**
Boundary-free Scaling Calculations of Laser-Atom Interactions
**

Z. X. Zhao, B. D. Esry and C. D. Lin

Department of Physics, Kansas State University, Manhattan, Kansas 66506-2601

The most common approaches developed to describe laser-atom
interactions are based on sovling
the time dependent Schrödinger equation(TDSE) either
directly on numerical grids or in a basis set
[1]. Neither approaches allow the continuum electrons
to escape beyond the boundaries and reflections from these
boundaries may result in unphysical
interference. Although it is possible to enlarge the
box or basis set at a given time step, or by introducing
ad hoc absorbers near the boundaries, these
approaches are inherently limited. Such limitations
can be avoided, however, by adopting a scaled coordinate system,
as shown recently by Sidky and Esry
[2]. The scaled coordinate is chosen by rescaling the
spatial coordinate according to
*ξ= x/ R(t)*,
where
*R(t)* is set to approach *γt* at large time *t*,
with γ being an arbitrary velocity. Thus in the scaled coordinate,
the electron position does not expand with time.

As an illustration in Fig. 1 we show the free propa-
gation of a Gaussian wavepacket. The velocity and
width of the wavepacket are both 1 a.u. at *t*=0. The
real part of the wavefunctions at *t*=10 and *t*=20 are
plotted. The solid lines are for the scaled wavefunction
and the dotted lines are for the weighted real function
*R*^{1/2}Ψ(*Rξ,t*).
The abscissa is the scaled coordinate ξ,
with the scaling paramter
*R(t)* = (1+*t ^{2}*)

where *a* and *v _{o}* are the initial width and
velocity, respectively. In this example the center of the
wavepacket is located at ξ=1.0 in the scaled coordinate ξ, but
the spread of the wavepacket in the
real space is large, and the oscillation of
Ψ(

**Figures:**

**Figure 1: **
Free propagation of a Gaussian wave packet.

**Figure 2:**ATI spectrum (dash line) and density plot (solid line). The horizontal

axis is scaled coordinates (or the velocity of electron divided by scaling contant γ).

**References:**

1) K. Burnett, V. C. Reed and P. L. Knight, J. Phys. B 26, 561 (1993);

M Protopapas, C H Keitel and P. L. Knight, Rep. Prog. Phys. 60 , 389 (1997)

2) E. Y. Sidky and B. D. Esry, Phys. Rev. lett. 85, 5086 (2000)

This work was supported by the
Chemical Sciences, Geosciences and Biosciences Division,

Office of Basic Energy Sciences,
Office of Science,
U.S. Department of Energy.

*Submitted to ICPEAC 2001, July 2001 in Santa Fe, NM.*

*This abstract is also available in
Postscript or
Adobe Acrobat formats.*