Radiat Environ Biophys (1999) 38:239–247
© Springer-Verlag 1999
R E V I E W A RT I C L E
Yoshihiko Hatano
Interaction of photons with molecules – cross-sections
for photoabsorption, photoionization, and photodissociation
Received: 2 September 1998 / Accepted in revised form: 10 September 1999
Abstract A survey is given of recent progress in measurements of photoabsorption, photoionization, and photodissociation cross-sections of molecules in the wavelength range of photons in the vacuum ultraviolet
(VUV), where the optical oscillator-strengths of most
molecules are predominantly distributed. Some remarks
are presented on molecules in the condensed phase. Particular emphasis is placed on the current understanding
of spectroscopy and dissociation dynamics of molecules
in the superexcited states which are produced through
the interaction of photons in this wavelength range. In
the VUV range, most of the observed superexcited states
are assigned to high-Rydberg states which are vibrationally (and/or rotationally), doubly, or inner-core excited,
and converge to each of the ion states.
Key words Oscillator-strength · Photoabsorption
cross-section · Photoionization cross-section ·
Photodissociation cross-section · Photoionization
quantum yield · Vacuum ultraviolet · Synchrotron
radiation · Superexcited states · High-Rydberg states
proportional to photoabsorption cross-sections have already been measured for various molecules in the wavelength region longer than the near-ultraviolet (UV). Until
recently, there were only a very few measurements in
the wavelength region shorter than the LiF cut-off at
105 nm, at which the photon energy is 11.8 eV, this being due to experimental difficulties in obtaining appropriate photon sources and because no suitable window
material was available. The cut-off energy of 11.8 eV
corresponds, roughly speaking, to the ionization potentials of commonly occurring molecules. The sum of the
oscillator-strengths below 11.8 eV amounts to only a few
percent of the total sum, which according to the ThomasKuhn-Reiche (TKR) sum rule is equal to the total number of electrons, Z, in a molecule. It is, therefore, concluded that the interaction of photons with molecules in
the VUV region, where synchrotron radiation (SR) is the
most promising photon source (Fig. 1), is predominant
over all other wavelength regions [4, 5, 6, 7, 8, 9, 10].
Introduction
Cross-section data on the interaction of photons with
molecules are of great importance in radiation physics,
chemistry, biology, therapy, and related fields, because
they are closely related to cross-sections for the interaction of fast charged particles with matter [1, 2, 3, 4, 5,
6, 7]. In this overview, particular emphasis is placed on
recent progress in the measurements of cross-section data in the vacuum ultraviolet (VUV) region, because they
dominate the total oscillator-strength distribution as there
are very few measurements reported in the literature
[4, 5, 6, 7]. The values of oscillator-strengths which are
Y. Hatano (✉)
Department of Chemistry, Tokyo Institute of Technology,
Ohkayama 2-12-1, Meguro-ku, Tokyo 152-8551, Japan
e-mail: [email protected]
Tel.: +81-3-57342235, Fax: +81-3-57342655
Fig. 1 Synchrotron radiation (SR) chemistry as a bridge between
radiation chemistry and photochemistry. The dipole oscillatorstrength df/dE is shown as a function of wavelength λ and photon
energy E. Note the relation E·λ=1.24×103 eV·nm. The intensity of
SR is also shown, as are the energies of photons from several line
sources. VUV vacuum ultraviolet, EUV extreme ultraviolet, SX
soft x-ray, HX hard x-ray [4, 5, 6, 7, 8, 9, 10]
240
This paper surveys recent measurements of cross-sections for the photoabsorption (σt), photoionization (σi),
and photodissociation (σd) of molecules in the VUV region and, furthermore, provides a summary of current
understanding in spectroscopy and dynamics of molecules in superexcited states [8, 9, 10, 11, 12]. Molecules
treated here such as hydrocarbons, alcohols, ethers, and
other organic molecules are chosen from the point of
view of basic radiation research. The survey also includes some remarks on molecules in the condensed
phase.
VUV-optical oscillator-strength distributions
of polyatomic molecules
The absorption of a single photon in this wavelength region by a molecule changes its electronic state from the
ground state to a final excited or ionized state. Its transition probability is expressed in terms of the optical oscillator-strength, which is proportional to the photoabsorption cross-section.
