Field ionization and photoionization of CH3I
perturbed by diatomic molecules: Electron
scattering in H2, HD, D2 and O2
C.M. Evans1 , Holden T. Smith2 ‡, Ollieanna Burke1 , Yevgeniy
Lushtak1 and G. L. Findley2
1
Department of Chemistry and Biochemistry, Queens College – CUNY, Flushing,
NY 11367, United States
E-mail: cherice.evans@qc.cuny.edu
2
Department of Chemistry, University of Louisiana at Monroe, Monroe, LA 71209,
United States
E-mail: findley@ulm.edu
Abstract. Photoionization and field ionization studies of CH3 I doped into the
diatomics H2 , HD, D2 and O2 (up to a density of 1.0 × 1021 cm−3 ) are presented.
These data are used to extract the zero-kinetic-energy electron scattering length of
each diatomic molecule from the density-dependent shift of the CH3 I ionization energy.
Scattering lengths obtained from fits of the photoionization spectra are compared to
those determined from field ionization measurements.
PACS numbers: 34.80.-i, 34.80.Bm, 33.80.Rv, 79.70.+q
Submitted to: J. Phys. B: At. Mol. Opt. Phys.
‡ Present address: Department of Chemistry, Louisiana State University, Baton Rouge, LA 70803,
United States.
Electron scattering in H2 , HD, D2 and O2
2
1. Introduction
We have shown [1–3] that the energy V0 (ρ) of a quasi-free electron in a fluid of density
ρ exhibits a dramatic increase near the critical point. This observation led to the
development of the local Wigner-Seitz model [2–4] for the quasi-free electron energy in
dense fluids. In this model, V0 (ρ) is comprised of three terms: the (strictly negative)
ensemble average electron/fluid polarization energy P− (ρ), the (strictly positive) zeropoint kinetic energy Ek (ρ) of the quasi-free electron, and the thermal energy of the
quasi-free electron (i.e., 3kB T /2, with kB ≡ Boltzmann’s constant). The local WignerSeitz model [2–4] assumes that the interactions within the first solvent shell of the fluid
dominate Ek (ρ), with the maximum interaction distance between the quasi-free electron
and a single fluid constituent (i.e., perturber) in the first solvent shell being defined
by the local Wigner-Seitz radius [2–4], and with the minimum interaction distance
being given by the absolute value of the zero-kinetic-energy electron scattering length
A. Since the local Wigner-Seitz radius [1–3] decreases near the critical point of the fluid
(due to an increase in clustering) while A is constant, the interaction range decreases.
This decrease in interaction range results in an increase in Ek (ρ) and, subsequently, an
observed increase in V0 (ρ). Thus, knowledge of an accurate zero-kinetic-energy electron
scattering length A is required to model V0 (ρ) successfully within the local Wigner-Seitz
approach.
Two methods have been used experimentally to determine the electron scattering
length in a low density fluid.
The first is the direct measurement of the total
electron/fluid scattering cross-section σT as a function of electron energy [5–15].
However, these measurements for very low kinetic energy electrons (i.e., electron energies
≤ 0.5 eV) can be difficult, since most of the techniques used to measure directly the
scattering cross-section depend on the electron number density remaining constant
Electron scattering in H2 , HD, D2 and O2
3
throughout the experiment [7–9]. Thus, the zero-kinetic-energy electron scattering
length must be obtained through extrapolating the low kinetic energy total scattering
cross-sections to zero. Since these cross-sections can change greatly in the low energy
region [8, 9], this extrapolation can be fraught with difficulty.
An alternative to the direct measurement of scattering cross-sections involves
determining A from the fluid density-induced energy shifts ∆(ρ) of high-n Rydberg
states [17–31] of a dopant molecule. In this approach, a dopant possessing a Rydberg
series observable in photoabsorption and/or photoionization is mixed with the fluid of
interest. As the fluid density increases, the dopant high-n Rydberg state energies – and,
therefore, the dopant ionization energy – shift as a result of dopant/fluid interactions.
