The intensity distribution over the H2(+) vibrational levels up to a quantum number of 15 was measured for H2 photoelectron spectra at a photon wavelength of 584 A. The data show reasonable agreement with recent calculations only in the quantum number of 0 through 8. The higher levels are populated significantly lower than predicted by theory

Gardner, J. L.

Samson, J. A. R.

English

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VIBRATIONAL INTENSITY DISTRIBUTIONS IN THE PHOTOELECTRON
SPECTRUM OF HYDROGEN.*
J. L. Gardner and James A. R. Samson
Behlen Laboratory of Physics
Lincoln, Nebraska 68508 U.S.A.
ABSTRACT
The intensity distribution over the H2+ vibrational levels
up to v = 15 has been measured for H 2 photoelectron spectra at
0
a photon wavelength of 584 A. The data show reasonable agree-
ment with recent calculations only in the range v = 0 through
8; the higher levels are populated significantly lower than
predicted by theory.
WSW
,7
(NASA-CR-142931) VIBRATIONAL INTENSITY
	 N75-24864
DISTRIBUTIONS IN THE PHOTOELECTRON SPECTRUM
OF HYDROGEN (Nebraska Univ.)
	 11 P HC $3.25
CSCL 07D	 Unclar-
63/25 24157
z1F026zs
*Research supported in part by the Atmospheric Sciences Section
of the National. Science Foundation and the National Aeronautics
and Space Administration under Grant No. DIG R 28-004-021.
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INTRODUCTION
A number of determinations of the vibrational intensity
distribution of the 584 A hydrogen photoelectron spectrum have
been reported in the literature. 1-3 The most recent measurement
is that of Berkowitz and Spohr, 3 who recorded intensities over
the range v 0 to . 9 (where v is the' vibrational quantum number
of the H2+ ionic ground state). These data were compared with
relative intensities calculated by Itikawa 4 and were found to be
in good agreement-, although considerable scatter is present in
the data at the higher vibrational levels.
The purpose of the present experiment was to extend the
measured intensities to higher vibrational le.Vels. The intensi-
ties calculated by Itikawa included the dependence of the
electronic transition moment on the internuclear separation and
on the kinetic energy of the departing electron, but did not
include the effect of rotational coupling on the vibrational
levels. This latter effect has been predicted to become signifi-
cant in the photoionization to the higher vibrational levels
of H2+.5
EXPERIMENTAL
Hydrogen photoelectron spectra were recorded at a photon
0
energy of 21.2 eV (58 11' A Hel radiation produced in a DC glow
discharge and dispersed with a 12- m Seya-Namioka monochromator)
with a cylindrical mirror electron energy analyzer whose response
is independent of the photoelectron angular distribution s.6
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The analyzer includes a lens* between the ionization region and
the deflection region; tie lens.voltage is scanned so that con-
stant resolution is maintained across the spectrum and peak areas
represent the electron intensity. The transmission of the ana-
lyzer has been calibrated to better than 5% over the energy range
covered here.?
Spectra were recorded at analyzer resolutions of 30, 23
and 15 meV. It should be noted that good'resolution is required
to accurately measure intensities in the hydrogen photoelectron
spectrum. The spectrum is dominated by the Q rotational branch 
whose extent increases as the vibrational separation increases.
The Q branch includes members (N', N") from (0,0) to (3,3), with
the (3,3) member approximately 10% as intense as the dominant
(1,1) member. 8 'At v = 13, the (0,0) and (3,3) members are
separated by 0.072 eV, whereas the (0,0) members of the v 	 12
and 13 vibrational levels are separated by 0.101 eV. 9 Thus an
analyzer resolution of the order of 20 meV is necessary to
determine the baseline between the vibrational levei.s.
RESULTS
A number of spectra were recorded with the varying resolu-
tion and atvarying gas pressures in the analyzer. The intensity
distribution was found to be independent of the gas pressure, in
contrast to previous measurements in CG and N 2 . 10 This was not
surprising, as the electron scattering cross section of hydrogen
shows little change over the range of energies covered by the
photoelectrons 11 and the analyzer has been shown to be comparatively
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insensitive to differential scattering when operated in the con-
stant resolution mode.6
A spectrum recorded at a resolution of 30 meV is shown in
Fig. 1; superimposed is a spectrum recorded over the higher
vibrational levels at a resolution-of 15 meV. The shoulder on
the main peak is mainly due to the W ,N ii ) = (3,3) member of the
Q rotational branch. No significant differences could be found
in the population of the higher vibrational levels in the spectra
recorded with resolutions of 15 and 23 meV, indicating that the
baseline determination between the peaks was not being compromised
by poor analyzer resolution.
Statistical averages wer3 obtained for the vibrational
intensity distribution by normalizing the total intensity of each
spectrum to the same value. From 6 to 10 spectra were averaged
