JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/,
Analysis of electron impact ionization properties of methane
Xianming Liu and Donald E. Shemansky
Planetary and Space Science Division, Space Environment Technologies, Pasadena, California, USA
Published experimental photon and electron impact ionization cross sections
of CH4 have been reviewed and analyzed. Absolute partial ionization oscillator strengths
+
+
+
+
(fij ) for CH+
and H+
4 , CH3 , CH2 , CH , H
2 have been obtained. Electron impact ionization cross sections are recommended based on agreement between the oscillator strength
values derived from photoionization and electron impact measurements. Analytic func+
+
+
+
+
+
tions for cross sections of CH+
produced by elec4 , CH3 , CH2 , CH , C , H2 and H
tron impact ionization of CH4 are established. The derived excitation cross section functions are accurate from threshold to impact energies limited by the relativistic effects.
The cross sections examined here are important for modeling Titan ionospheric chemistry.
Abstract.
electron-impact cross section measurements is examined by
comparing measurement techniques and the consistency between derived electron and photon ionization partial oscillator strengths. For non-dissociative ionization, the electron
impact oscillator strength of CH+
4 is found to be statistically identical to its photoionization counterpart. The oscillator strength of CH+
3 , the major species of dissociative
ionization of CH4 , also agrees with the photoionization oscillator strength within 2%. The electron impact ionization
cross sections of Straub et al. (1997), as revised by Lindsay & Mangan (2003), are found to be the most accurate.
The derived analytic excitation functions for various significant dissociative ionization channels are consistent with various experimental observations. While the partial oscillator
strengths for minor species deviate from the photoionization counterparts, total ionization oscillator strengths and
partial oscillator strengths of major species fully agree with
the photoionization measurements. In addition to qualitative consistency with physical features of various ionization
channels, the obtained oscillator strengths and excitation
functions quantitatively reproduce the measured CH4 ionization cross sections of Lindsay & Mangan (2003). The partial oscillator strengths and analytical excitation functions
thus provide accurate functional representations of partial
ionization cross section from threshold to the non-relativistic
limit.
The ground state electronic configuration of methane,
classified according to the irreducible representation of the
Td point group, is (1a1 )2 (2a1 )2 (1t2 )6 . The 1t2 and 2a1 orbitals are essentially formed by atomic hydrogen 1s with the
carbon 2p and 2s orbitals, respectively. The inner shell 1a1
orbital is formed almost exclusively by the carbon 1s orbital.
The ionization of CH4 primarily takes place via the valence
single-hole states, (1t2 )−1 and (2a1 )−1 , and the core excited
(1a1 )−1 state, obtained by removal of an electron from each
orbital. The (1t2 )−1 ionic state, with electronic symmetry
of 2 T2 in the Td group, is unstable against Jahn-Teller coupling. Early theoretical calculations predicted D2d or C3v
equilibrium structures for the ground state CH+
4 [Arents &
Allen 1970, Dixon 1971]. Subsequent ab initio calculations
and experimental investigations suggested a large distortion from the Td geometry to 12 equivalent C2v equilibrium
structures [Takeshita 1987; Frey & Davidson 1988; Boyd et
al. 1991; Paddon-Row et al. 1985; Knight et al. 1984; Vager
et al. 1986 ]. The large Jahn-Teller distortion has so far prevented the rotational structure of CH+
4 from being analyzed.
As a result, the most accurate measurement of the first adiabatic ionization potential, 101773 cm−1 (12.618 eV), has an
uncertainty of ±35 cm−1 (4.3 meV) [Signorell & Merkt 1999,
1. Introduction
Methane is a critically important molecule in the atmosphere of Titan [Yung et al. (1984)]. It is the second most
abundant molecular species after molecular nitrogen. The
chemical evolution of its atmosphere is essentially driven by
the photon and electron impact interactions of N and N2 and
CH4 . Nitrogen and methane are the fundamental building
blocks of most neutral and ionic species in the atmosphere
of Titan. As no emission attributable to electronic excited
states of CH4 has been observed in the laboratory, the excitation of CH4 leads to either neutral dissociation or ionization. The excitation of CH4 by photons or electrons is,
therefore, the most important source of simple hydrocarbon
radicals and ions. The subsequent reactions of the hydrocarbon radicals and ions among themselves or with CH4 lead
to formation of higher order alkanes, alkenes and alkynes
[Banaszkiewicz et al. (2000), Wilson & Atreya (2004)]. Additionally, the reaction of CH4 with N+ and N+
2 is the source
of nitriles.