In the low density region of the fluid (i.e., ρ ≤ 1 × 1021 cm−3 ), these energy shifts are
linear as a function of density and can be modeled within a theory by Fermi [16], as
modified by Alekseev and Sobel’man [18, 32]. In this model [16, 18, 32]
[(
∆(ρ) =
2 π ~2
me
)
(
A − 10.78
αv e2
8 π ε0
]
)2/3
(~ v)1/3
ρ,
(1)
where αv is the polarizability volume of the fluid, e is the charge on the electron, ε0 is the
vacuum permittivity, ~ is the reduced Planck constant, v is the relative thermal velocity
√
of the fluid constituents (i.e., v = 8kB T /m, with m ≡ mass of the fluid constituents),
and me is the mass of the electron. However, the requirement of an observable dopant
Rydberg series restricts the type of dopants that can be selected, as well as the type of
fluids that can be investigated. Reininger et al. [33–41] developed a method – dopant
field ionization – that allows ∆(ρ) of the dopant ionization energy to be monitored in
the absence of an observable dopant Rydberg series. To the best of our knowledge,
this method has not been used at low fluid densities to extract the zero-kinetic-energy
electron scattering length of any fluid.
Electron scattering in H2 , HD, D2 and O2
4
In this paper, we present the fluid density-induced shift ∆(ρ) of the CH3 I ionization
energy, both by fitting the autoionizing Rydberg series of CH3 I (when observable) and
from dopant field ionization of CH3 I in H2 , HD, D2 and O2 , for ρ ≤ 1.0×1021 cm−3 at 300
K. We then apply these data to Equation (1) in order to extract the zero-kinetic-energy
electron scattering lengths for the above diatomics. Finally, we compare the scattering
lengths obtained from a fit to the photoionization spectra with those extracted from
dopant field ionization. Since H2 has been investigated previously using photoabsorption
to monitor the H2 density-induced shifts of dopant Rydberg states [25, 27–29], we will
compare the scattering lengths obtained here to these previous results. We will also
contrast the total electron scattering cross-section σT obtained from
σT = 4πA2
(2)
for H2 and O2 with the zero-kinetic-energy cross-sections measured directly [8–15].
2. Experimental
Photoionization spectra were measured with monochromatic synchrotron radiation
having a resolution of ±4 meV in the energy region of interest, using the University
of Wisconsin Synchrotron Radiation Center stainless steel Seya-Namioka beamline
equipped with a high energy (5–35 eV) grating [42]. The copper sample cell possesses
an entrance MgF2 window coated with a thin (10 nm) layer of platinum to act as an
electrode [42]. The second electrode (stainless steel) is placed parallel to the window
with a spacing of 1.05 mm. The MgF2 window is 2 mm thick, allowing the cell to
withstand pressures of up to 100 bar. A positive electric field is applied to the stainless
steel electrode, while the photoionization signal is detected at the platinum electrode.
CH3 I was selected as the dopant in this study because the first two ionization energies
Electron scattering in H2 , HD, D2 and O2
5
of this molecule fall below the energy cut-off of the MgF2 window, and because the
autoionization spectra [17–28, 30, 31] and field ionization response [33–37] of CH3 I have
been well characterized. (The spectra reported here are current saturated, which was
verified by measuring selected spectra at different electric field strengths.) Photocurrents
within the cell were of the order of 10−9 A. The flux from the Seya beamline was
monitored using a nickel mesh intersecting the beam prior to the sample cell. All
photoionization spectra were normalized to this current. Since the platinum electrode
photoemits in the energy region of interest, dopant photoionization spectra were also
normalized to an empty cell to correct for this small background photoemission signal.
All spectra were measured at a temperature of 300.1 K, which was maintained using an
Advanced Research Systems DE-204SB 4 K closed cycle helium cryostat system. (This
sample cell and cryostat system is used also to investigate the quasi-free electron energy
in near critical point fluids [1–3].)
CH3 I (Aldrich Chemical Company, 99%), H2 (Matheson Gas Products, 99.9999%),
D2 (AirGas, 99.999%; 99.8% isotopic enrichment), HD (Cambridge Isotopes, 98%; 97%
isotopic enrichment) and O2 (Matheson Gas Products, 99.998%) were used without
further purification. For the fluids investigated here, 300.1 K is above the critical
temperature. However, the maximum pressures of ≤ 40 bar are below the critical
pressures of these fluids. Thus, these systems can be denoted as superheated gases or,
more generally, low density fluids. The densities of H2 [43], D2 [44] and O2 [45] were
calculated using the NIST Standard Reference Database 23 Version 9.1 [46]. However,
since an accurate equation of state for HD has not been published [47], the density of
HD was determined under a perfect gas assumption. At the low fluid densities used
in these studies, this assumption results in a maximum error of approximately 1% in
the density of HD. (This error was estimated by comparing the densities of H2 and D2
Electron scattering in H2 , HD, D2 and O2
6
Table 1. The polarizability volume αv and the relative thermal velocity v at 300.1 K
of each fluid.
fluid
αv (Å3 )
v (m/s)
H2
HD
D2
O2
0.8023a
0.7976a
0.7921a
1.5812b
3146.