to obtain the mean intensities reproduced in Table 1, where the
data are normalized to 100 at v = 2. The errors quoted on these
values represent standard deviations due to statistical varia=
tions only. The present intensity distribution is '.n reasonable
agreement with that obtained by Berkowitz and Spohr 3 for v = 0
to 9. Berkowitz and Spohr recorded their data 3 peaks 'at a time,
introducing subsequent normalization errors when the peaks were
combined to give the total intensity distribution.
Also included Jn Ta%;•'e 1 are the intensity distributions
predicted by Franck-Condo¢'.cfactors from the v = 0 level of the
neutral ground state and by the calculations of Itikawa. The
Franck-Condon factors were calculated by numerically integrating
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the Schroedinger equation using the potential energy curves
tabulated by Sharp, 12 and evaluating the overlap of the vibra-
tional wavefunctions. The resulting numbers agree with those
of Peek, for v = 0 to 10. 13 Franck-Condon factors ignore the
.electronic part of the wavefunction. Itikawa included the
electronic transition moment in his calculation, allowing for
depci,dence on both the internuclear separation and the energy of
the departing electron. The two values Quoted in Table 1
represent different fields for the ejected electron; case B
values were calculated with a modified two center Coulomb field
and case C with the true electrostatic potential.
The ratio of the measured intensity to the calculated
values is plotted in Fig. 2 for the various levels, normalized
to unity at v 2. A smooth curve is drawn for each comparison,
although in general this curve does not fall within the
statistical error bars (omitted for clarity) on the data at the
lower vibrational levels. The Franck-Condon distribution
clearly does not provide a good representation of the measured
distribution, as noted previously. 3 The best agreement with the
theory of Itikawa occurs with his case B. which is surprising
as the case C calculation uses a better approximation for the
electronic wavefunction. However, both case B and C disagree
significantly with the measured data for levels above v = 9,
predicting intensities higher than those.observed.
Some systematic error could be present in our data above
about v = 12 because of the proximity of the rotational
transitions for the different H 2+ vibrational levels. This
would lower the observed intensity from the true value, with an
estimated 20% possible error at v = 14. However this systematic
error would still not explain all the discrepancy between
experiment and theory.
The rotational coupling effects calculated by Villare,jo5
are also too weak to explain the observed discrepancy. His data
show = 1% variation for the Q branch (N' ='N") and = 15% for the
0 and S branches (IN' - N"I = 2); these latter branches occur.
with only a 10% of the intensity of the Q branch 8 and thus the
overall effect is too weak to explain the effect seen.
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v
 Present Itikawa Theory
Expt FCF (3ase B Case C
0 44.8±0.9 52.1 46.8 44.6
1 92.2±0.7 91.8 87.4 85.3
2 100.0±1.1 100.0 300.0 100.0
3 96.9±1.2 87.9 91.8 94.0
4 71.3±0.9 68.9 74.8 78.3
5 57.2±0.8 50.8 56.9 60.8
6 42.3±0.5 36.1 41.6 45.4
7 30.8±0.5 25.3, 29.8 33.0
8 20.8±0.4 17.6 •21.2 23.8
9 13.2±0.3 12.2 15.0 17.0
10 8.9±0.2 8.5 10.6 12.2
11 5. 8=.0.1 6.o -- --
12 3.9±0.1 4.2 5.4 6.3
13 2.4±0.1 3.0
-- --
14 1.5±0.1 2.1 2.7 3.2
15 0.5±0.1 1.4 -- --
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TABLE 1. Observed and Calculated Vibrational Distributions
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REFERC14CES
1. D. C. Frost, C. A. McDowell and D. A. Vroom, Proc. Roy. Soc.
(London), A 296 (1967) 566.
2. D. W. Turner, Proc. Roy. Soc. (London), A 307 (1968) 15.
3. J. Berkowitz and R. Spohr, J. Electron Spectrosc., 2 (1973)
143.
4. Y. Ztikawa, J. Electron Spectrosc., 2 (1973) 125•
5. D. Villarejo, J. Chem. Phys., 49 (1968) 2523.
6. J. L. Gardner and J. A. R. Samson, J. Electron Spectrosc.,
2 (1973) 267.
7. J. L. Gardner and J. A. R. Samson, J. Electron Spectrosc.,
6 (1975) 53.
8. L. Asbrink, Chem. Phys. Letts., `( (1970) 549.
9• Energies calculated from the spectroscopic constants given
by G. Herzberg, Spectra of Diatomic Molecules, Van Nostrand,
New York • (1950) 3 p . 534.
10. J. L. Gardner and J. A. R. Samson, J. Chem. Phys. , 60 (1974)
3711.
11. D. E. Golden, H. W. Bandel and J. A. Salerno, Phys. Rev.,
146 (1966) 40.
i 12. T. E. Sharp, Atomic Data, 2 (1971) 119.
j	 13• J. M. Peek, data appearing in Ref. 3.
19
FIGURE CAPTIONS
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1. Hydrogen photoelectron spectra recorded at a wavelength of
584 A, corrected for the analyzer response. Lower trace:
complete spectrum recorded with 30 meV resolution. Upper
trace: spectrum for levels v	 6 and higher at,a resolution
of 15 meV. 7
2. Ratio of measured vibrational intensity to calculated values.
x - Franck-Condon factors; o - Itikawa case B; n- Itikawa,
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Vibrational intensity distributions in the photoelectron spectrum of hydrogen

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