60 research outputs found
Photoionization accompanied by excitation at intermediate photon energies
We calculate the photoionization with excitation-to photoionization ratios
for atomic helium and heliumlike ions at intermediate values of the photon
energies. The final state interactions between the electrons are included in
the lowest order of their Sommerfeld parameter. This enables us, in contrast to
purely numerical calculations to investigate the roles of various mechanisms
contributing beyond the high energy limit. The system of the two bound
electrons is described by the functions obtained by the Correlation Function
Hyperspherical Harmonic Method. For the case of heliumlike ions we present the
high energy limits as power expansion in inverse charge of the nucleus. We
analyse the role of excitation of states with the nonzero orbital momenta.Comment: 3 figure
Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators
Ground state energies and wave functions of quartic and pure quartic
oscillators are calculated by first casting the Schr\"{o}dinger equation into a
nonlinear Riccati form and then solving that nonlinear equation analytically in
the first iteration of the quasilinearization method (QLM). In the QLM the
nonlinear differential equation is solved by approximating the nonlinear terms
by a sequence of linear expressions. The QLM is iterative but not perturbative
and gives stable solutions to nonlinear problems without depending on the
existence of a smallness parameter. Our explicit analytic results are then
compared with exact numerical and also with WKB solutions and it is found that
our ground state wave functions, using a range of small to large coupling
constants, yield a precision of between 0.1 and 1 percent and are more accurate
than WKB solutions by two to three orders of magnitude. In addition, our QLM
wave functions are devoid of unphysical turning point singularities and thus
allow one to make analytical estimates of how variation of the oscillator
parameters affects physical systems that can be described by the quartic and
pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl
Two-electron photoionization of endohedral atoms
Using as an example, we demonstrate that static potential of the
fullerene core essentially alters the cross section of the two-electron
ionization differential in one-electron energy . We found that at high photon energy prominent oscillations
appear in it due to reflection of the second, slow electron wave on the shell, which "dies out" at relatively high values, of about
23 two-electron ionization potentials. The results were presented for
ratios , where is the two-electron differential
photoionization cross section. We have calculated the ratio , that accounts for
reflection of both photoelectrons by the shell. We have calculated
also the value of two-electron photoionization cross section and found that this value is close to that of an isolated
atom.Comment: 13 pages, 4 figure
Relativistic quasipotential equations with u-channel exchange interactions
Various quasipotential two-body scattering equations are studied at the
one-loop level for the case of - and -channel exchange potentials. We
find that the quasipotential equations devised to satisfy the one-body limit
for the -channel exchange potential can be in large disagreement with the
field-theoretical prediction in the case of -channel exchange interactions.
Within the spectator model, the description of the -channel case improves if
another choice of the spectator particle is made. Since the appropriate choice
of the spectator depends strongly on the type of interaction used, one faces a
problem when both types of interaction are contained in the potential.
Equal-time formulations are presented, which, in the light-heavy particle
system corresponding to the mass situation of the system, approximate
in a reasonable way the field-theoretical result for both types of
interactions.Comment: Revtex, 20 pages, 12 PostScript figures, to appear in Phys. Rev.
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