Measurement of the autoionization lifetime of the superexcited atomic sulfur S(3S23p3(2D°)4d) state using tunable vacuum ultraviolet (VUV) radiation

Article abstract of DOI:10.1139/v04-039

A new method is described that combines a tunable coherent vacuum ultraviolet (VUV) radiation source and an ion velocity imaging apparatus to study the autoionization of superexcited sulfur atoms. The photolysis of CS ₂ at 193 nm is used to produce metastable sulfur atoms in the ¹D₂ state. The S(¹D₂) atom is then directly excited to the neutral superexcited state 3s²3p ³(²D°)4d (¹D₂°) at 11.317 eV with a tunable VUV photon at ～121.896 nm. This excited state then undergoes autoionization into the first ionization continuum state of S⁺( ⁴S_3/2°) + e^-, which is not directly accessible from the S(¹D₂) state through optical transition. By monitoring the S⁺ signal in the time-of-flight mass spectrometer while scanning the excitation wavelength, the line profile of the 3s²3p³4d ¹D₂° ← 3s ²3p4 ¹D₂ transition is recorded and found to have a full width at half maximum (FWHM) of 0.9 cm^-1. This has been used to determine an autoionization lifetime of the neutral superexcited 3s ²3p³4d ¹D₂° state of 5.9 ps. The accurate measurement of the autoionization lifetime provides a benchmark for testing fundamental theoretical models of processes occurring in excited states of atoms.

Full text of DOI:10.1139/v04-039

885
Measurement of the autoionization lifetime of the
superexcited atomic sulfur S(3s23p3(2Do)4d) state
using tunable vacuum ultraviolet (VUV) radiation1
Jianhua Huang, Dadong Xu, Alexei Stuchebrukhov, and William M. Jackson
Abstract: A new method is described that combines a tunable coherent vacuum ultraviolet (VUV) radiation source and
an ion velocity imaging apparatus to study the autoionization of superexcited sulfur atoms. The photolysis of CS2 at
1
193 nm is used to produce metastable sulfur atoms in the D2 state. The S(1D2) atom is then directly excited to the
neutral superexcited state 3s23p3(2Do)4d (1D2o) at 11.317 eV with a tunable VUV photon at ~121.896 nm. This excited
state then undergoes autoionization into the first ionization continuum state of S+(4S3o/2) + e–, which is not directly ac-
cessible from the S(1D2) state through optical transition. By monitoring the S+ signal in the time-of-flight mass spec-
1
trometer while scanning the excitation wavelength, the line profile of the 3s23p34d D2o ← 3s23p4 1D2 transition is
recorded and found to have a full width at half maximum (FWHM) of 0.9 cm–1. This has been used to determine an
1
autoionization lifetime of the neutral superexcited 3s23p34d D2o state of 5.9 ps. The accurate measurement of the
autoionization lifetime provides a benchmark for testing fundamental theoretical models of processes occurring in ex-
cited states of atoms.
Key words: autoionization, atomic sulfur, vacuum ultraviolet (VUV), full width at half maximum (FWHM).
Résumé : On décrit une nouvelle méthode qui combine une source cohérente et réglable de rayonnement ultraviolet
du vide avec un appareil d’imagerie de la vitesse des ions pour étudier l’autoionisation d’atomes de soufre surexcités.
1
On a utilisé la photolyse du CS2 à 193 nm pour produire des atomes de soufre métastables dans l’état D2. L’atome
S(1D2) est alors directement excité à l’état surexcité neutre 3s23p3(2Do)4d (1Do2), à 11,317 V, à l’aide d’un photon VUV
réglable à ~121,896 nm. Cet état excité subit alors une autoionisation dans le premier état d’ionisation continue du
S+(4S3o/2) + e– qui n’est pas directement accessible à partir de l’état S(1D2) par le biais d’une transition optique. En sui-
vant le signal du S+ dans un spectromètre de masse à temps d’envol alors qu’on balaye la longueur d’onde
1
d’excitation, on a enregistré le profil de la raie de la transition 3s23p34d D2o ← 3s23p4 1D2 et on a trouvé que la lar-
geur totale à demi-hauteur maximale (« FWHM ») est de 0,9 cm–1. Cette valeur a été utilisée pour déterminer que le
temps de vie de l’autoionisation de l’état surexcité neutre 3s23p34d(1D2o) est de 5,9 ps. La mesure précise du temps de
vie d’autoionisation fournit une référence pour évaluer les modèles théoriques fondamentaux des processus se produi-
sant dans les états excités d’atomes.
