Absolute Doubly Differential Electron-Bremsstrahlung
Cross Sections from Free Atoms
S. Portillo*, C.A. Quarles
Dept. Of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76109
Abstract: Absolute doubly differential bremsstrahlung cross sections from 28 and 50 keV electron bombardment of Xe, Kr, Ar
and Ne have been measured. The cross sections are differential with respect to emitted photon energy and angle. A CockcroftWalton accelerator was used to accelerate the electrons and a SiLi detector measured the resulting radiation at 90º emission
angle. The experimental cross sections are compared with the tabulated values of normal bremsstrahlung and with the stripping
approximation (SA) that includes the contribution from polarization bremsstrahlung (PB). The very good agreement of the
experimental data with the SA theory is clear evidence of the PB contribution.
of PB from neighboring lattice atoms in the thin
film.12 What was needed were accurate
measurements of absolute doubly differential cross
sections from free gas atoms.
The measurement of absolute cross sections
requires a thorough understanding and modeling of
the thick target bremsstrahlung (TTB) background
that is present in all bremsstrahlung experiments.13
Over the past several years this has been
accomplished. A semi-empirical model14 has been
developed and rigorously tested and validated by
comparing its predictions with absolute TTB
experimental yields.15
Absolute doubly differential cross sections
from 28 and 50 keV electron bombardment of Xe,
Kr, Ar and Ne are presented here. The data are
compared with the theoretical values from the nonrelativistic stripping approximation (SA),16,17 that
includes the PB contribution, and with the tabulated
values of normal bremsstrahlung.18
INTRODUCTION
The fundamental bremsstrahlung process
arises from two amplitudes. First, there is normal
bremsstrahlung from the radiation of the charged
projectile deflected in the Coulomb field of the atom.
Second, there is radiation from the atomic electrons
that are dynamically polarized by the projectile. This
second process has been called atomic or polarization
bremsstrahlung (PB). The PB process was first
discussed by Buimistrov,1 Trackenburg2 and Amusia
et al.3 There have been two extensive reviews of
PB.4,5 The earliest experimental work was the
attribution to PB of an enhancement observed in xray region at low photon energies.6,7
This
enhancement was also shown, recently, for Xe but
also at low energies.8
Recent
calculations9,10
on
electron
bremsstrahlung have predicted a significant increase
in the overall radiative spectrum due to PB. Initial
attempts11 in the search for PB focused on finding the
predicted structure near the atomic absorption edges.
These experiments measured relative cross sections
from thin film targets and did not find any evidence
for a PB contribution to the spectrum. Perhaps this
was due to the cross sections being relative, perhaps
it was due to inadequate characterization of
backgrounds, or perhaps there was some suppression
EXPERIMENT
The experimental layout is shown in Figure
1. The electrons are produced by an electron gun and
accelerated by a Cockcroft-Walton accelerator. They
are guided to the scattering chamber by three sets of
magnetic coils placed along the beam line. Prior to
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
115
τ is the thickness of the gas target in atoms/cm2. ∆Ω
is the solid angle, which was calculated using a
Monte Carlo routine from the parameters shown in
Fig. 2. A(k) is the absorption of the detector and
Kapton windows. N0 is the total number of incident
electrons, N(k) is the total number of counts incident
on the detector. ∆k is the width of the energy
channel and ε(k) is the detector efficiency. The
Z2(TTB) is the TTB background due to electrons
elastically scattered into the scattering chamber walls
and the Kapton window.
The absolute doubly differential cross sections
(ADDCS) are given in Barns/sr/keV. The principal
background source in this experiment is the TTB
background. The TTB cannot be eliminated nor
experimentally measured directly since it is only
present when the target is present. Therefore it is
imperative to employ a model that describes the TTB
accurately.14 Natural background and beam-only
background are very small in comparison to the
bremsstrahlung from targets such as Kr and Xe, but
cannot be ignored for the low to medium Z targets
such as Ar and Ne.
entering the scattering chamber the electrons were
collimated by a 0.15" diameter Al collimator. A
diagram of the scattering chamber and the detector
orientation is shown in Fig.2. The scattering chamber
was constructed from Al in order to reduce the Z
dependent TTB. The gas was fed into the scattering
chamber by a micro-valve connected to a positive
pressure gas reservoir. Charge was collected in an Al
Faraday cup. Bremsstrahlung was detected by a SiLi
detector placed at 90 º to the beam line. The detector
was connected to the scattering chamber by a 4.91"
stainless steel nipple and a 0.5" Lexan flange. The
Lexan serves as an electrical isolator and holds the 2
mil Kapton electron absorber. Since the cross
sections increased substantially for higher Z, typical
run times ranged from 4 hours for Xe to 11 hours for
Ne.