It is important to obtain photoabsorption and related
cross-sections for polyatomic molecules such as hydrocarbons and other organic molecules and to correlate
them to molecular structure [4, 5, 6, 7, 8, 9, 10]. With
this idea in mind, photoabsorption and photoionization
cross-sections for molecules in several stereo-isomer series have been systematically measured and compared to
each other [13, 14, 15, 16]. The main purpose of these
investigations is to reveal how oscillator-strength distribution (df/dE) or differential oscillator-strength changes
with changing molecular structures. For this purpose,
isomers have been chosen as examples. Since isomer
molecules consist of the same kind and same number of
atoms, their df/dE are expected to have the following
properties:
Fig. 2 Absorption cross-sections of cyclopropane and propylene
[13]
with the sum rule under the above assumptions. Figure 2
shows, as an example, the absorption cross-sections, i.e.,
the oscillator-strength distributions of C3H6 isomer molecules, cyclopropane and propylene. Similar cross-section data have also been obtained for the other isomer series listed above. The common and new features of absorption cross-sections or oscillator-strength distributions are summarized as follows:
1. The sum of df/dE of an isomer over all energy regions
is expected to be equal to that of another isomer as
well as to the number of electrons in the molecule, according to the TKR sum rule.
2. The gross features of df/dE of isomers are expected to
be almost identical to each other in the wavelength region where inner-core electrons are excited, because
the isomers’ molecular structure has relatively little
influence on the excitation of their inner-core electrons. Moreover, the value of df/dE in such a wavelength region would be almost equal to the sum of
df/dE values of the constituent atoms.
1. The σt values show a maximum at 70–80 nm (16–
18 eV) for each molecule.
2. In the wavelength region shorter than that at the maximum, σt values are almost the same among the isomer molecules (e.g., cyclopropane and propylene as
shown in Fig. 2) and are equal to the sum of the
cross-sections for the constituent atoms.
3. In the longer wavelength region, the cross-sections
have different peaks and shoulders depending on the
isomer, i.e., on its molecular structure (see again
Fig. 2). The sum of the cross-sections in this wavelength region is, however, almost equal among the
isomer molecules. This means, therefore, that on the
one hand the total oscillator-strength distribution, normalized to Z according to the TKR sum rule, can be
divided into two wavelength regions, the longer and
the shorter one, and on the other hand, the sum of the
oscillator-strengths in each region does not depend on
the molecular structure of an isomer and is constant
among the isomer molecules. In other words, the partial sum rule satisfies the oscillator-strength distribution in each region.
Using the assumptions stated above, the photoabsorption
cross-sections have been measured for isomers C3H6 (cyclopropane and propylene), C4H8 (1-butene, isobutene,
cis-2-butene, and trans-2-butene), C6H12 (cyclohexane,
1-hexene, and tetramethylethylene), C2H6O (ethyl alcohol and dimethyl ether), and C3H8O (n-propyl alcohol,
i-propyl alcohol, and ethylmethyl ether) in the wavelength region of about 30–140 nm. Values of df/dE for
different isomers are compared with one another and
These results make an important contribution to the future development of research in chemical physics and
physical chemistry, particularly to motivating the development of new quantum chemistry. They will also contribute to estimating the energy deposition spectra of
molecules in the interaction of ionizing radiation with
matter. The results, e.g., those in Fig. 2, satisfy well the
TKR sum rule as summarized in Table 1. There is an
extremely good agreement between the sum of the ob-
241
Table 1 Sum of dipole oscillator-strength distributions of C3H6
[13] (Ip ionization threshold)
Wavelength (nm)
Cyclopropane
Propylene
Below Ip
Ip–105
105–35
35 >
Total
Z
0.746
0.715
11.744
10.251
23.46
24
0.507
0.666
12.176
10.251
23.60
24
Fig. 3 Absorption cross-sections of ethyl alcohol: solid line experiment [14], dotted line theory by Platzman [3]
tained oscillator-strength values (partly including semiempirical ones in the higher-energy region) and the number of electrons, Z. Table 1 also clearly shows that the
sum of the oscillator-strength distributions in the energy
region below the first ionization potential occupies only
a few percent of the total oscillator-strength. The distributions in the VUV region are of great importance for
understanding the ionization and excitation of the molecules. The distribution of the oscillator-strength of ethyl
alcohol, shown in Fig. 3, presents an interesting comparison between the results of recent experimental measurements [14] and those derived from Platzman’s theory [3].
Although general features of the spectra agree well with
each other, several large peaks expected by Platzman are
absent in the new measurements.
