190 research outputs found
Back-to-back emission of the electrons in double photoionization of helium
We calculate the double differential distributions and distributions in
recoil momenta for the high energy non-relativistic double photoionization of
helium. We show that the results of recent experiments is the pioneering
experimental manifestation of the quasifree mechanism for the double
photoionization, predicted long ago in our papers. This mechanism provides a
surplus in distribution over the recoil momenta at small values of the latter,
corresponding to nearly "back-to-back" emission of the electrons. Also in
agreement with previous analysis the surplus is due to the quadrupole terms of
the photon-electron interaction. We present the characteristic angular
distribution for the "back-to-back" electron emission. The confirmation of the
quasifree mechanism opens a new area of exiting experiments, which are expected
to increase our understanding of the electron dynamics and of the bound states
structure. The results of this Letter along with the recent experiments open a
new field for studies of two-electron ionization not only by photons but by
other projectiles, e.g. by fast electrons or heavy ions.Comment: 10 pages, 2 figure
Computation of microdosimetric distributions for small sites
Object of this study is the computation of microdosimetric functions for sites which are too small to permit experimental determination of the distributions by Rossi-counters. The calculations are performed on simulated tracks generated by Monte-Carlo techniques.
The first part of the article deals with the computational procedure. The second part presents numerical results for protons of energies 0.5, 5, 20 MeV and for site diameters of 5, 10, 100 nm
Qualitative difference between the angular anisotropy parameters in fast electron scattering and photoionization
It is demonstrated for the first time that in spite of well known big
similarities between atomic ionization by photons and fast electrons, a
qualitative difference exists in angular anisotropy parameters of electrons
knocked out in these processes. The difference is disclosed here and attributed
to distinction between normal (transverse) and virtual (longitudinal) photons.
Formulas are derived for dipole and non-dipole angular anisotropy parameters in
fast electronatom scattering. The ratio of quadrupole-to-dipole matrix elements
is determined by the parameter \omega R/v << 1 where \omega is the transferred
in collision energy, R is the ionized shell radius and v is the speed of
projectile. This factor can be much bigger than in the case of photoionization,
where one has the speed of light c that is much bigger than v . We illustrate
general formulas by concrete results for outer s-subshells of noble gas atoms
Ar and Xe. Even for very small transferred momentum q, in the so-called optical
limit, the deviation from photoionization case is prominent and instructive.Comment: 8 pages, 3 figures. arXiv admin note: substantial text overlap with
arXiv:1012.546
Electron impact double ionization of helium from classical trajectory calculations
With a recently proposed quasiclassical ansatz [Geyer and Rost, J. Phys. B 35
(2002) 1479] it is possible to perform classical trajectory ionization
calculations on many electron targets. The autoionization of the target is
prevented by a M\o{}ller type backward--forward propagation scheme and allows
to consider all interactions between all particles without additional
stabilization. The application of the quasiclassical ansatz for helium targets
is explained and total and partially differential cross sections for electron
impact double ionization are calculated. In the high energy regime the
classical description fails to describe the dominant TS1 process, which leads
to big deviations, whereas for low energies the total cross section is
reproduced well. Differential cross sections calculated at 250 eV await their
experimental confirmation.Comment: LaTeX, 22 pages, 10 figures, submitted to J. Phys.
Time-Fractional KdV Equation: Formulation and Solution using Variational Methods
In this work, the semi-inverse method has been used to derive the Lagrangian
of the Korteweg-de Vries (KdV) equation. Then, the time operator of the
Lagrangian of the KdV equation has been transformed into fractional domain in
terms of the left-Riemann-Liouville fractional differential operator. The
variational of the functional of this Lagrangian leads neatly to Euler-Lagrange
equation. Via Agrawal's method, one can easily derive the time-fractional KdV
equation from this Euler-Lagrange equation. Remarkably, the time-fractional
term in the resulting KdV equation is obtained in Riesz fractional derivative
in a direct manner. As a second step, the derived time-fractional KdV equation
is solved using He's variational-iteration method. The calculations are carried
out using initial condition depends on the nonlinear and dispersion
coefficients of the KdV equation. We remark that more pronounced effects and
deeper insight into the formation and properties of the resulting solitary wave
by additionally considering the fractional order derivative beside the
nonlinearity and dispersion terms.Comment: The paper has been rewritten, 12 pages, 3 figure
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