Mots clés : autoionisation, soufre atomique, ultraviolet du vide, largeur totale à demi-hauteur maximale.
[Traduit par la Rédaction] Huang et al. 890
Introduction
fects in determining the properties of the excited state can be
important. The electronic configuration of atomic sulfur is
The study of the photoionization of sulfur is of great in-
terest because of its applications in astrophysics. Spectro-
scopic measurements indicate that sulfur and oxygen
dominate the torus plasma of the Jupiter satellite Io (1, 2).
Furthermore, the study of the photoabsorption spectrum of
sulfur is interesting because it is an open-shell heavy atom
where spin–orbit coupling can be large and correlation ef-
3
1
1
1s22s22p63s23p4, which gives rise to the P2,1,0, D2, and S0
3
terms. The ground state is the P2 state. The photoionization
of ground-state sulfur (3P2) has been extensively studied in
the past. The absolute values of the cross sections were re-
ported by Tondello (3) for photon energies from the ioniza-
tion threshold at 119.67 to 90 nm using the flash pyrolysis
method. Sarma and Joshi (4) did the same work but made
more detailed analysis in the region between 109 and
100 nm. Berkowitz and co-workers (5) observed the photo-
ionization spectrum of sulfur in the region between the first
ionization threshold and 92.5 nm. They assigned many of
Received 7 Novenber 2003. Published on the NRC Research
Press Web site at http://canjchem.nrc.ca on 26 August 2004.
J. Huang, D. Xu, A. Stuchebrukhov, and W.M. Jackson.2
Department of Chemistry, University of California, Davis,
One Shields Ave., Davis, CA 95616, USA.
4
2
2
the autoionization states that converge on the So, Do, Po
states of the S+ ion originating from the ground state of sul-
fur (3P2). They also showed that the autoionization features
3
of the 3p3(2Do)nd Do levels are broad, while those of the
1This article is part of a Special Issue dedicated to the
memory of Professor Gerhard Herzberg.
2Corresponding author (email: wmjackson@ucdavis.edu).
3
3p3(2Do)nd So,3Po levels are narrow. However, surprisingly,
we failed to find previous measurements of the lifetimes
Can. J. Chem. 82: 885–890 (2004)
doi: 10.1139/V04-039
© 2004 NRC Canada

886
Can. J. Chem. Vol. 82, 2004
Fig. 1. Energy level diagram of the sulfur atom and ion.
from these line widths for atomic sulfur. For atomic oxygen,
with the similar electronic configuration 1s22s22p4, Smith
and co-workers (6, 7) measured the autoionizing lifetimes
3
originating from the P state by a variety of techniques in-
cluding Rabi oscillation. All of their measurements were
based on multiphoton ionization of atomic oxygen (6, 7).
Some lifetime measurements of weakly autoionizing states
in O I in the region of 75–125 nm were also done by observ-
ing the decay rate of emitted photons (8). Fewer studies
have been carried out on the superexcited singlet states of
oxygen atoms compared to the triplet states, most likely be-
cause of the difficulty of producing a high density of atoms
in the lower singlet state, from which optical excitation orig-
inates. We will show that this limitation can be overcome by
using laser photolysis of the proper precursor for the
metastable atom in a pulsed molecular beam along with a
tunable coherent vacuum ultraviolet (VUV) source to excite
the atom to the autoionization state. Strong signals can be
obtained for the autoionizing state because the lasers cross
the molecular beam at the point in both space and time at
which the atom density is at a maximum, as well as because
of the high sensitivity of the ion velocity imaging system.
The photodissociation dynamics of CS2 at 193 nm has
been extensively studied (9–14). It is well known that the
photolysis of CS2 gives rise to sulfur atoms in both the
ground (3P2,1,0) and excited (1D2) states. The S(1D2) in the
beam is then excited using a single VUV photon at
into the flight tube that is perpendicular to the plane defined
by the laser and the molecular beams. The typical voltage
ratio in our experiment was 1500 V/1042 V. To avoid any
field effects on the line width measurement, the voltages on
the ion optics were applied 300 ns after the arrival of the
VUV light in the ionization region. The pressure in the flight
tube during an experiment was about 8 × 10–7 Pa. This is
low enough so that the ion cloud can fly for 62 cm without a
collision in a field-free region before it strikes the detector.