Photoionization quantum yields
A molecule that has received energy exceeding its ionization threshold (IP) does not necessarily ionize. In general, there are other decay channels, such as dissociation
into neutral fragments as the ionization process competes
with neutral fragmentation. Various pathways are schematically represented for a molecule AB [3, 4, 5, 6, 7, 8,
9, 10, 11, 12] as follows:
AB + energy → AB+ + e- Direct ionization
(1)
AB + energy → AB’
Superexcitation
(2)
→ AB+ + e- Autoionization
(3)
AB’
AB’
→ A+ B
→Others
Dissociation
(4)
(5)
In this mechanism, AB’ is a superexcited molecule which
decays through autoionization or dissociation. The crosssection, σi, corresponds to the sum of the cross-sections
for both direct and auto-ionization processes, while σt
corresponds to the sum of the cross-sections for direct ionization and super-excitation. The value of
η(=σi/σt) in the energy region below Ip is zero, while
above Ip it increases with increasing energy, as described
in the preceding section, and eventually approaches unity
in the energy region well above Ip. However, in the energy region close to Ip, the dissociation process plays a very
important role in the decay of a superexcited molecule.
It has been pointed out both theoretically and experimentally that superexcited states, and hence neutral fragments formed from their dissociation, play an important
role in radiolysis [3, 4, 5, 6, 7, 8]. The neutral fragments
are translationally, vibrationally, or sometimes electronically excited, due to a large internal energy of superexcited states. Such fragments are called hot atoms or free
radicals, and have anomalous chemical reactions.
The electronic structures and dissociation dynamics
of molecular superexcited states have been clearly substantiated by electron impact spectroscopy and more recently by spectroscopy combined with SR. It is concluded that a major part of the superexcited states of molecules involves molecular high-Rydberg states which are
vibrationally (and/or rotationally), doubly, or inner-core
excited, and converge to each of ion states [8, 9, 10, 11,
12].
In summary, photoionization cross-sections and photoionization quantum yields are of great importance as
key features of superexcited states, which characterize
the primary processes, (1)–(5), of both photolysis and radiolysis of molecules.
The photoionization quantum yield, η, is a quantity of
considerable importance and serves as an index for the
degree of competition between ionization and dissociation. Several experimental efforts have been devoted to
the measurement of η. Serious conflict exists even for
simple molecules, not only between photon impact experiments and ‘simulated’ ones by electron impact, but
also between photon impact experiments themselves.
The problems have originated mainly from the lack of an
intense light source and a suitable window material in
the VUV region, particularly in the wavelength region
shorter than the lithium fluoride (LiF) cut-off at 105 nm.
Experiments with differential pumping and without a
window for the entrance of a photon beam into an ionization chamber also present several significant problems. These include effusion of sample gases into the
beam and contribution from a diffracted photon beam in
the higher order, making it difficult to determine absolute and comprehensive values of η. In most cases, the
η−values have been assumed to be unity in the energy
region far above the first ionization potential (say
>25 eV).
242
Fig. 4 Photoionization quantum yields of C3H6 isomers
[15]
Fig. 5 Photoionization quantum yields of several molecules
in the wavelength regions
shorter and longer than the LiF
cut-off at 105 nm [4, 6, 8, 9,
10]
Systematic measurements have recently been reported
of the photoionization quantum yields as well as of the
photoabsorption cross-sections of C3H6, C4H8, C6H12,
C2H6O, and C3H8O isomers using a multiple-staged photoionization chamber and an SR light source in the
wavelength region from 105 nm (11.8 eV) up to their respective ionization potentials at about 120–140 nm
(9–10 eV) [15]. This work has been further extended to
the first attempt of measuring photoionization quantum
yields in the wavelength region of 54–92 nm (13–23 eV)
using SR in a combination with thin metal foil windows
[4, 6, 8, 9, 10]. In what follows, a survey is given of the
recent progress in the measurement of η-values.
The values of η have systematically been measured in
the wavelength region below the LiF cut-off at 105 nm
(11.8 eV) for those molecules in several isomer series
whose photoabsorption cross-sections have been measured. Some of the results for cyclopropane and propylene are shown in Fig. 4 [15]. The η-curves for the same
C3H6 isomer molecules are very different from each other. The η-curve for cyclopropane rises almost monotonically and indeed much more rapidly than that for propylene, which has a step or a shoulder at 110–120 nm. The
η-curves for other molecules not presented here have
shown interesting common features of η-curves as a
function of photon energy. A more pronounced energy
difference corresponds to a longer step length, as seen
for propylene in Fig. 4. This result means that the η-value increases rapidly in the wavelength or energy region
close to the ionization potential and agrees well with the
conclusion that the most important part of the superexcited states is the high-Rydberg state converging to each
ion state. It is, therefore, concluded that the shape of the
η-curve as a function of the energy at least for these
chemically important molecules is determined by the
density of converging Rydberg states, i.e., superexcited
states, which increase rapidly with increasing energy in
the energy region close to the ionization potential.
