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Experimental determination of the absolute dipole oscillator strengths for the helium 11S to
n1P (n=2-7) series
View the table of contents for this issue, or go to the journal homepage for more
1990 J. Phys. B: At. Mol. Opt. Phys. 23 L523
(http://iopscience.iop.org/0953-4075/23/18/002)
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J.
Phys.
B:
At. Mol. Opt. Phys.
23
(1990) L523-LS26. Printed in the UK
LETTER TO
THE
EDITOR
Experimental determination
of
the absolute dipole oscillator
strengths for the helium
llS+
n'P
(n
=
2-7)
series
Wing-Fat Chan, Glyn Cooper, Kong-Hung Szet and C
E
Brion
Department of Chemistry, University of British Columbia, Vancouver BC, Canada V6T 1Y6
Received
8
June 1990
Abstract.
The
absolute optical oscillator strengths for the individual
He
1's
+
n'P
(n
=
2-7)
transitions have been measured using dipole
(e, e)
spectroscopy at high energy resolution.
The results, which include the first measurements above
n
=
3,
are in excellent agreement
with earlier published quantum mechanical calculations performed using very accurate
correlated wavefunctions for helium.
The absolute dipole oscillator strengths for optical electronic excitation of ground-state
helium provide a stringent and important test for quantum mechanical calculational
methods and for the evaluation of the most accurate correlated wavefunctions for the
fundamental two-electron atomic system. However little or no experimental data are
available for the helium l'S+
n'P
dipole-allowed series for values of
n
greater than
two. This is because most optically based techniques (e.g. lifetime, level crossing, Hanle
effect, self absorption etc) are not readily applicable beyond the main,
n
=
2,
resonance
line of the helium series because of various complicating effects.
As
a result, although
there are numerous experimental determinations for
n
=
2
there are only two reported
optical values for
n
=
3 (Burger and Lurio 1971, Tsurubuchi
et
al
1989). Furthermore,
any attempt to apply Beer-Lambert law photoabsorption in the discrete excitation
region at any value of
n
is liable to lead to large errors. Such accurate photoabsorption
measurements are extremely difficult, if not impossible, to carry out particularly in the
case of helium where the transitions have narrow natural linewidth and quite high
cross section. This situation occurs because of the effects of the finite bandwidth
of
the optical monochromator (e.g. in a synchrotron beam line) which can result in a
significant reduction in the measured oscillator strength (cross section) due to well
known 'line saturation' effects (Lothian 1963, Hudson 1971). These spurious effects
on experimentally measured optical oscillator strengths originate from the inherently
resonant nature of the optical absorption process and the need to use the logarithmic
Beer-Lambert law in order to relate the experimental measurements (percentage
absorption) to oscillator strength (cross section). It is not always appreciated that the
Beer-Lambert law can never give an exact photoabsorption cross section for discrete
excitation since it is only exact in the hypothetical case
of
infinitely narrow bandwidth.
While such 'line saturation' bandwidth effects can be minimized by careful studies as
a function of pressure and extrapolation to zero column number (Hudson 1971, Chan
et
al
1990) they cannot be entirely eliminated. Although 'line saturation' effects can
t
Present address: Inorganic Chemistry Laboratory, South Parks Road, Oxford, OX1 3QR, UK.
0953-4075/90/ 180523 +04%03.50
@
1990 IOP Publishing Ltd
L523
L524
Letter to the Editor
in principle occur in any region of the electromagnetic spectrum, even at long
wavelength (Johns
et
a1
1976) they are likely to be a particular hazard in the vacuum
uv
and soft x-ray regions of electronic excitation because the often low light fluxes
frequently result in the use of wider slit widths. It is probably for these reasons that
no direct photoabsorption measurements have been reported for discrete optical
excitation of ground-state helium despite the apparent appealing simplicity of exploita-
tion of the Beer-Lambert law.
For the reasons discussed above routine application of the photoabsorption method
is precluded not only for the narrow electronic transitions of atomic spectroscopy but
also in particular for molecules where the additional complications of narrow vibra-
tional and rotational fine structure occur in the electronic spectra.
A
particularly graphic
case of such effects has been reported in the electronic spectrum of
N2
(Geiger and
Stickel 1965, Meyer
et
a1
1965, Lawrence
et
a1
1968). Such bandwidth effects can be
entirely eliminated by using the alternative dipole excitation mechanism of electron
impact at negligible momentum transfer under conditions where the Bethe-Born
approximation is valid (Inokuti 1971, Brion and Hamnett 1981, Brion 1985). Such
electron impact excitation avoids the 'line saturation' problem encountered in direct
optical spectroscopy since it is a non-resonant process and there is no need to employ
the logarithmic Beer-Lambert law to obtain oscillator strengths (cross sections). These
alternative ideas have been extensively utilized in dipole (e, e) and related electron
impact methods to yield accurate measurements of optical oscillator strengths for a
variety of continuum and excitation processes at low
(-
1 eV
FWHM)
energy resolution
(Brion and Thomson 1984, Gallagher
et
a1
1988). However until the presently reported
work the dipole (e, e) method had not been routinely applied
to
direct dipole excitation
at high energy resolution because of severe experimental constraints for such quantita-
tive work.