The ionic species of nitrogen (N+ , N+
2 ) and simple hydro+
+
carbons (CH+
4 , CH3 , and CH2 ) in the ionosphere of Titan
are generated by solar photon, photoelectron, and magnetospheric electron ionization. Additional ionization sources
such as ions from micrometeoroids [Molina-Cuberos et al.,
2000] and X-ray photons from solar flares [Banaszkiewicz &
Zarnecki 1999] have also been suggested. Both CH+
4 and
CH+
3 are destroyed primarily by reaction with CH4 and by
dissociative recombination with low energy electrons. In Titan ionospheric models [Fox & Yelle 1997; Banaszkiewicz et
al. 2000; Cravens et al. 2004; and Wilson & Atreya 2004],
+
+
+
N+
2 , N , CH4 and CH3 are considered to be the initial
ionic species of ion-molecule reactions. Most models pre+
dict HCNH+ , CH+
5 , and C2 H5 as the dominant ionospheric
+
+
+
species while N2 , N , CH4 and CH+
3 appear only as minor
constituents. In the first fly-by of Titan by Cassini UVIS,
however, the emission from N+ was observed to be strong.
Analysis of the data suggests that N+ is a major ionospheric
component [Liu et al. 2004]. Accurate ionization cross sections of methane will clearly help to clarify the discrepancy.
This paper presents the results of analyzing ionization
CH4 by electron impact. First, partial ionization oscillator
strengths for the valence transition are obtained from various photoionization measurements. The accuracy of several
Copyright 2005 by the American Geophysical Union.
0148-0227/05/$9.00
1
X-2
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
2000]. In contrast, the ionization potentials of isotope substituted methane, CDH3 , CH2 D2 , and CD4 , have been accurately determined within ±1.4∼1.6 cm−1 [Signorell et al.
1999, Signorell & Merkt (2000)]. Ionization via the (1t2 )−1
+
state primarily produces CH+
4 and CH3 ions, with a very
small percentage (≤ 3%) of CH+
[Backx
& Van der Wiel
2
(1975), Latimer et al. 1999]. Threshold photoelectron photoion coincidence investigations by Stockbauer (1973), Dutuit et al. (1990), and Field & Eland (1995) have shown
that CH+
4 is produced only in the region from methane ionization threshold to 14.323±0.001 eV, the threshold for the
+
formation of CH+
3 [Weitzel et al. 1999]. Beyond the CH3
+
+
threshold, CH4 rapidly dissociates into CH3 . The stable
CH+
4 ion has not been observed when CH4 is excited above
14.6 eV [Dutuit et al. (1990), and Field & Eland (1995)].
The (2a1 )−1 state lies ∼ 22.411 eV above the neutral
−1
ground state [Göthe et al. 1991]. CH+
state
4 in the (2a1 )
+
+
is not stable and dissociates into CH2 , CH and H+ and
their corresponding neutral fragments [Backx & Van der
Wiel 1975; Field & Eland 1995]. CH+
2 is the major fragment,
and CH+
3 ion, if produced, amounts at most 0.4% of the total. Energy-resolved electron-ion coincidence measurements
of CD4 by Kukk et al. (2002) and Riu et al. (2003) at 70 eV
photon excitation energy failed to detect any CD+
3 produced
in the (2a1 )−1 state. CH+
observed
in
some
photoelectron
3
studies has been attributed to npt2 Rydberg states that con−1
verges to the (2a1 )
state [Wu & Judge 1981; Mitsuke et
al. 1991; Furuya et al. 1994; Sorensen et al. 1995].
The core ionized (1a1 )−1 state has a threshold of 290.735
eV [de Simone et al. 2002]. Once the core ionized (1a1 )−1
methane is generated, it is quickly followed by a normal
Auger decay process to produce doubly ionized methane,
which, in turn, dissociates into ion fragments such as CH+
3 ,
+
+
and H+ [Kukk et al. 2002].