The detector assembly consists of two microchannel plates
and a fast P47 phosphor screen. A CCD camera and a photo-
multiplier tube are mounted behind the screen to collect im-
ages and TOF spectra, respectively.
The CS2 molecular beam is crossed with a 193 nm laser
beam, which is produced by a GAM laser (EX5). The S(1D2)
atom is ionized by a coherent VUV radiation beam that is
obtained by frequency tripling. A Scanmate 2 (or FL2002)
dye laser operating with the Pyridine 2 dye is pumped by the
532 nm output of an Nd:YAG laser (Spectra-Physics, Pro-
230–30). The wavelength of the dye laser is calibrated by a
wavelength meter (COHERENT WaveMasterTM). The dye
laser output is frequency doubled in an Inrad auto-track unit,
which keeps the intensity of the UV output the same while
the wavelength is scanned. The UV beam is separated from
its fundamental with a prism and is focused with a quartz
lens into a gas cell, which contains Kr gas that is used for
generating the VUV radiation. The focal length of the quartz
lens is 15 cm, and the UV light is focused about 6.5 cm in
front of a LiF lens with a 6.5 cm focal length at the VUV
wavelength so that the VUV light is nearly collimated
through the reaction chamber.
1
121.896 nm (10.17 eV) to the 3s23p3(2Do)4d D2o neutral
state at 11.317 eV, which is above the first ionization thresh-
old of the sulfur atom. This superexcited state then under-
goes autoionization into the first ionization continuum of
S+(4S3/2) + e–, with its threshold at 10.36 eV. The energy of
the photon (10.17 eV) is not high enough to ionize the
ground state S(3P2). The relevant energy level diagram of the
sulfur atom and ion is shown in Fig. 1. The 3s23p3(2Do)4d
1Do2 ← 3s23p4 1D2 transition line profile is then recorded by
monitoring the S+ signal in the time-of-flight mass spec-
trometer (TOF-MS), while scanning the excitation wave-
length.
Experimental
The measurements were performed using an ion velocity
imaging apparatus, which has been described in detail else-
where (15). It consists of three stainless steel chambers that
are all pumped with separate turbo-molecular pumps. The
first chamber is the molecular beam source chamber, which
houses a piezoelectric pulsed valve with a nozzle having a
diameter of 0.25 mm. The molecular beam is skimmed twice
before it interacts with the laser beams. The second chamber
is the reaction chamber where the skimmed molecular beam
crosses the laser beams. During the experiments, the typical
pressure in this chamber was 4 × 10–5 Pa. The laser beams
enter the reaction chamber in a direction that is perpendicu-
lar to the molecular beam and intercept the molecular beam
in the center of the ion optics of the TOF-MS. The ion op-
tics of the TOF-MS consists of three plates, a repeller, an ac-
celerator, and a ground plate, the last of which is the
entrance to the flight tube for the mass spectrometer. High
voltages with the appropriate ratio for ion velocity imaging
are applied to the repeller and accelerator to focus the ions
Results
Figure 2 shows a series of mass spectra that were obtained
under different excitation conditions. A pure CS2 beam with
50 torr (1 torr = 133.322 Pa) backing pressure was used for
© 2004 NRC Canada

Huang et al.
887
Fig. 2. Time-of-flight mass spectra of CS2: (a) beam + 193 nm
light; (b) beam + 121.896 nm light; (c) beam + 193 nm light +
121.896 nm light (121.896 nm light arrives 20 ns later relative to
193 nm light).
lasers. The natural line width can be determined from these
scans by assuming the dye lasers have Gaussian profiles,
which have to be convoluted with the expected Lorentzian
profile to produce the measured line shape. Figure 4 shows
the fits obtained for the experimental line profiles using this
convolution. The FWHM of the Lorentzian profiles obtained
by these convolutions was 0.90 cm–1 for scans using both
Scanmate 2 and FL2002 dye lasers. Different Gaussian
bandwidths of 0.5 and 0.9 cm–1 have to be used in the con-
volution for the measurements using the Scanmate 2 and
FL2002 dye lasers, respectively. The fits are excellent, and
they yield a FWHM of 0.90 0.05 cm–1 for the natural line
width in both cases, which corresponds to an autoionization
lifetime of 5.90 0.31 ps. The bandwidths of the fundamen-
tals of the two dye lasers are 0.09 and 0.16 cm–1 for the
Scanmate 2 and the FL2002, respectively. The VUV band-
widths obtained by tripling the doubling output of the dye
lasers should be at most 6 times those for the fundamentals,
which turn out to be 0.54 and 0.96 cm–1, respectively. How-
ever, during the fitting it was found that the width of the
Gaussian function for the FL2002 could be chosen between
0.9 and 1.2 cm–1 to obtain a reasonable fit, with 0.9 cm–1
producing the best fit. Similarly, the width of the Gaussian
function for the Scanmate 2 could be chosen between 0.4
and 0.6 cm–1, with 0.5 cm–1 producing the best fit. The iden-
tical results for the natural line width from measurements
using different dye lasers indicate the results are reliable.