2570.
2226.
789.7
a
Polarizability volumes are for the ν = 0, J = 0 state of the diatomic molecule, as
obtained from Kolos W and Wolniewicz L 1967 J. Chem. Phys. 46 1426–32.
b
Obtained from Newell A C and Baird R C 1965 J. Appl. Phys. 36 3751–9.
calculated from the NIST standard equations of state with those determined from the
assumption of a perfect gas.) The polarizability volumes αv and the relative thermal
velocities for each fluid at 300 K are given in Table 1. Both the gas handling system
and the procedures employed to ensure homogenous mixing of the dopant and perturber
have been described previously [42]. The concentration of CH3 I in the fluid was kept
below 10 ppt.
3. Results and Discussion
Sample photoionization spectra of CH3 I in H2 , HD, D2 and O2 at the fluid density of
ρ = 6.0 × 1020 cm−3 and a temperature of 300.1 K, in comparison to neat CH3 I, are
presented in Figure 1. (The photoionization spectra of CH3 I in the various diatomic
fluids at other densities are not shown for brevity.) The CH3 I nd ′ Rydberg series is
assigned by comparison to previously published absorption spectra [18, 27]. Clearly,
this Rydberg series is observable in H2 and D2 , but only incompletely in HD and O2 .
(A transition in HD creates a dip in the CH3 I autoionization spectrum, obscuring the
nd ′ = 10 and nd ′ = 11 Rydberg states. Since this transition is not observed in the H2
and D2 systems, this transition is probably a dipole forbidden transition in these more
symmetric gases [48]. Similarly, the absorption of O2 [49] obliterates all of the high-nd ′
Electron scattering in H2 , HD, D2 and O2
7
Figure 1. Photoionization spectra (T = 300.1 K) of pure CH3 I (1.0 mbar) and CH3 I
(1.0 mbar) doped into the fluids H2 , HD, D2 and O2 . The density of the perturbing
fluid is 6.0 × 1020 cm−3 . The applied electric field is 2.5 kV/cm for neat CH3 I and 2.0
kV/cm for CH3 I in the perturbing fluids. All spectra are intensity normalized to the
same spectral feature above the CH3 I 2 E3/2 ionization limit. I2 marks the CH3 I 2 E1/2
ionization limit. Spectra were assigned in comparison to those in Reference [18]. See
text for discussion.
CH3 I Rydberg states.)
For CH3 I/H2 and CH3 I/D2 , however, the photoionization spectra can be used to
determine the shift ∆(ρ) in the CH3 I 2 E1/2 ionization energy (≡ I2 ). The Rydberg
equation
En = I2 −
Ry
,
(n − δ)2
(3)
is used to define a convergence function F (n) through [18]
F (n) = En+1 − En =
Ry (2n + 1 − 2δ)
(n − δ)2 (n + 1 − δ)2
(4)
for the nd ′ autoionizing CH3 I Rydberg series. In Equations (3) and (4), En is the
excitation energy of the nth d ′ Rydberg state converging to the second ionization limit
I2 of CH3 I, Ry is the Rydberg constant, and δ is a constant quantum defect pertaining
to the nd ′ Rydberg series. A nonlinear least-squares analysis of F (n) for neat CH3 I
Electron scattering in H2 , HD, D2 and O2
8
Figure 2. Fluid induced shift ∆(ρ) of the CH3 I 2 E1/2 ionization limit in (•) H2 and in
() D2 plotted as a function of fluid number density ρ. This shift was obtained from
Equation (5) with the ionization energies extracted from a fit of the CH3 I nd ′ series
to the Rydberg equation, following the procedures given in [18]. The lines represent
linear least-squares analyses of Equation (2). The energy uncertainty in ∆(ρ) is ±14
meV at the highest fluid density.