CH+
2 , CH , C
In addition to the transitions to the single-hole states,
ionization of methane also takes place by autoionization of
the Rydberg states lying above the first ionization potential. Mitsuke et al. (1991) and Furuya et al. (2000) have
shown that the (2a1 )−1 (npt2 )1 Rydberg series is a significant source of CH+
3 . Moreover, the independent electron
is not a rigorous model for CH4 . As a result, transitions
involving the change of two electron configurations is possible. Dissociative ionization via double ionization [Dujardin
et al. 1985; Fournier et al. 1985; Hatherly et al. 1989] and
transition to doubly excited states, while weak, are not negligible. Kato et al. (2002) and Fukuzawa et al. (2005) have
shown that transitions to some doubly excited states are
stronger than or comparable to some singly excited states.
Furthermore, many core excited Rydberg states near threshold contribute significantly to the absorption and ionization
processes [Ueda et al. 1995; Kivimäki et al. 1996; Köppe
et al. 1996]. These core excited neutral states decay almost exclusively by electron emission. For states below the
threshold, the decay takes place via the so-called participator Auger process, where the excited electron participates in
the decay and an electron with the same energy as valence
photoelectron is emitted, leaving the molecule with a hole
in a valence orbital. The final state is thus the same as the
singly ionized (valence) state. For higher Rydberg states,
however, the decay occurs by the spectator process in which
the excited electron acts as a spectator and an electron with
the same energy as valence photoelectron satellites is emitted. The spectator decay channel leads to so-called doublehole-one-electron satellite state, with two holes in valence
orbital and an electron in the excited orbital in the final
state. The resulting feature of the spectator process is thus
similar to the normal Auger transition that produces doubly ionized methane. Experimental investigations of Ueda
et al. (1995) and Kivimäki et al. (1996) have shown that
the spectator transition is the principal decay channel of the
Rydberg excited states.
Electron impact ionization cross sections of methane have
been reported in many studies since the pioneer work of
Rapp & Englander-Golden (1965). Schram et al. (1966) reported the total ionization cross section of CH4 from 600 eV
to 12 keV. Duric et al. (1991), Nishimura & Tawara (1994),
Tarnovsky et al. (1996) subsequently reported the total ionization cross section from threshold to 240, 1000, and 200
eV, respectively. Backx et al. (1975) obtained absorption
oscillator strengths in 8.6 to 90 eV region by utilizing the
electron-electron coincidence method at high energy and low
momentum transfer and by using the Thomas-Reiche-Kuhn
sum rule. Backx & Van der Wiel (1975) and Van der Wiel et
al. (1976) reported partial oscillator strengths of CH+
n (n=04) and H+ from 14 to 80 eV and partial oscillator strengths
for (1t2 )−1 and (2a1 )−1 states. Aarts et al. (1971), Pang et
al. (1987), Motohashi et al. (1996), and Sasic et al. (2004)
measured the emission cross section of CH and other fragments. Adamczyk et al. (1966), Chatham et al. (1984),
Orient & Srivastava (1987), Tarnovsky et al. (1996), Straub
et al. (1997), Tian & Vidal (1997, 1998) measured both partial and total ionization cross sections over various energy
regions. In addition to the partial and total cross sections,
Gluch et al. (2003) also measured the initial kinetic energy
distribution of the CH+
n (n=0-4) ions from threshold to 1000
eV. They found that CH+
4 is produced with negligible kinetic
energy and are independent of the excitation energy over the
measured energy range. CH+
3 has the next smallest kinetic
energy (810-970 meV) and shows fairly weak dependence on
the excitation energy. Other ion fragments, however, are
produced with much higher (850-6600 meV) energies and
have very significant dependence on impact energy. Stano
et al. (2003) measured the threshold energies and examined methane threshold behavior at different temperatures.
Lindsay et al. (2001) and Wang & Vidal (2002) reported
electron impact positive ion pair-ionization cross sections
of CH4 . Lindsay & Mangan (2003) summarized and recommended experimental values of the CH4 electron impact
ionization cross section. Tawara et al. (1973) measured the
X-ray emission cross section due to K-shell (1a1 ) excitation
of CH4 in the 0.3-18 keV range and found that the emission
yield is independent of incident electron energy. Fainelli et
al. (2002) investigated the fragmentation of core ionized
CH4 by electron impact. Malhi et al. (1987), Knudsen et
al. (1995), and Luna et al. (2003) reported partial ionization cross sections by proton impact. The positive ion-pair
formation cross sections by protons have also been investigated in detail by Ben-Itzhak et al. (1993, 1994). Luna et
al. (2003) also proposed a decay scheme to explain both
electron and proton impact dissociative ionization.
