Threshold laws in (multiple) ionization processes
(with J.M. Rost)
In ionization processes where three or more charged particles end up in the
continuum, the mutual influence those particles exert on each other due to
the Coulomb interaction and its consequences for the fragmentation behavior
is of interest. Naturally, these interaction effects are least pronounced in
the limit of high energies, where they can be treated perturbatively. On
the other hand, when (in the case of ionization by charged particle impact)
the projectile is very slow, all particles have to be treated on an equal
footing. Nevertheless, Wannier showed as early as 1953 in a seminal paper
that exactly in this low energy limit certain aspects of the behavior of
the ionization cross sections can be treated analytically. Originally, the idea
that the 'threshold law', i.e. the energy dependence of the cross section
at threshold, is relatively easier to treat than the whole cross section, goes
back to Wigner who applied it to two-particle break-up processes for different
kinds of interaction potentials. Wannier applied this idea to the case of
three particles (two electrons and a nucleus, i.e. double photoionization or
single ionization by electron impact) and derived the threshold law in the
form of a power law with an exponent slightly larger than one, the exact value
depending on the charge of the remaining nucleus. This threshold law has been
generalized in the following decades to single ionization processes by impact
of other charged projectiles (protons, antiprotons, positrons, ...), to the
case of nucleus plus three electrons, and finally as late as 1998 to threshold theories
for general break-up processes into N charged particles by Kuchiev and Ostrovsky
and by ourselves. Thereby, we could make clear the meaning of the threshold
exponent as the instability of a fixed point in a reduced phase space.
Recently, we also formulated the threshold law for dipole interactions [2].
[1] Degenerate Wannier theory for multiple ionization; T. Pattard
and J.M. Rost, Phys. Rev. Lett. 80 (1998) 5081; Erratum ibid. 81
(1998) 2618; Reply to Comment ibid. 85 (2000) 4410
[Abstract]
[2] Threshold fragmentation under dipole forces;
T. Pattard and J.M. Rost, Foundations of Physics 31 (2001) 535
[Abstract]
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last change: 11/30/01