Discussion
these experiments. The timing for the pulse valve opening
was carefully adjusted so that no clusters were observed in
When an electron combines with the 3s23p3 ion-core
states of the sulfur atom, Rydberg series are formed whose
energies converge to the associated 4So, 2Do, or 2Po ion
+
the TOF spectra. Figure 2a shows that CS2 and CS+ ions
are produced by multiphoton ionization even though the
193 nm laser fluence is very low (~1 mJ/cm2) (16). This is
because the single and multiphoton absorption cross sections
of CS2 are very large. Figure 2b is the TOF spectrum taken
when only the VUV light at 121.896 nm (10.17 eV) was
4
states. The So core forms a series of triplet and quintet S, P
Rydberg states, while Do forms singlet and triplet P, D, F
2
Rydberg states, and Po forms singlet and triplet S, P, D
2
Rydberg states. Photoabsorption and photoionization spectra
of sulfur have been studied extensively in this region (3–5).
Berkowitz and co-workers (5) reported the photoionization
spectrum of sulfur in detail between the first ionization
threshold and 92.5 nm. They assigned many of the auto-
+
present. The CS2 signal is the result of single-photon ion-
ization of the CS2 molecule whose ionization energy is
10.07 eV. Figure 2c shows the TOF mass spectrum when
both lasers were present. The 121.896 nm light is delayed
20 ns with respect to the 193 nm laser. A strong S+ signal is
now seen in the TOF mass spectrum as expected. The S+ ion
comes from the VUV ionization of the S(1D2) atom that is
produced by the photodissociation of CS2 at 193 nm. The S+
ion signal disappears when the Kr gas is evacuated from the
VUV cell.
ionization states that converge to the So, Do, Po states of
the S+ ion originating from the ground state of sulfur (3P2)
(5).
4
2
2
Even though there have been many studies on the photo-
ionization of sulfur atoms and the autoionization levels for
these sulfur atoms have been previously assigned, to our
knowledge no autoionization lifetime measurements have
been reported. On the other hand, there are measurements on
the autoionization lifetimes for atomic oxygen. The O
The S+ ion signal as a function of ionization wavelength
was recorded using a Stanford Research Boxcar Averager
(SR 250). Figure 3 shows the line profiles obtained when the
wavelength of the ionization laser was scanned through the
1
1
(2Do)3p P1 and F3 levels were first observed in the emis-
sion studies by Edlen and Sven (17) and by Eriksson and
Isberg (18). The transitions involving the 1P1 level were
broadened by approximately 0.2 cm–1 with an autoionization
lifetime of 3 × 10–11 s to the 4S3o/2 continuum; the transitions
1
3s23p3(2Do)4d D2o ← 3s23p4 1D2 transition using different
gas pressures in the four-wave mixing cell with Scanmate 2
and FL2002 dye lasers. Different conversion efficiencies oc-
cur at these different pressures for frequency tripling that re-
sult in different VUV intensities. The absolute intensities at
different Kr pressures vary by more than one order of mag-
nitude. Figure 3 shows that the line profile does not change
as the Kr pressure changes, which indicates that it is free
from power broadening. The FWHM is a little different for
the two dye lasers because of the different bandwidths of the
1
involving the F3 level were sharper, and hence the lifetimes
were longer (18). Instances of forbidden autoionization in
atomic oxygen have been discussed by Huffman et al. (19)
and Dehmer and co-workers (20–22) for Rydberg states ex-
3
1
1
cited from the P, D2, and S0 lower states. Recently, Pratt
et al. (23) reported the autoionization of O (2Do)3p P1 and
1
© 2004 NRC Canada

888
Can. J. Chem. Vol. 82, 2004
Fig. 3. The line profiles obtained under different Kr pressures in the VUV cell (indicated on the figure in torr (1 torr = 133.322 Pa))
and using different dye lasers. The curves are individually normalized to 1 at the highest point. The absolute intensities differ by more
than one order of magnitude at different pressures.