Photoabsorption and photoionization cross sections of
CH4 have also been measured extensively. Denne (1970)
and Lee et al. (1973, 1977) measured the absorption cross
section of CH4 in the 23.7-82.1 Å and 175-700 Å regions,
respectively. Lee & Chiang (1983) and Ma et al. (1990) also
reported absorption and dissociative fluorescence cross sections in the 520-1060 Å and 1060-1420 Å regions. Dujardin
et al (1985) obtained the double ionization cross section of
methane over the range of 32-52 eV. Samson et al. (1989)
measured both absorption and ionization cross sections in
the 950 to 100 Å wavelength range and reported partial os+
+
cillator strengths for the CH+
ions
n (n=0-4), H2 and H
from threshold up to 78 eV. Samson & Yin (1989) subsequently refined the absorption cross sections of CH4 at a
few selected wavelengths. Au et al. (1993), using electron
energy loss and dipole (e,e) technique, obtained photoabsorption cross sections of CH4 from 7 to 220 eV. Latimer et
al (1999) measured the dissociative ionization cross sections
of CH4 and CD4 at 100 K and room temperature from 12
+
to 60 eV. They found that the CH+
n /CDn cross section ratios show significant isotope and temperature dependences.
X-3
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
Kato et al. (2002) investigated the fluorescence cross section
of CH4 and its dissociation fragments. More recent experimental work on photoabsorption and ionization has been
reported by Kameta et al. (2002) and Chen & Wu (2004).
Extensive calculation of photon and electron impact ionization cross sections of methane have been performed. Rabalais et al. (1974) and Seabra et al. (2004) calculated
the relative photoionization cross sections of the (1t2 )−1 ,
(2a1 )−1 and (1a1 )−1 states. Watanabe & Nishikawa (1975)
calculated the relative dissociative photoionization cross sec+
+
tions leading to CH+
4 , CH3 and CH2 . Van Dishoeck et al.
(1980) derived ab initio correlation diagrams for dissociative ionization of methane. Braunstein et al. (1988) calculated cross section and asymmetry parameter for the (1t2 )−1
state. Stener et al. (2002) performed similar calculation
with time-dependent density function theory. Since ab initio calculations of electron impact ionization of molecules is
a non-trivial task, many theoretical investigations have focused on semi-empirical and semi-classical formulation. Kim
et al. (1997) obtained electron impact ionization cross sections of methane via their binary-encounter-Bethe (BEB)
model. The K-shell ionization cross sections have also been
obtained with the relativistic version of BEB model [Santos
et al. 2003] and its improved variation [Uddin et al. 2005].
Khare et al. (1999), Deutsch et al. (2000), and Probst et
al. (2001) also calculated the ionization cross section with
slightly different formulations. While these models are typically capable of reproducing experimental peak cross sections within 5%-15%, they are difficult to apply to partial
ionization because they are based on collisions between a
free and a bound electron. Dose et al. (2000) obtained
Bayesian inference cross section formulas and derived functional forms for partial ionization cross sections of CH4 from
experimental data of Adamczyk et al. (1966) and Chatham
et al. (1984).
2. Theory
h
σ(vi , vj )
Ry Ry C0
= 4f (vi , vj )
Eij E C7
πa20
4
X
Cm
m=1
C7
C7
1
1
− 3
X2
X
(X − 1) exp(−mC8 X)
C5
C6 1
+
+ ln(X)
C7
C7 X
2
4πa0 Ry
f (vi , vj )
=
Eij
+
h
σi,j
Ry
C0
=
C5
E
C5
πa20
+
1
1
− 3
X2
X
4
X
Cm
m=1
1
(X − 1) exp(−mC8 X) + 1 −
C5
X
#
(3)
where i, j are the electronic indices.
In electron impact ionization cross section measurements,
the vibrational states are not distinguished. Equation (1)
needs to be summed over the vj .
f (vi , vj ) = fij q(vi , vj )
(4)
where fij is oscillator strength of the electronic band system
i→j, and q(vi , vj ) is the Franck-Condon factor. Since vibrational structure of CH+
4 is not well-known, one can assume a
single threshold energy, Eij , for an electronic excitation and
replace the f (vi , vj ) in equation (1) by electronic oscillator
strength, fij .
