Electron-correlation effects in the angular distribution of photoelectrons from Kr investigated
by rotating the polarization axis of undulator radiation
Kai Godehusen and Hans-Christoph Mertins
BESSY GmbH, Albert-Einstein-Strasse 15, D-12489 Berlin, Germany
Tobias Richter and Peter Zimmermann
Technische Universita ¨t Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
Michael Martins
Universita ¨t Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany
Received 21 March 2003; published 15 July 2003
The angular anisotropy parameter for the 3 p and 3 d photoionization of krypton was investigated in the
photon energy range from 325 eV to 1000 eV. Using the new UE52 undulator at the BESSY II storage ring the
results were obtained by rotating the polarization axis of the linearly polarized synchrotron radiation. With this
method high-precision measurements of are possible, showing significant deviations between experiment
and theoretical calculations. This gives strong evidence for the importance of intrachannel and interchannel
electron correlations for the photoionization processes of Kr.
DOI: 10.1103/PhysRevA.68.012711 PACS numbers: 32.80.Fb, 32.80.Hd
I. INTRODUCTION
Photoelectrons from single atoms or molecules are emit-
ted in a characteristic angular distribution pattern. This pat-
tern is determined by the angular anisotropy parameter .
Parameter is a sensitive tool to test the electron-correlation
effects in the photoemission and to validate theoretical pre-
dictions obtained with state-of-the-art many-body calculation
methods. In contrast to the photoionization cross section,
not only depends on the absolute amplitudes of the transition
dipole matrix elements, but also on the phases of the outgo-
ing electron waves 1.
Recently, the breakdown of the independent-particle ap-
proximation for x-ray photoemission was shown for Ne, Ar,
and Kr 2–4. The approximation was thought to be valid at
least for photon energies far above threshold. Even for inner
atomic shells and energies far above threshold, electron cor-
relations in the form of interchannel coupling have to be
considered to correctly describe the photoionization process
2–5.
For the Kr 3 p and 3 d photoemission it is assumed that
these influences from the interchannel coupling on the value
of are only small 3. With the experimental data available
for the anisotropy parameter so far, it was not possible to
judge the different theoretical models for the description of
the photoionization.
For the photoionization of an unpolarized unoriented
atom, with linearly polarized radiation, and within dipole
approximation, the differential cross section is given by
Yang’s theorem 6:
d
d
=
4
1 + P
2
cos . 1
Here is the angle between the polarization vector of the
ionizing light and the momentum vector of the ejected elec-
tron, P
2
is the second Legendre polynomial, and is the
isotropic angle-integrated cross section of the investigated
photoionization process. The key to determine is to mea-
sure the photoelectron intensity under various angles .
The established ways to measure the angular distribution
of photoelectrons are either to rotate the electron spectrom-
eters around the synchrotron beam or to use multiple spec-
trometers to measure under different angles simultaneously.
Because of their size and weight, very complex constructions
are necessary to rotate a high-resolution hemispherical elec-
tron spectrometer with high angular accuracy. To inhibit
variations in the source volume seen by the spectrometer
depending on the rotation angle, one also has to be very
careful to properly align the rotation axis with the propaga-
tion axis of the photons. To measure the photoelectron inten-
sity simultaneously under multiple angles on the other hand
calls for compact analyzers, and therefore often time-of-
flight TOF spectrometers are used in this application. Using
TOF electron spectrometers, one is restricted to a special
operation mode single bunch mode of the storage ring
7,8. With multiple detectors, one also has to take special
care to correct for possible differences in the efficiencies of
the individual detectors used 7.
In this paper we present an experimental method to deter-
mine values for with high precision and over a large pho-
ton energy range. The measurements have been carried out at
the new UE52-SGM beamline at the electron storage ring
BESSY II in Berlin. With this undulator it is possible to
select the linear polarization axis at arbitrary angles between
0° and 90° with respect to the horizontal plane.
Using one fixed-in-space detector and rotating the angle
of the polarization of the ionizing radiation eliminates most
of the sources for uncertainties that are inherent to common
methods mentioned above and results in a much improved
accuracy of the values obtained. A standard chamber can be
used during normal storage ring operation.
II. METHOD
The APPLE-II type 9–11 undulator UE52 magnetic pe-
riod length 52 mm used has four identical rows of perma-
PHYSICAL REVIEW A 68, 012711 2003
1050-2947/2003/681/0127114/$20.00 ©2003 The American Physical Society 68 012711-1