mobility two-dimensional
electron systems. We show that electrodynamic effects -- the radiative decay,
plasma oscillations, and retardation effects, -- are important under the
experimental conditions, and that their inclusion in the theory is essential
for understanding the discussed and related microwave induced magnetotransport
phenomena.Comment: 5 pages, including 2 figures and 1 tabl
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