The electronic oscillator strength, fij , is related to the
ph
partial photoionization cross section, σij
[Berkowitz 2002]
fij =
mc
πhe2
Z
∞
σ ph (i, j)d
Z
0
= 9.1107 × 10
15
∞
σ ph (i, j)d
(5)
0
where the cross section, σ ph , is in cm2 and kinetic energy of
photoelectron, , is in eV. If multiple ionization is negligible, the partial ionization oscillator strength for the species
k
k, fij
, can be obtained from its partial photoionization cross
k
section, σij
via the same equation.
3. Analysis and Results
For dipole-allowed ro-vibrational excitation from electronic state i to state j, the cross section, σ, based on the
modified Born approximation is given by [Shemansky et al.
1986a, 1986b; Liu et al. 2003]
+
al. (2003) have shown that the excitation function can be
conveniently represented by
i
(1)
(2)
where a0 and Ry are Bohr radius and Rydberg constant, f
(vi ,vj ) is the (integrated) electric dipole absorption oscillator strength, Eij is the transition energy from vi to vj , E
is the impact energy, and X = E/Eij is the dimensionless
electron energy. The collision strength coefficients Cm /C7
(m=0-6) and C8 can be determined by fitting the experimentally measured relative excitation function. If the absolute excitation function of is available, the oscillator strength
can also be determined. Cm /C7 (m=0-6) and C8 reflect the
atomic or molecular electronic properties and are, usually,
assumed to be dependent on electronic state but independent of rotation and vibration.
For a dipole-forbidden excitation i → j, both electric
dipole oscillator strength and C7 vanish. The asymptote
of the cross section is determined by the value of C5 . Liu et
3.1. Photoionization oscillator strengths
Partial photoionization cross sections of CH+
4 and its ionic
fragments have been measured by Backx & Van der Wiel
(1975), Samson et al. (1989) and Latimer et al. (1999)
from threshold to 80, 78 and 60 eV, respectively. Samson et
+
al. reported partial cross sections of CH+
n (n=0-4) and H2
and H+ while Backx & Van der Wiel (1975) and Latimer
et al. (1999) measured listed the cross sections of CH+
4 ,
+
CH+
,
and
CH
.
Backx
&
Van
der
Wiel
(1975)
also
listed
3
2
the value of H+ . The measured cross sections of CH+
4 , and
+
CH3 , the two major species, are in good agreement. For the
other ions the difference is significant. The cross section of
CH+
2 , the third most abundant species, obtained by Samson
et al. (1989) is significantly lower than the other two studies
between threshold and 23 eV and is higher between 23 and
30 eV. The difference in relative value of H+ is even more
serious.
The total ionization cross sections of Samson et al.
(1989), and Au et al. (1993) and ionization branching ratio
of Samson et al. (1989) were used to derive the partial valence shell photoionization cross sections. The measurement
of Samson et al (1989) ranges from 13.05 to 123 eV, while
that of Au et al. (1993) is from 7.5 to 220 eV. Samson & Yin
(1989) estimated an overall error of 1-2% for the absorption
measurement Samson et al (1989). Between 20 and 112 eV,
the maximum difference between the Samson et al (1989)
and Au et al. (1993) is less than 4%, with the root-meansquare difference being <1.8%. The cross section of Au et al
(1993) from 112 to 220 eV was adjusted upward by 0.38% to
combine with the Samson et al (1989) data. The combined
data from 18 to 220 eV is then fitted with a polynomial
X-4
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
to obtain values beyond 220 eV. The ionization branching
ratios measured by Samson et al. (1989) were used to obtain partial ionization cross sections. Experimental data of
Kameta et al. (2002) was used to obtained the CH+
4 ionization oscillator strength below 13.05 eV. Since the Samson et
al. (1989) branching ratios were measured only from thresh+
+
+
+
+
old to 52-78 eV, the ratios CH+
4 , CH3 , CH2 , CH , C , H
and H+
beyond
the
highest
measured
energies
were
frozen
2
at 27%, 29.7%, 17.7%, 7.5%, 1.9%, 14.5% and 1.7%, respectively. These frozen values are very close but not equal to
the available ratios at or near the highest measured energies. The branching ratios of H+ and H+
2 by Samson et al.
(1989) were terminated at lower energy (52 eV) than the
CH+
n (n=4-0) species (78 eV). Small adjustments of the ratios are required to make the sum of branching ratios unity.