yields the quantum defect δ = 2.23 for the nd ′ Rydberg series. This quantum defect is
used in Equation (3) to obtain I2 for neat CH3 I and for CH3 I in H2 and D2 . (We should
note here that the quantum defect and ionization energy I2 were independent of applied
electric field F for fields less than 3.5 kV/cm, which indicates that the Rydberg states
used in the analysis were not Stark shifting.) ∆(ρ) is given by
∆(ρ) ≡ I2 (ρ) − I2 (ρ = 0) = En (ρ) − En (ρ = 0) ,
(5)
under the assumptions that δ is independent of n and that the individual dopant
Rydberg states En are influenced by the fluid in the same manner as the ionization
energy I2 . For neat CH3 I, I2 (ρ = 0) = 10.160 ± 0.007 eV in this study, which is
comparable to the value 10.164 eV that has been published previously [18]. (As the
fluid density increases, the asymmetric fluid-induced broadening of the CH3 I Rydberg
state transitions results in an increase in the uncertainty of the CH3 I ionization energy
from ±7 meV of the neat CH3 I to ±12 meV for CH3 I in the various fluids at the highest
fluid densities.)
Electron scattering in H2 , HD, D2 and O2
9
Figure 2 presents the shift ∆(ρ) of I2 – determined from Equations (3) and
(5) – perturbed by H2 and by D2 . One observes that ∆(ρ) changes only slightly
between H2 and D2 and that this change is within experimental error. Clearly, at
densities below 1.0 × 1021 cm−3 , ∆(ρ) is linearly dependent on the fluid density ρ, with
∆/ρ = 1.18 ± 0.03 × 10−23 eV cm3 for H2 and with ∆/ρ = 1.33 ± 0.03 × 10−23 eV cm3 for
D2 . Thus, the zero-kinetic-energy electron scattering length extracted from Equation (1)
is A = 0.44 ± 0.03 Å for H2 and A = 0.45 ± 0.02 Å for D2 . (We should note here that the
nd ′ series was utilized in this study because it is the only series with enough observable
high-n Rydberg states to extract the ionization energy. However, the fluid-induced shift
of high-n Rydberg states is independent of the Rydberg series chosen [18, 27, 29].)
Unlike the aforementioned analysis, dopant field ionization does not require an
observable Rydberg series in order to extract the dopant ionization energy.
A
dopant field ionization spectrum is obtained by subtracting a photoionization spectrum
measured at a low applied electric field FL from a spectrum measured at a high
applied electric field FH , after intensity normalization (necessary to remove the effects
of secondary ionization) [33–41]. Figures 3a and 3b show the photoionization spectra
of CH3 I in O2 at a density of 6.0 × 1020 cm−3 and at applied fields of 2.0 kV/cm and
4.0 kV/cm, before and after intensity normalization, respectively. The field ionization
spectrum (cf. Figure 3c, for example) results from high-n dopant Rydberg states that are
field ionized by FH but not FL . Because fluid absorption is independent of the applied
electric field, the dips in the photoionization spectra caused by strongly absorbing fluids
do not affect the field ionization spectrum, unless the fluid absorption occurs at the
same energy as the dopant ionization. Variation in the strength of the electric fields
leads to a shift in the energetic position of the field ionization peak (cf. Figure 2c),
√
√
with the shift being linearly dependent on FL + FH . Since an observable Rydberg
Electron scattering in H2 , HD, D2 and O2
10
Figure 3. Photoionization spectra (T = 300.1 K) of CH3 I (1.0 mbar) in O2 at
a density of 6.0 × 1020 cm−3 before intensity normalization (a) and after intensity
normalization (b). (The intensity normalization is necessary to correct for secondary
ionization [33–41].) The applied electric field was (—) FL = 2.0 kV/cm and (- - -)
FH = 4.0 kV/cm. (c) Field ionization spectrum obtained from the data presented in
(b).
series is not required, both the CH3 I 2 E3/2 ionization energy (≡ I1 ) and 2 E1/2 ionization
energy (≡ I2 ) can be determined using this method. At any given fluid density, ∆(ρ) is
obtained from [33–41]
√
√
∆(ρ) = Ij,F (ρ) + cD ( FL + FH ) − Ij (ρ = 0) ,
(6)
where Ij,F (ρ) is the dopant ionization energy perturbed by the electric field and the
fluid, cD is a dopant-dependent/fluid-independent empirical constant, and Ij (ρ = 0) is
Electron scattering in H2 , HD, D2 and O2
11
the 2 E3/2 or 2 E1/2 ionization energy of neat CH3 I for j = 1 or j = 2, respectively. (The
applied electric fields must be selected to saturate the photocurrent, while remaining
below those field strengths leading to dielectric breakdown via collisional ionization.)