In the wavelength region shorter than the LiF cut-off
at 105 nm (11.8 eV), metal foil filters are employed as
window material for the incoming SR beam from a VUV
monochromator. The filters prevent sample gas effusion
and eliminate higher-order radiation. In the wavelength regions of 54–80 nm (16–23 eV) and 74–92 nm
(13–17 eV), Sn and In foils are used, respectively. Their
thickness is about 100 nm, with a transmittance of about
1%.
Figure 5 shows the ionization quantum yields measured in the wavelength region of 54–92 nm (13–23 eV)
together with those in the wavelength region longer than
105 nm (11.8 eV) [4, 6, 8, 9, 10]. No data are given in
the wavelength region between these two because there
243
is no thin metal window convenient for the measurement
of ionization quantum yields and because there are large
effects of higher-order light. The results are summarized
as follows:
1. η-values in the region above, but close to, the first
ionization potential are much less than unity, which
means that most of the molecules, at least the molecules shown in Fig. 5, are not easily ionized even if
they have received enough energy to be able to ionize. In this region, therefore, the neutral fragmentation
of superexcited molecules is of great importance in all
decay channels as expressed by processes (1)–(5).
2. η-values do not reach unity even in the energy range
more than about 10 eV above the first ionization potential.
3. η-values increase with increasing photon energy and
reach unity at around 23 eV (or 54 nm).
4. η-curves show considerable structures.
From the results (1–4) listed above, it is concluded that
non-ionizing processes, such as the neutral fragmentation of superexcited molecules, play an important role in
their decay channels. Since an important part of the magnitude of the oscillator-strength distributions of most
molecules exists in the wavelength range of 60–100 nm
in which the η-values clearly and largely deviate from
unity, it is concluded in general that molecules are not
easily ionized but dissociated into neutral fragments
even when they have energies much larger than their ionization thresholds.
Fig. 6 Photoionization quantum yields of acetylene: ⊕ Metzger
and Cook [41], ★ Person and Nicole [42], + Cooper et al. [43],
− Ukai et al. [17]
Dissociation of superexcited states
of polyatomic molecules
This section deals with a comparative study of ionization
quantum yields with excitation spectra of optical emission from dissociation fragments. Neutral fragments
formed from the dissociation of superexcited molecules
often have excess energies electronically, vibrationally,
rotationally, and/or translationally excited because the
photon energies corresponding to the wavelengths in
Fig. 5 are much higher than the bond dissociation energies to form fragments in their ground states. It is, therefore, of great interest to observe optical emissions from
excited fragments as a function of wavelength, i.e., to
obtain excitation spectra of optical emission and to compare these with the structures in η-curves. In the following, examples of such a comparison are presented to
clarify in detail the dynamics of superexcited molecules.
Acetylene
Figure 6 shows recent measurements of the photoionization quantum yield of acetylene using SR combined
with a thin metal foil window. Also shown are previous
measurements using discharge lamps or electron beams
as a virtual photon source [17]. In the energy range of
Fig. 7 Photoabsorption (σt), photoionization (σi), photodissociation (σd), cross-sections (upper panel), and photoionization quantum yield (lower panel) of C2H2 [17]
244
18–24 eV, the yields obtained by using the virtual photon
source are considerably larger than those obtained with
SR as a real photon source. The yields obtained in the
lower energy range by using different methods agree
fairly well. The yields obtained using SR and represented by the solid curve show distinct structures with at
least three minima, contrary to those obtained using either the virtual photon source or discharge lamps. Obvious deviations from unity in the ionization quantum
yield of acetylene in Fig. 6 indicate the neutral dissociation of a superexcited acetylene molecule predominantly
competing with autoionization. Figure 7 shows the photoabsorption cross-sections of acetylene [17], the structures of which are assigned to Rydberg series converging
to each of the ionic states, (3σg)–1, (2σu)–1, and (2σg)–1.
Combining the photoionization quantum yields and the
photoabsorption cross-sections, the cross-sections for the
total ionization (σι) and for non-ionizing decay processes
(σδ) are obtained as shown in Fig. 7.