Fig. 4. The convolution fits of the experimental line profiles and the deconvoluted Lorentzian profile with a FWHM of 0.9 cm–1 in
both cases: (a) for measurements with the Scanmate 2 dye laser, whose fundamental bandwidth is 0.09 cm–1, and (b) for measurements
with the FL2002 dye laser, whose fundamental bandwidth is 0.16 cm–1.
© 2004 NRC Canada

Huang et al.
889
1F3 levels excited from the O(1D2) state by two-photon ab-
sorption. They evaluated the autoionization lifetimes of the
between this electron and the core results in their energy ex-
change, a process in which the 4d electron is excited to an
unbound state with kinetic energy sufficient to escape the
Coulomb cage of the core, while the ionic core itself relaxes
1
1P1 and F3 levels and found that they were longer than 3 ×
10–10 and 5.8 × 10–10 s, respectively. Smith and co-workers
(6, 7) have done a considerable amount of work on the
autoionizing states of atomic oxygen. They measured the
4
to its ground state of S3/2. In the latter process, one of the
electrons in the doubly occupied p orbital of the 3s23p3(2Do)
configuration is transferred to an empty p orbital, simulta-
neously changing its spin, so that in the final state of the
core all three electrons occupy three different p orbitals and
have parallel spins, yielding 3s23p3 S+(4S3o/2). Owing to the
exchange effects, the same final state can be obtained by a
transfer of the 4d electron to an empty orbital of the 3p
shell, while one of the paired electrons from the 3p shell of
the core is promoted to an unbound state and ejected from
the atom. However, the contributions of the exchange effects
in the latter type of interactions are typically small (29). The
exact evaluation of the rate of the described process requires
rather sophisticated computational work as, e.g., in ref. 30.
However even a rough estimate described in the Appendix
gives FWHM values in the range 10–40 cm–1, which is
about an order of magnitude higher than the experimental
measurements.
3
autoionization lifetimes for the (2Do)3p 1,3P and (2Do)3p D,
3F states by measuring the Rabi oscillations that were in-
3
duced when the atoms were excited from the P2 ground
state by the multiphoton process. The autoionization life-
times are on the order of 10–10 s for all the states except the
3
(2Do)3p P state, which has a 6-fs lifetime (7). More re-
cently, single-photon ionization of atomic singlet oxygen O
(1D2) was investigated by Flesch et al. (24). The photo-
ionization efficiency spectrum was recorded between the
onset of the first (4So) and the second (2Do) ionization thres-
holds. However, no lifetimes were reported in this paper.
Within the LS coupling approximation, direct photoioni-
4
zation to the So + e– state between the first and the second
ionization threshold (to (2Do)) is optically forbidden from
the singlet states of the atom, since it violates the spin con-
servation rule. Thus, the only way these states can be ion-
4
ized is via autoionization to So as a result of spin–orbit,
spin–spin, or other possible weaker interactions that couple
atomic states with different spins (25–27). As discussed
above, the lifetimes of the singlet states for atomic oxygen
were found to be of the order of 10–10 s. In the current mea-
Conclusion
For the first time, we are able to record the 3s23p34d 1D2o ←
3s23p4 1D2 transition line width of atomic sulfur using single
VUV photon excitation by monitoring the S+ signal in a
TOF-MS while scanning the excitation wavelength. The
deconvolution of the measured excitation line shape with the
finite laser bandwidth yields a natural line width (FWHM)
of 0.90 0.05 cm–1, from which the autoionization lifetime
1
surements for singlet atomic sulfur Do2, the lifetime was de-
termined as 5.9 ps. This much faster autoionization rate for
1
sulfur Do2 compared with singlet oxygen atoms can be un-
derstood in terms of spin–orbit and spin–spin interactions.
The mass of the sulfur atom is much greater than that of the
oxygen atom; one would therefore expect that spin–orbit in-
teraction in the heavier sulfur atom would be much stronger
than in the oxygen atom. This is seen in the spin–orbit
of the neutral superexcited state 3s23p34d D2o is found to be
1
5.90
0.30 ps. These results show that this is a general
method to measure the lifetimes of atomic autoionization
states with strong spin–orbit and spin–spin interactions.
