26 research outputs found
About disposition of energy levels
The unique properties of central potential of the form were studied using the recently developed critical parameter
technique. The particular cases of and yield,
respectively, the exponential and Yukawa potentials widely used in the atomic,
molecular and nuclear physics. We found different behavior of the energy levels
of this potential for three different ranges of the value of . For
it was found that the energy of bound states with the same
principal quantum number decreases with increasing angular momentum .
The Gaussian and Woods-Saxon potentials also show this behavior. On the
contrary, for increasing gives a higher energy,
resembling the Hulthen potential. However, a potential with
possesses mixed properties, which give rise to several interesting results. For
one, the order of energy levels with different quantum numbers is not preserved
when varying the parameter . This leads to a quantum degeneracy of the
states, and in fact, for a given value of we can find the values
for which two energy levels with different quantum numbers
coincide. Another interesting phenomena is the possibility, for some values of
in this range, for two new energy levels with different quantum
numbers to appear simultaneously when reaches their common critical
value.Comment: 10 pages, 3 table
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
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
Angular distributions of secondary electrons in fast particle-atom scattering
We present the angular distribution of electrons knocked out from an atom in
a fast charge particle collision at small momentum transfer. It is determined
not only by dipole but also by quadrupole transitions, the contribution of
which can be considerably enhanced as compared to the case of photoionization.
There the non-dipole parameters are suppressed as compared to the dipole ones
by the parameter \omega R/c << 1, where is the photon energy, R is the ionized
shell radius and c is the speed of light. This suppression in fast
electron-atom collisions can be considerably reduced: the corresponding
expansion parameter \omega R/ \nu << 1 is much bigger than in photoionization,
since the speed of the incoming electron is much smaller than c. In formation
of the angular distribution it is decisively important that the ionizing field
in collision process is longitudinal, while in photoionization - it is
transversal.
We illustrate the general formulas by concrete results for outer s-, p-, and
some nd-subshells of multi-electron noble gas atoms Ar, Kr and Xe, at several
transferred momentum values: q=0.0, 0.1, 1.1, 2.1. Even for very small
transferred momentum q, i.e. in the so-called optical limit, the deviations
from the photoionization case are prominent.Comment: arXiv admin note: substantial text overlap with arXiv:1012.5465 and
arXiv:1108.101
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