Table 1 lists the derived partial oscillator strengths for
the ionic species. It should be mentioned that the measurement of Samson et al. (1989) was carried out with a
double-ionization chamber in which the total charge production cross section was actually measured. The contributions of multiple ionizations, which are very small, would
therefore be over counted. Analysis of double ionization
data from Dujardin et al (1985) leads to a double ionization oscillator strength of 0.00578 in the 35 to 52 eV region.
Taking into account of over counting, the net photoionization oscillator strength for the valence shell is 6.7976. The
total oscillator strength for neutral dissociation, obtained
from measurements of Chen & Wu (2004) (8.67-9.95 eV),
Kameta et al. (2002) (9.95-23.82 eV) and Samson et al.
(1989) (23.82-27 eV), is 1.5492. The total oscillator strength
of the valence shell excitation is thus 8.3468, which leads to
a value of 1.6532 for the K shell oscillator strength. The K
shell partial oscillator strength listed in the third column are
obtained from relative proton impact ion-pair cross sections
normalized to the expected K shell oscillator strength (see
section 3.2.5).
3.2. Electron-impact ionization
+
3.2.1. e + CH4 → CH4
The CH+
4 parent ion is the major species of electron impact ionization. In addition, it is produced only in low energy levels of the (1t2 )−1 (or X 2 B1 in terms of C2v classification) state. The branching ratio of CH+
4 vanishes as
CH4 is excited 14.323 eV above the vi =0 level of the X 1 A1
state [Stockbauer 1973; Field & Eland 1995;]. The precise
measurements with pulsed field ionization photoelectronphotoion coincidence technique by Weitzel et al. (1999) and
+
Song et al. (2001) shows that the CH+
4 and CD4 signal
both vanish when photon excitation energy is at or above
14.3240 and 14.4302 eV, respectively. Furthermore, CH+
4 is
produced with negligible kinetic energy. Gluch et al. (2003)
found that the kinetic energy distribution of CH+
4 essentially
reflects that of the thermal profiles of ionization source and
is independent of electron excitation energy. All these characteristics should enable a good and complete detection of
the CH+
4 ion. A comparison of its measured cross sections
provides insight on the accuracy of overall measurement.
As mentioned in section 1, the partial ionization cross
sections of methane have been reported by Adamczyk et al.
(1966), Chatham et al. (1984), Orient & Srivastava (1987),
Straub et al. (1997), and Tian & Vidal (1998). The cross
section of Straub et al. (1997) has been revised down slightly
after a subsequent recalibration of their instrument. Unless
otherwise stated, the Straub et al. (1997) cross sections in
this paper refer to the revised data set as given by Lindsay
and Mangan (2003). Only 5 data points, from 15 to 100
eV, were reported by Chatham et al. (1984). A meaningful comparison with other measurements can not be made.
Cross sections measured by Orient & Srivastava (1987) and
Tian & Vidal (1998) are from threshold to 510 and 600 eV,
while those by Adamczyk et al. (1966), and Straub et al.
(1997) are from threshold to 2500 eV and 1000 eV, respectively. Comparing with the CH+
4 cross section of Straub et
al. (1997), all other measurements are lower in energy region below 25 eV. Part of the difference is probably due to
the electron beam profiles and uncertainty in absolute energy scale. Above 35 eV, the Tian & Vidal (1998) cross
section is consistently 7%-12% higher than that of Straub
et al. (1997). From 50 to 510 eV, the Orient & Srivastava (1987) value is likewise 10%-22% higher. Above 50
eV, the Adamczyk et al. (1966) CH+
4 cross section is 1%
-8% lower than the Straub et al. (1997) until 1000 eV, at
which point it drops to the 80% of the Straub et al. (1997).
The absolute partial cross sections of Straub et al. (1997)
were directly measured by extracting, mass analyzing and
counting ions formed along a known path length. The complete collection of ions was achieved. Stebbings and Lindsay
(2001) found that the sum of their partial cross sections to
be fully consistent with the total charge production cross
section of Rapp and Englander-Golden (1965). The error
in their data, according to Lindsay and Mangan (2003), is
less than ±5%. The cross section of Orient & Srivastava
(1987) was measured with a quadrupole mass spectrometer
and the absolute value was established by using ionization
cross section of rare gas with relative flow method. Orient
& Srivastava (1987) estimated the error in their cross section to be ±15%. The measurement of Tian & Vidal (1998)
was made with a focusing time-of-flight mass spectrometer
and the complete detection of ions was demonstrated. The
absolute value of their ionization cross sections was established using that of Ar by Straub et al. (1995). Tian &
Vidal (1998) estimated the error in their CH+
4 cross section
to be ∼10%. Like methane, the Ar ionization cross section of
Straub et al. (1995) has been revised as a result instrument
recalibration. Between 35 and 600 eV, the revised Ar cross
section is 2%-6.4% lower than the originally published value.