THEORY
The theoretical ordinary bremsstrahlung cross
sections were taken from the tabulated values18 of the
work of Tseng and Pratt.19 The theoretical predictions
for the singly differential cross sections were
calculated using the stripping approximation (SA)
algorithms developed by Avdonina and Pratt.16
These in turn were multiplied by the tabulated normal
bremsstrahlung shape functions to obtain the doubly
differential cross sections. In this we have assumed
that the shape functions or angular distribution of the
total bremsstrahlung cross section is not very
different from ordinary bremsstrahlung.
It is
expected that a more accurate calculation of the total
bremsstrahlung cross section including PB will be
available for comparison with the data presented here
in the near future.
Figure 1. Schematic of the experimental apparatus.
Figure 2. Schematic of scattering chamber, showing
scattering center and location of Kapton window.
EXPERIMENTAL CROSS SECTIONS
RESULTS
The results for 50 keV electrons on Xe are shown
in Figure 3. The data are in very good agreement with
the stripping approximation.
This is the first
confirmation of the contribution of polarization
bremsstrahlung in the electron bremsstrahlung
spectrum.
The absolute doubly differential cross
sections are given by:
 N (K)

d 2σ
1
=
− Z 2 ( TTB ) 

d Ωdk τ∆Ω A ( k )  N 0 ∆k ε ( k )

116
data in the 5 to 15 keV photon energy range and was
typically much less than 1% at any photon energy.
The error due to the TTB background is small
compared to the statistical error and has been
compounded with the statistical error at each point.
The data for 50 keV incident electrons are
systematically
higher
than
the
stripping
approximation prediction in the 10 to 30 keV emitted
photon energy range. At higher emitted energy,
above 35 keV, the data are lower than theory due to
insufficient modeling of the detector efficiency. The
detector is not as thick as we have assumed in our
current efficiency model. This only affects the
efficiency above ~30 keV.
The results for 28 keV electrons on Kr are shown
in Figure 4. The data at 28 keV, both for Kr and Xe,
are in very good agreement with the stripping
dσ/dΩdk Barns/sr/keV
3.0
2.5
2.0
1.5
1.0
0.5
Xe 50 keV Data
SA Theory
NB Theory
0.0
0
10
20
30
40
50
Photon Energy, keV
Figure 3. The absolute doubly differential cross section
(ADDCS) at 90o for 50 keV electrons on Xe. The data are
compared with the theory of normal bremsstrahlung (NB
theory) (open circles) and with total bremsstrahlung
calculated in the stripping approximation (SA theory) (solid
line).
0.8
Kr/Xe Cross Section
The data are absolute and the total scale error is
about 3.4%. The error is due to solid angle target
length (1%), charge collection (1%), detector
efficiency (2.8%), and target pressure and
temperature (1%). The major errors are statistical
and range from about 2% at low photon energy up to
about 25% near the kinematic end point. In the
geometry of this experiment, the TTB background
calculated from the thick target model14 was small.
0.6
0.4
0.2
Kr/Xe SA Theory
R
i ADDCS
Kr/Xe
R ti
0.0
0
20
30
40
50
Photon Energy, keV
3.0
dσ/dΩdk in Barns/sr/keV
10
Figure 5. The ratio of Kr to Xe at 50 keV compared with
the ratio predicted by the stripping approximation. Sixteen
channels have been added together to reduce statistical
fluctuations.
2.5
2.0
1.5
approximation. The agreement is better over the
whole photon energy range than was observed for 50
keV.
It is interesting to consider the ratio of data at 50
keV for Kr to Xe. In the ratio, systematic errors in
detector efficiency and solid angle and target
thickness cancel out. It can be shown13 that the TTB
background also cancels out to first order in the ratio.
Thus the ratio is much more sensitive to the photon
energy dependence. The ratio of Kr to Xe data at 50
keV is shown in Figure 5. The ratio is compared to
the corresponding ratio of theory from the stripping
1.0
0.5
SA Theory
NB Theory
Kr 28 keV Data
0.0
0
5
10
15
20
25
30
Photon Energy, keV
Figure 4. Same as Figure 3 except for 28 keV electrons on
Kr.
Uncertainty in the TTB correction only affected the
117
machine shop is gratefully acknowledged.
approximation. It can be seen that the agreement
with theory is excellent at higher photon energy.