3
splittings that are observed in the P2,1,0 ground state of the
3
sulfur atom, which are 396 and 177 cm–1 for P1–3P2 and
3P0–3P1, respectively, whereas they are only 158 and 69 cm–1
for the oxygen atom (28). The spin–spin interaction can also
play an important role in the autoionization process. In the
highly excited states, mixing between states with different
spin is expected because of spin–spin interaction. The exis-
tence of state mixing between the very rapidly ionizing trip-
let state and the singlet state could promote the autoionizing
rate of the singlet state.
Acknowledgements
This work was supported by the National Science Founda-
tion (NSF) (grant No. CHE-0100965) and NASA (grant No.
NAG5–12124).
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h
[1]
k =
V
2ρf
if
where Vif is the transition matrix element and ρ is the den-
f
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where V is the volume of the system, and p is the momen-
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gives the density of states,
m
π2h3
mE
[A3] ρ = V
2
where E is the kinetic energy of the ejected electron
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rr
ipr 
r
[A4] ͦ p〉 =
1
exp




h
V
For an estimate of the matrix element, we can then write
3/ 2
r
a
↑
↑
4d
$
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[A5]
V
= 〈ϕ↓3 px(1)ϕ4d(2)V(1,2) ϕ3 pz(1)p(2)〉 ≈ V
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12
V
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12
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the above estimate. Here, we neglect factor 2 2/π, which is
on the order of unity. Thus, for the rate we roughly have
67, 195 (1977).
23. S.T. Pratt, P.M. Dehmer, and J.L. Dehmer. Phys. Rev. A, 43,
282 (1991).
24. R. Flesch, M.C. Schurmann, J. Plenge, H. Meiss, J.
Hunnekuhl, and E. Ruhl. Phys. Rev. A, 62, 52 723 (2000).
25. E.U. Condon and G.H. Shortley. The theory of atomic spectra.
Cambridge University Press, Cambridge, UK. 1979.
26. P. Feldman and R. Novick. Phys. Rev. 160, 143 (1967).
27. M.E. Rudd and K. Smith. Phys. Rev. 169, 79 (1968).
28. NIST atomic spectra database data [online]. Available from
http://physics.nist.gov [accessed 24 February 2004].
29. H.A. Bethe and E.E. Salpeter. Quantum mechanics of one and
two electron atoms. Plenum, New York. 1977.
V 2 a42dm a4d mE
12
[A6] k ≈
2h h2
h
The last term in the above expression is roughly the angular
momentum of the ejected electron; since the kinetic energy
of the electron is about 1 eV, the last term gives a factor
close to 4. The second term is the inverse kinetic energy of
the 4d electron, the order of magnitude of which is also
1 eV. A typical value of spin–orbit interaction in the sulfur
atom can be estimated from the splittings of the 3P2–3P1
(396 cm–1) and 3P1–3P0 (177 cm–1) energy levels of the
ground state (A1). For V = 200 cm–1, the FWHM is esti-
mated to be 10 cm–1; for1V2 = 400 cm–1, FWHM = 40 cm–1.
Given the crude nature of12the estimate, it is not surprising
that the estimation is an order of magnitude higher than the
30. H.P. Saha and D. Lin. Phys. Rev. A, 63, 042 701 (2001).
Appendix A
Here, we estimate the order of magnitude of the
autoionization rate of the process described in the text, using
experimental data for typical spin–orbit interactions in sul-
fur. The rate is given by the Golden Rule formula,
observed value. Note that the term V in eq. [A5] should be
12
the interaction between the 4d Rydberg electron and the 3p
core electrons. Considering the large diameter of the
Rydberg orbital, the interaction V should be much weaker
than that in the ground state S(3P1)2. Using the measured line
2π
h
[A1] k =
V
2ρf
if
where Vif is the transition matrix element, and ρ is the den-
sity of the final states. The final states result frfom the ion-
ized electron moving in the field of the ionic core. The
number of such states is given by the usual expression:
width of 0.9 cm–1, we can estimate V to be 60 cm–1.
12
References
r
dp
A1. NIST atomic spectra database data [online]. Available from
http://physics.nist.gov [accessed 24 February 2004].
[A2] dn = V
(2πh)3
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