If the Tian & Vidal (1998) cross section had been normalized
to the revised Ar cross section, their CH+
4 would have only
been 1%-7% higher than the revised Straub et al. (1997)
value. A cycloid mass spectrometer was utilized in the work
of Adamczyk et al. (1966). Their total ionization cross section was normalized to that of Schram et al (1966). Above
500 eV, Adamczyk et al. (1966) found that their measurement suffered from the interference of secondary electrons
in the mass spectrometer. Based on the experiment setups,
it can be concluded that the values of Straub et al. (1997)
and Tian & Vidal (1998) are more accurate than those of
Orient & Srivastava (1987) and Adamczyk et al. (1966) and
that the cross section of Straub et al. (1997) is probably the
most reliable.
Additional insight on the accuracy of various measurement can be obtained by comparing the electron impact
ionization oscillator strength of CH+
4 with the corresponding
photoionization oscillator strength. To obtain electron impact ionization oscillator strength, a non-linear least-square
fit of experimental CH+
4 cross section to equation (1) is performed. Since the vibrational structure and Franck-Condon
+
factors of CH4 are not well-known, the analysis is carried
out with a single threshold. Equation (1) shows that the
value of oscillator strength depends on the value of threshold energy Eij . It is thus important to obtain an accurate
value of Eij . We obtained the average value of Eij by using
the relation
Rb
Eij = R b
a
a
σ phi dE
σ phi E −1 dE
(6)
where a = 12.618 eV, corresponding to the first adiabatic
ionization potential of CH4 obtained by Signorell & Merkt
(1999), and b = 14.323eV, corresponding to the threshold for
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
the formation of CH+
3 measured by Weitzel et al. (1999).
When the photoionization cross section of Kameta et al.
(2002) is used, the averaged value of Eij = 13.844 eV is
obtained.
The second column of Table 2 lists the collision strength
parameters and oscillator strength determined from CH+
4
cross section of Straub et al. (1997). The oscillator strength,
2.992, agrees with the photoionization oscillator strength,
3.064, within one standard error (0.072). The renormalized
partial cross section of Tian & Vidal (1998), being 1%-7%
higher, produces an oscillator strength ∼5% higher. The
Orient & Srivastava (1987) cross section is expected to give
an even larger oscillator strength.
The second and third columns of Table 3 list the mea+
sured and model CH+
4 cross sections. The CH4 model cross
section below or equal to 15 eV were obtained with parameters listed in the second column of Table 2 with multiple
threshold energy and normalized Franck-Condon factors obtained from the photoionization cross section between 12.618
and 14.343 eV measured by Kameta et al. (2002). All other
model entries were calculated with a single threshold and
parameters listed in Table 2.
+
3.2.2. e + CH4 → CH3
Similar analyses can be carried out for electron impact
ionization leading to the formation of CH+
3 . However, significant difference in the CH+
formation
mechanism
makes
3
the analysis more difficult. While the majority of CH+
3 is
formed via excitation to the (1t2 )−1 state, production by
other electronic states is possible. Mitsuke et al. (1991)
have shown that two kinds of CH+
3 can be produced in
ion-pairs with the H− (1 Sg ). The ground (X̃ 1 A01 ) state
CH+
3 is formed between 13.4 and 16.5 eV while the excited (Ã 1 E 0 ) state CH+
3 is produced between 19.8 and 23
eV. Since the maximum quantum yield of the H− + CH+
3
ion-pair is 0.03%-0.04% [Mitsuke et al., 1993], its contri+
bution to the production of CH3 negligible. Furuya et al.