Excitation spectra of fluorescence from excited fragments produced in the dissociation of a superexcited
acetylene molecule have been observed [17]. According
to the emission spectra of excited fragments which may
be produced from a superexcited acetylene molecule,
band-pass filters were chosen to disperse the total fluorescence. In Fig. 8, the excitation spectra of the dispersed fluorescence for some excited fragments are summarized and compared with the η-curve from Fig. 6
[17]. In comparison with the threshold wavelengths of
the excitation spectra in Fig. 8, as well as with the
thresholds of related dissociation processes calculated
from the dissociation energies based on the heats of formation and the electronic energies of excited fragments,
the spectra (b)-(e) in Fig. 8 are interpreted as due to the
following dissociation processes, respectively [17]:
C2H2+hv → C2(d3Πg)+2H
C2(C1Πg)+2H
CH(A2∆)+CH (or CH(A2∆))
H(2p)+C2H (or C2+H)
(6)
(7)
(8)
(9)
The five peaks as denoted by (1)–(5) in Fig. 8f correlate
well with characteristic structures observed in the excitation spectra in Fig. 8b–e. By comparison with the correlation further with σt and σi curves, the precursor superexcited states for the dissociation processes (6)–(9)
above have been assigned [17] in detail to high-Rydberg
states and/or inner-valence excited states which have
been investigated theoretically.
The excitation spectrum in Fig. 8d as well as the corresponding dissociation (8) is of particular interest from
a chemical viewpoint because of a predominant breaking
of the triple bond of acetylene in a specific energy range.
This is similar to a theoretical investigation by Jesse and
Platzman [18] indicating a predominant breaking of the
double bond of ethylene in interpreting the hydrogen isotope effect on η. Meisels [19] made a critical comment
on this conclusion based on the experimental results of
the radiolysis of C2H4 and C2H4-Ar systems.
Fig. 8 Fluorescence excitation spectra for (a) total emission
in 200–650 nm detection range, (b) C2(d3Πg → a3Πu, ∆υ=0),
(c) C2(C1Πg → A1Πu, ∆υ=1), (d) CH(A2∆ → X2Π, 0 → 0),
(e) Lyman-α from H(2p) (121.6 nm) [17]
Silane
Dynamic studies of superexcited states of silane sand
heavier group IV compounds are of particular interest in
comparison with those of hydrocarbons. Optical crosssection data on these compounds, however, are rare in
comparison with the relatively more abundant data on
hydrocarbons as described above.
Absolute values of the photoabsorption cross-section,
the photoionization cross-section, and the ionization
quantum yield of SiH4 have been measured in the energy range of 13–40 eV using SR [20]. Figure 9 shows total absorption, photoionization quantum yield and neutral fragmentation cross sections. A broad peak is observed in the photoabsorption cross-section curve, with
the main peak maximum at 14.6 eV. This is also observed in electron energy-loss spectra and assigned to
the optically allowed transition of a 3a1 electron to an
antibonding σ*(t2) orbital. In the energy region around
this broad peak, the ionization quantum yield, as clearly
shown in Fig. 9, deviated from unity, and the cross-section curve for the neutral fragmentation has a maximum.
In the energy range just above this range, a notable
structure is observed in both absorption and ionization
245
Fig. 9 Absorption cross-sections (σt), photoionization
cross-sections (σi), photoionization quantum yields (η), and
neutral-fragmentation crosssections (σn) of silane in the
energy range between 13.6 and
22 eV [20]
cross-sections. Both of the cross-sections are nearly
equal; in other words, the ionization quantum yield is
unity. This structure is assigned to the (3a1)–1(npt2)
Rydberg state which predominantly decays through autoionization.
Subtracting the photoionization from the photoabsorption cross-sections, as shown in Fig. 9, one obtains
the total cross-sections for processes other than ionization, namely, neutral fragmentation. An outstanding feature of the cross-section is a peak centered at 14.6 eV.
The peak position corresponds well with the maximum
of the photoionization cross-section and the minimum of
the photoionization quantum yield. The cross-section for
the neutral fragmentation decreases with increasing photon energy to almost zero at 16 eV and rises again slightly up above 17 eV. In view of the rising-up behavior of
the photoionization quantum yield above the ionization
threshold, which is systematically observed for various
molecules, the cross-section for neutral fragmentation
should have a considerable magnitude in the lower-energy region than the present lowest limit of the photon energy in Fig. 9.