This demonstrates that the decrease in cross section
observed above 35 keV in Figure 3 is due to
efficiency. The efficiency correction cancels in the
ratio. On the other hand, in the region from about 5
to 15 keV, the data disagrees with the stripping
approximation. This disagreement in photon energy
dependence is significantly outside the systematic
and statistical error. It will be very interesting to
compare the present data to more accurate total
bremsstrahlung calculations when they become
available.
REFERENCES
*
Now at Sandia National Laboratory, MS 1193
Albuquerque, New Mexico 87185-1193
1. Buimistrov, V.M., Ukr. Fiz. Zh. 17, 640 (1972).
2. Buimistrov, V.M. and Trakhtenberg, L.I., Zh.
Eksp. Teor. Fiz. 69,108 (1975) [Sov. Phys. JETP 42,
54 (1975)].
3. Amusia, M. Ya., Baltenkov, A. S. and Paiziev,
A.A., Letters to J. Exp. Theor. Phys. (USSR Acad.
Sci.), 24, 366 (1976) [JETP Lett. 24, 332 (1976)].
4. Amusia, M. Ya., Physics Reports, 162, 249 (1988).
5. Tystovich, V. N. and Oiringel, I. M., editors
Polarization Bremsstrahlung of Particles and Atoms,
New York: Plenum Press, 1992.
6. Liefield, R. J., Burr, A. F. and Chamberlain, M.B.,
Phys. Rev. A 9, 316 (1973).
7. Wendin, G. and Nuroh, K., Phys. Rev. Lett. 39, 48
(1977).
8. Verkhovtseva, E.T., Gnatchenko,E.V., Zon, B. A.,
Nekipelov, A. A. and Tkachenko, A. A., Zh. Eksp.
Teor. Fiz. 98, 797 (1990). (in Russian).
9. Korol, A.V., Lyalin, A. G., Obolenskii, O. I.,
Solov’yov, A. V. and Solov’yov, I. A., JETP 94, 704
(2002).
10. Korol, A.V., Obolenskii, O. I., Solov’yov, A. V.
and Solov’yov, I. A., J. Phys. B: At. Mol. Opt Phys.
34, 1589 (2001).
11. Quarles, C. A. and Portillo, S., CP475,
Applications of Accelerators in Research and
Industry, eds. J. L. Duggan and I. L. Morgan, AIP
Press, New York, (1999) pp. 174-177.
12. Klein, S., Rev. Mod. Phys. 71, 1501 (1999).
13. Quarles, C. A., Chapter 8, Accelerator-Based
atomic physics: techniques and applications, Editors:
S. M. Shafroth and J. C. Austin, American Institute
of Physics, Woodbury, New York, 1997.
14. Seeman, M., and Quarles, C. A., X-ray Spec. 30,
37 (2001).
15. Portillo, S., and Quarles, C. A., unpublished.
16. Avdonina, N. B. and Pratt, R. H., J. Phys. B: At.
Mol. Opt. Phys. 32, 4261 (1999).
17. Korol, A.V., Lyalin, A. G., Solov’yov, A. V.,
Avdonina, N. B. and Pratt, R. H., J. Phys. B: At. Mol.
Opt Phys. 35, 1197 (2002).
18. Kissel, L., Quarles, C. A. and Pratt, R. H.,
Atom. Data Nucl. Data Tables 28, 381 (1983).
19. Tseng, H. K. and Pratt, R.H., Phys. Rev. A 3,100
(1971).
CONCLUSIONS
We have presented the first absolute doubly
differential bremsstrahlung cross sections for
electrons on free gas atoms. Furthermore, the data
with systematic errors of the order of 3.4% are the
most accurate absolute doubly differential
bremsstrahlung cross sections ever reported. The
data are in very good agreement at 28 keV with the
prediction of the total bremsstrahlung cross section
calculated in the stripping approximation and
disagree with normal bremsstrahlung at photon
energies where the two theories diverge. At 50 keV
the data are in better agreement with the stripping
approximation than with normal bremsstrahlung, but
there is significant disagreement with the photon
energy dependence at lower photon energies. The
data provide the first observation of the contribution
of polarization bremsstrahlung to the total
bremsstrahlung spectrum in electron bombardment
over the photon energy range from a few keV to the
kinematic endpoint.
Initial results have also been obtained for Ar and
Ne at 50 keV, but the statistics are poorer than those
of Kr and Xe shown here. The complete results will
be submitted for publication.
Further work is
planned to reduce the statistical error in the gases
studied. We also plan to study additional photon
emission angles, additional electron energies from 10
to 100 keV and additional targets with atomic
number from 2 to 80.
ACKNOWLEDGMENTS
The authors would like to thank the TCU
Research and Creative Activity fund for support. The
help of Mike Murdock and David Yale in the TCU
118