Measurement of the d-state Electron Distribution in Calcium Atoms
Matthew B. Campbell, MSFC 1994
University of Virginia Physics Department
Rarely in atomic physics (in my experience) do experiments performed in the laboratory
correlate directly to topics learned in undergraduate physics and chemistry courses.
In an experiment performed with calcium atoms, we have mapped out the familiar d-state orbital in a novel way. The d-state corresponds to L=2, where L is the quantized
angular momentum state in an atom, and is characterized by its dumbell like appearance
with a doughnut centered around the middle. An atomic orbital shows the electron
probability distribution in an atom, or where one expects to find an electron in relation
to the nucleus. The electron is strictly a quantum mechanical beast when it is bound
by the nucleus, but we analyze the interaction of the electron with strong radiation fields classically. Remarkably, our efforts are successful.
Calcium atoms are excited from the 4s 1S0 ground state to the 4p 1P0 intermediate
state with 423 nm, 5 nsec dye-laser pulse. A short 393 nm, 1.5 psec laser pulse
photo-ionizes the atom, giving the electron enough energy to leave the atom. Both
excitation laser pulses are linearly polarized along the same axis and the continuum electron
has d-state character according to dipole selection rules. Because the excitation
laser pulses are polarized along the same axis, the component of angular momentum
along that axis is zero. Therefore, we expect the electron distribution to leave with the
angular dependence of the Y2,0 spherical harmonic.
A free or loosely bound electron cannot gain energy from a photon. In order to absorb
energy from a laser pulse an electron must be near another particle, such as the
atomic nucleus, which ensures conservation of momentum. Therefore, it is difficult
to monitor the electron when it is leaving the atomic core with conventional laser pulses.
Using Half-cycle pulses (HCPs) of far-infrared (THz) radiation, we probe the electron
distribution as it leaves the atomic core. The time integrated oscillating electric
field of a laser pulse is zero, whereas the time integrated electric field of a HCP is non-zero. The electric field amplitude (which can be upwards of 20 kV/cm) in
a HCP starts at zero, rises to a maximum value, and returns to zero in about 1 picosecond.
Because the time integrated electric field of a HCP is non-zero, it can interact
with the electron when it is far from the nucleus and deliver an impulsive 'kick'
along its polarization axis. The impulse can prevent a portion of the electron distribution
from departing the nucleus, leaving it in a bound state. Initially, the photo-ionized electron has a total energy greater than zero. The total energy of the electron
can become less than zero due to the change in momentum brought on by the HCP impulse.
Classically, the total energy of the electron has a kinetic term and a potential
term (due to the coulomb potential of the nucleus). If the kinetic term becomes less
than the potential term in magnitude, the electon is bound. The once-free electron
has recombined with the parent atom due to the interaction with a HCP.
A HCP is created by illuminating a biased GaAs photoconducting switch with a 120 fsec,
786 nm laser pulse. The laser pulse turns on the switch, creating a rapidly accelerating
electron plasma to flow along the biased field axis. The acceleration of electrons creates a nearly unipolar electric field which radiates away from the GaAs wafer
and is steered into the laser/atom interaction region. The HCP delivers an impulse
along the direction of the biased field axis and is proportional to the biased field
strength. More information on HCPs and their interaction with atoms can be found in
an article by Jones et.al.: R.R. Jones, D. You, and P.H. Bucksbaum, Physical Review
Letters v 70, pp 1236 (1993).
We are able to map out the d-state character of the continuum electron distribution
by measuring how much electron/ion recombination there is for different relative
angles between the laser excitation polarization axis and the HCP field axis. We
use the HCP to place part of the electron distribution back onto the atom. The relative amount
of electron/ion recombination for each angle tells us how much of the electron distribution
is present at that particular angle. We expect there to be more recombination along the laser polarization axis than in the plane perpidicular to that axis.
The measurement is made for a given HCP impulse amplitude and delay with respect
to the excitation of the continuum electron, and the impulse strength is chosen to
produce the maximum electron/ion recombination. The amount of recombination measured is proportional
to the electron distribution at that angle. The measurement is made for relative
angles in one quadrant of the cartesian axes, but we assume symmetry along the excitation laser pulse polarization axis about zero and azimuthally about this axis.
The measurement is shown in Figure 1 and resembles the expected d-state electron distribution
of the Y2,0 spherical harmonic also shown. Due to limited angular resolution, the
hard zero found in the spherical harmonic is not observed in the data. Using HCPs to reattach contiuum state electrons to the parent ion, we have successfully mapped
out the angular distribution of an L=2 angular momentum state.
Other work has been perfomed which monitors the dynamics of free electrons as they
leave the nucleus, whether ionization be attributed to photo-ionization or to strong
static electric fields. This work has been performed under the direction of Dr.
Robert R. Jones with assistance from Dr. Thomas J. Bensky at the University of Virginia.
This work is supported by the Air Force Office of Scientific Research and by the
Packard Foundation.
The diagram on the left is the Y2,0 spherical harmonic displaying the expected angular
dependence of the electron distribution in a d-state orbital. The diagram to the
right shows the measured angular distribution of a continuum electron in a calcium
atom. The relative distances along the vertical and horizontal axes are identical for
each figure. The electron exciation laser pulses are polarized along the vertical
dimension of the figure.