As
part of the careful evaluation procedures involved in the recent development
of a new and generally applicable high resolution dipole (e,e) method (Chan
et
a1
1990) for the accurate measurement of absolute optical oscillator strengths for discrete
electronic transitions in atoms and molecules, we have made test measurements on
helium gas, including the 1's
+
n'P
(n
=
2-7) resonance series. The new method extends
previous dipole (e, e) techniques by using a high-resolution electron monochromator
to produce the high-impact-energy incident beam. In addition the Bethe-Born conver-
sion factor for this earlier constructed high-performance electron energy loss spec-
trometer (Daviel
et
a1
1984) has now been carefully determined over the complete
spectral range of interest. The absolute oscillator strength scale is obtained by using
Thomas-Reiche-Kuhn
(TRK)
sum rule considerations (Brion and Hamnett 1981, Brion
1985, Gallagher
et
a1
1988). Full details of the new experimental method and its
application to atomic and molecular targets will be published later (Chan
et
a1
1990).
The results of the present measurements for the He l'S+
n'P
series are shown in
table
1
and figure 1. The spectrum in figure 1 shows the Bethe-Born converted electron
energy loss spectrum
(0.048
eV FWHM) on an absolute differential optical oscillator
strength scale established using the
TRK
sum rule (Chan
et
a1
1990). The full curve in
the near-edge continuum region represents both the optically determined absolute total
photoionization data from the compilation of West and Marr (1976) and the calculated
data reported by Fernley
et
a1
(1987) (these data are too close to be distinguished in
this region). It can be seen that excellent quantitative agreement with the present work
exists in the ionization continuum. The present data for the dipole-allowed discrete
excitation of helium represent the first experimental determinations for transitions
Letter to the Editor
L525
Table
1.
Absolute optical oscillator strengths
for
helium
1's
+
n'P excitation.
Optical oscillator strength
Method
n=2 n=3 n=4 n=5 n=6 n=7
Theory
Schiff and Pekeris
(1964)
Wiese
et
al
(1966)
Schiff
et
al
(1971)
Fernley
et
al
(1987)
Experiment
This work, dipole (e, e)t
0.280
Geiger
(1963),
electron impact
0.312
Lassettre
et
a1
(1970),
electron impact
0.269
Fry
and Williams
(1969),
Hanle effect
0.273
Burger and Lurio
(1971),
lifetime
0.275
Tsurubuchi
et
al
(1989),
self absorption
0.273
0.276 16
0.276 2
0.276 2
0.281 1
0.073 4
0.073 4 0.030 2 0.015 3
0.008
48
0.005
93
0.073 0.030 0.015
0.074 34 0.030 28 0.015 24
0.074
1
0.030 3 0.015
2
0.008
92
0.005
87
0.089
8
0.073
0.07 1
~~~ ~
t
Estimated uncertainty
*5'/0.
I
He
11s
--t
DIP
n=
2
20 21
3
I
uv
I
i
I
22 23 24 25 26
ENERGY
(eV)
Figure
1.
Absolute dipole oscillator strength spectrum for helium
(1's
+
n'P) excitation
using high-resolution dipole (e, e) spectroscopy. The original experimental data has been
Bethe-Born converted and placed on an absolute oscillator strength scale using TRK sum
rule considerations. The full curve in the continuum above
24.6
eV represents both the
experimental data from the compilation by West and Marr
(1976)
and the calculations
reported by Fernley
et
al
(1987).
L526
Letter to the Editor
above
n
=
3.
Previously published data from some other selected optical and electron
impact studies are also given in table
1
(see Chan
et
a1
(1990)
for
a
more complete
discussion of all existing experimental data). In table 1 the results of the quantum
mechanical calculations reported by Schiff and Pekeris (1964), Wiese
et
al
(1966),
Schiff
et
al
(1971) and Fernley
et
al
(1987), which are all considered to be highly
accurate, are compared with the experimental data. The presently reported high-
resolution dipole (e, e) measurements and all calculations are seen to be
in
very good
quantitative agreement. These ‘state of the art’ calculations have however, not been
experimentally tested beyond
n
=
3 prior to the present work. It can also be seen that
there is good agreement between the present measurements and the lifetime (level
crossing) studies reported by Burger and Lurio (1971) for
n
=
2
and
n
=
3. The results
of
other optical and electron impact studies (for a discussion see Chan
et
al
1990),
which are of generally lower precision and are mainly for
n
=
2
only, show a spread
in values but are in most cases consistent with the present work. The oscillator strengths
of
0.312
(n
=
2)
and 0.0898
(n
=
3)
reported by Geiger (1963) in much earlier electron
impact work are substantially in error due to the normalization procedures used, and
show inconsistencies as has been discussed earlier (Kim and Inokuti 1968).
Based upon the accuracy of the test data including the presently reported helium
excitation optical oscillator strengths, further application of the high-resolution dipole
(e, e) method is now in progress.
Financial support for this work was provided by the Natural Sciences and Engineering
Research Council
of
Canada. One of us (WFC) gratefully acknowledges the receipt
of
a University of British Columbia Graduate Fellowship. We should like to thank
Professor
M
J
Seaton and
Dr
M
Inokuti for helpful discussions.
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