In summary, there are at least two kinds of superexcited states with different characters in the energy
range shown in Fig. 9. The superexcited state produced
by the transition 3a1 electron to the optically allowed
antibonding σ*(t2) orbital, shown as the 14.6-eV
broad band in both η and σn curves, decays through
fast neutral fragmentation processes competing with
autoionization. In contrast, the superexcited Rydberg
states in the 16–17 eV region converging to the second
ionization potential of silane decays mainly through autoionization. As a result, the neutral fragmentation
cross-section is inappreciable in this region. The neutral fragmentation in the energy region above 17 eV is
ascribed to the dissociation of doubly excited states
[20].
Fig. 10 Photoionization quantum yield and Lyman-α excitation
spectrum of dimethyl ether [21]
Dimethyl ether
An interesting structure has been observed in the ηcurve in the wavelength region of 54–92 nm. Figure 10
shows the optical emission at a wavelength of 115–
200 nm, at which one expects under these experimental
conditions a Lyman-α emission from fragment H*(n=2).
The ionization quantum yield is shown for comparison
[21].
246
A clear deviation of the η-value from unity with the
three characteristic minima shows a superexcited dimethyl ether molecule decaying into dissociation and
other non-ionizing channels. The minima correspond
well with the energies of ionic states with the vacancies
of the πCH3 and σCO orbitals or the MO correlating to the
C(2s) orbital, which are known from the HeII photoelectron spectra for dimethyl ether. This correspondence has
led to the conclusion that the superexcited states corresponding to the minima are high-Rydberg states converging to each of these ionic states; i.e., the (3b2)–1, (5a1)–1,
and (1b1)–1 ionic states at around 80 nm and the (4a1)–1
and (2b2)–1 states at around 61 and 66 nm. The large deviation of the η-value from unity, which diminishes with
the increase in photon energy, is explained by the rate of
autoionization in competition with dissociation and the
state density of the continuum correlating with the superexcited states. The rate of autoionization decreases inversely with the excess energy above the ionization potential. If the photon energy further exceeds other ionization limits, then the new possible channels correlating
with other ionization continua make the rate increase.
Cross-sections for molecules in the condensed phase
Cross-section data for molecules in the condensed phase
are very scarce compared with those in the gas phase
[4, 5, 6, 8, 9, 10]. Understanding ionization in the condensed phase is still an unresolved and important problem. We have little understanding of the ionization potential of condensed matter, nor can we discriminate between ionized states and highly excited states. It is also
of great importance to investigate in detail geminate
electron-ion pairs and superexcited states or highRydberg states in the condensed phase. It should be noted that a key experiment to clarify these problems, on
which there have been very few reports, is the absolute
measurement of ionization quantum yields in the condensed phase using SR.
SR has been applied to the measurement of ionization
threshold energy values of liquids [22, 23] as well as to
experiments in order to give evidence for Rydberg states
near the threshold in liquid alkanes [24]. Photoionization
studies of doped supercritical fluids using SR are of considerable importance to substantiate the ionization mechanisms of molecules in the condensed phase [25, 26].
Autoionization of highly excited states has been observed in the laser photoionization experiment of molecules in the condensed phase [27, 28, 29, 30]. Photoionization quantum yields are measured as a function of excitation energy. Similar phenomena have also been observed in the VUV single-photon ionization of molecules
in the condensed phase [31, 32].
Optical oscillator-strength and related data have been
measured extensively for a variety of organic and biological molecules in the condensed phase [33, 34, 35]. An
important role of superexcited states has been considered
also in the VUV photolysis of biological systems using
SR [36]. It should be noted that a new method was developed recently for the measurement of the oscillatorstrength distribution of liquids by inelastic x-ray (SR)
scattering spectroscopy [37, 38]. It is interesting to compare the oscillator-strength distribution of gas-phase water [39] with liquid [37] and amorphous ice [40].
Acknowledgements The author wishes to thank Drs. M. Inokuti,
F.J. de Heer, and C.E. Brion for helpful discussion and comments.
He has been indebted to Drs. N. Kouchi, M. Ukai, K. Kameta, T.
Odagiri, H. Koizuni, S. Arai, A. Ehresmann, M. Kitajima, and S.
Machida in his group for their excellent collaboration. The authors
SR research described herein at the photon factory was supported
scientifically by Drs. K. Ito, K. Tanaka, T. Hayaishi, and A. Yagishita, and financially by the Ministry of Education, Science,
Sports, and Culture.
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