The field ionization constant cD and the CH3 I ionization energies I1 and I2 were
determined empirically from field ionization studies of neat CH3 I at various electric
field strengths to be cD = 3.9 ± 0.2 × 10−4 eV cm1/2 V−1/2 , I1 (ρ = 0) = 9.533 ± 0.005
eV and I2 (ρ = 0) = 10.163 ± 0.005 eV. Thus, the ionization energies for neat CH3 I
are comparable to the previously published results [18] of I1 (ρ = 0) = 9.538 eV and
I2 (ρ = 0) = 10.164 eV and, for I2 , are consistent with that obtained here from the
fit of the nd ′ Rydberg states. The energy of the field ionization peak was found using
a nonlinear least-squares analysis with a Gaussian fit function having a goodness of
fit error determined within a 95% confidence level. The total error range for any
experimental point, therefore, must include the field correction error (i.e., ≤ ±2 meV for
the electric fields used here), the energy uncertainty for CH3 I Ij (ρ = 0), the goodness
of fit error (i.e., ≤ ±0.3 meV), and the error arising from the energy uncertainty due to
the resolution of the monochromator (i.e., ±4 meV). Thus, the total energy uncertainty
in this study at the highest fluid densities was ±7 meV, thereby making field ionization
a more precise technique in comparison to the photoionization method described in the
previous section.
Figure 4 presents the shift ∆(ρ) of I1 , extracted from the field ionization data, as
a function of fluid density for H2 , HD, D2 and O2 . Similar ∆(ρ) data for I2 in H2 and
in D2 were obtained, but are not shown for brevity. ∆(ρ) data for I2 in HD and in O2
could not be extracted because of the strong absorption transitions in the fluid near the
CH3 I 2 E1/2 ionization energy (cf. Figure 1). As was observed for the data obtained from
photoionization, ∆(ρ) extracted from field ionization is linearly dependent on the fluid
Electron scattering in H2 , HD, D2 and O2
12
Figure 4. Fluid induced shift ∆(ρ) of the CH3 I 2 E3/2 ionization limit in (•) H2 , (N)
HD, () D2 and () O2 . This shift was obtained from Equation (6) with the ionization
energies determined from CH3 I field ionization. The lines represent linear least-squares
analyses of Equation (2). See text for discussion. The energy uncertainty in ∆(ρ) at
the highest fluid density is ±7 meV.
density ρ at densities below 1.0 × 1021 cm−3 for H2 , HD and D2 and at densities below
6.0 × 1020 cm−3 for O2 . The slopes, as determined from linear least-squares analyses of
the data in Figure 4 are given in Table 2, along with the zero-kinetic-energy electron
scattering lengths extracted from these data using Equation (1). These results show
that field ionization allows one to obtain data of high enough precision to observe a
distinct difference between the zero-kinetic-energy electron scattering lengths of H2 , HD
and D2 . However, the scattering lengths determined from field ionization of CH3 I in H2
and D2 differ greatly from those determined from the shift of high-n CH3 I autoionization
Rydberg states.
A similar discrepancy in A in H2 has been observed previously by Asaf et al. [27] in a
study of the shift of C6 H6 high-n Rydberg states in H2 via photoabsorption spectroscopy.
They showed that, for constant quantum defect, the shifts of the 7 ≤ n ≤ 10 R ′ C6 H6
Rydberg series were not constant, with ∆(ρ)/ρ increasing as n increased [27]. Thus,
Electron scattering in H2 , HD, D2 and O2
13
Table 2. The slope ∆/ρ obtained from field ionization of CH3 I in various diatomic
molecules, as determined from linear least-squares analyses of the data in Figure 4,
and the zero-kinetic-energy electron scattering length extracted from these data using
Equation (1).
∆/ρ (10−23 eV cm3 )
H2
HD
D2
O2
1.641 ± 0.008
1.77 ± 0.02
1.914 ± 0.008
−1.38 ± 0.04
A (Å)
0.541 ± 0.003
0.555 ± 0.006
0.575 ± 0.002
−0.091 ± 0.002
they concluded that H2 perturbed the high-n nature of the C6 H6 Rydberg series, and
they chose to extract a scattering length for the n = 10 Rydberg series only, since this
scattering length (i.e., A = 0.57 Å) compared favorably with A = 0.54 Å obtained
from CH3 I in H2 [27]. Both of these values are comparable to A = 0.541 ± 0.007 Å
extracted from the field ionization data presented here. If the full C6 H6 Rydberg series
had been utilized in the original analysis, however, Asaf et al. [27] would have obtained
A = 0.45 Å, which is comparable to A = 0.44 ± 0.03 Å determined from the CH3 I nd ′
Rydberg series analysis presented here. The difference in ∆(ρ)/ρ as a function of n is an
artifact arising from the fact that the quantum defect is not constant for low to medium
principal quantum number Rydberg states. Only for high-n Rydberg states does the
quantum defect become constant. Thus, the resolution of the monochromators utilized
in this study and in the previous investigation by Asaf et al. [27] prevented detection of
a significant number of high-n Rydberg states to ensure constant quantum defects and,
therefore, more accurate ionization energies. The field ionization results presented here,
on the other hand, indirectly utilize only very high-n Rydberg states (i.e., n > 20 for
the fields employed here) and, therefore, offer a more accurate scattering length A for
the same resolution monochromator.
Table 3 presents the zero-kinetic-energy electron scattering cross-sections σT
calculated using Equation (2) and the data from this study in comparison to data
Electron scattering in H2 , HD, D2 and O2
14
Table 3. Summary of the zero-kinetic energy electron scattering cross-sections σT
for H2 and O2 , as determined from Equation (2) for the data presented here. Results
from previous studies using photoabsorption of a dopant in H2 and from total electron
scattering cross-section measurements for both H2 and O2 are also presented.
Fluid
Method
H2
CH3 I field ionization
CH3 I autoionization
CH3 I photoabsorption
C6 H6 photoabsorption
C6 H6 photoabsorptiona
Na, Cs or Rb photoabsorption
Ramsauer method
TOF spectrometer
O2
CH3 I field ionization
Electron swarm
Electron swarm
a
σT (Å2 )
Reference
3.67 ± 0.02
2.4 ± 0.2
3.7
4.1
2.5
5.3
5.53
5.75
This work
This work
[27]
[27]
[27]
[29]
[10]
[11, 12]
0.104 ± 0.002
0.35
≤ 0.1
This work
[9, 13]
[9, 14, 15]
Includes data from the full nR ′ Rydberg series. See text for discussion.
obtained from high resolution studies of the fluid-induced energy shift of atomic [29]
and molecular [27] high-n Rydberg states in H2 . The zero-kinetic-energy cross-section
results obtained from extrapolating the cross-section experiments to zero energy are also
shown for H2 [10–12] and for O2 [9, 13–15]. The field ionization results presented here
more closely match those from previous studies [9–15,25–29]. However, the predicted σT
is significantly lower than those obtained from extrapolations of the low kinetic energy
electron scattering cross-sections for H2 [10–12]. In O2 the predicted σT is close to that
extracted from electron swarm studies [9, 13–15], although the swarm studies present
a broad variance in σT . This variance in σT is a result of difficulties in measuring the
total electron scattering cross-sections at extremely low electron energies [8,9]. The field
ionization technique presented here, however, yields high precision zero-kinetic-energy
electron scattering lengths and, therefore, precise zero-kinetic-energy total cross-section
data.
In conclusion, the differences between the zero-kinetic-energy electron scattering
Electron scattering in H2 , HD, D2 and O2
15
lengths obtained from the fluid density-induced shift of high-n Rydberg states and
those determined from field ionization studies arise because of the resolution of
the monochromator used in this study.
Therefore, when using medium (or low)
resolution monochromators, field ionization is the better technique for obtaining precise
and accurate zero-kinetic-energy electron scattering lengths.
As discussed in the
Introduction, the determination of A in H2 , D2 , HD and O2 is necessary for the
measurement of the quasi-free electron energy V0 (ρ) in dense fluids of these diatomic
molecules. The analyses of V0 (ρ) in H2 , D2 and O2 using the local Wigner-Seitz model
are currently underway [50], and the experimental studies of V0 (ρ) in HD and CO are
ongoing by us [51]. All of this work will continue to expand and test the local WignerSeitz model for both repulsive and attractive molecular dense fluids and near critical
point fluids.
Acknowledgments
The experimental measurements reported here were performed at the Synchrotron
Radiation Center, which is primarily funded by the University of Wisconsin-Madison
with supplemental support from facility Users and the University of WisconsinMilwaukee. This work was supported by a grant from the National Science Foundation
(NSF CHE-0956719).
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