(1994) and Sorensen et al. (1995) have demonstrated that
−1
(npt2 )1 and
CH+
3 is also formed via transition to the (2a1 )
−1
1
(2a1 ) (ndt2 ) Rydberg states. It is not clear whether excitation to the (2a1 )−1 state itself produces CH+
3 [Samson
et al. 1989; Furuya et al. 1994]. If CH+
3 is formed in
the state, however, it has to be produced in the low vibrational levels of the (2a1 )−1 and is smaller than 0.4% of
the (2a1 )−1 cross section [Field & Eland 1995]. CH+
3 can
also be formed via positive ion-pair production by a direct
excitation to a doubly ionized state or an indirect K shell
excitation followed by a normal Auger process. Based on
the measurements of McCulloh et al. (1964), the contribution of positive ion-pair production of CH+
3 is estimated
to be smaller than 2.1×10−19 cm2 or 0.54% of total CH+
3
cross section at 1000 eV. The positive ion-pair production
+
is thus negligible for CH3 . Finally, Field & Eland (1995)
have shown that CH+
3 is also produced from states above
32 eV but below the doubly ionized states. These states
are believed to be double-hole-one-electron satellite states
such as (1t2 )−2 (3a1 )1 , and (2a1 )−1 (1t2 )−1 (2t2 )1 [Göthe et
al. (1991); Fukuzawa et al. (2005)]. The photoelectron spectrum and branching ratio measurements of Field & Eland
(1995) show that the contribution of these satellite states
to the CH+
3 is very small. Additionally, transitions to the
double-hole-one-electron states are expected to be weak as
they require simultaneous change of two electron configurations. The double-hole-one-electron states can be viewed as
Rydberg series converging to the doubly ionized states. The
cumulative oscillator strengths of Rydberg states are generally smaller than those of their corresponding ionic states.
The fact that the positive ion-pair production of CH+
3 is negligible suggests that transitions via double-hole one-electron
states must be negligible, too.
X-5
The final analysis is made by assuming that the ob−1
served CH+
and (2a1 )−1 (npt2 )1
3 is formed only in the (1t2 )
−1
states. The threshold energy for (1t2 ) state is set to 14.323
eV, corresponding to the appearance potential of CH+
3 measured by Weitzel et al. (1999). The observed vibrational levels of (2a1 )−1 (npt2 )1 ranges from 19.96 to 22.96 eV above
the ground state of CH4 [Sorensen et al. 1995]. The autoionization yield of 3pt2 and 4pt2 is >95% [Furuya et al.
2000]. The oscillator strength for the neutral dissociation of
the (2a1 )−1 (npt2 )1 and (2a1 )−1 (ndt2 )1 series has been estimated to be 0.017 by Kato et al. (2002) from the measured
data of Kameta et al. (2002). Furuya et al. (1994; 2000)
obtained a >60% CH+
3 production branching ratio for the
(2a1 )−1 (4pt2 )1 state and suggested that the contribution of
the Rydberg states to CH+
3 is comparable to that of the
(1t2 )−1 state.
The third and fourth columns of Table 2 list collision
strength parameters derived from the Straub et al. (1997)
+
CH+
3 cross section. The first shape function of CH3 (term
1 in third column) is the same as that of CH+
.
The
sec4
ond shape function (term 2) in the fourth column describes
the 2a2 → npt2 Rydberg excitation and subsequent autoionization to CH+
3 . The Rydberg excitation contributes about
42% of the total CH+
3 cross section. It can be noted that the
sum of the CH+
3 oscillator strength, 2.864, is very close to
the valence shell photoionization oscillator strength, 2.813.
It is also interesting to note that the Tian & Vidal (1998)
CH+
3 cross section above 35 eV is consistently 10%-13%
higher than the Straub et al. (1997) cross section. Again,
a renormalization to the revised Ar ionization cross section
results in the former cross section being 3%-9% higher than
the latter. However, the value of Orient & Srivastava (1987)
is 30%-54% higher. In fact, the Orient & Srivastava (1987)
+
CH+
3 cross section above 90 eV is greater than their CH4
cross section. Surprisingly, between 50 and 700 eV, the
Adamczyk et al. (1966) CH+
3 cross section agrees with that
of Straub et al. (1997) within ±4%. Like CH+
4 , the Straub
et al. (1997) CH+
3 cross section below 25 eV is higher than
those obtained by others. Gluch et al. (2003) have shown
that 0.8-1.0 eV average kinetic energy is released during the
fragmentation process that leads to the formation of CH+
3 .
The fourth and fifth columns of Table 3 compares the
+
observed and model cross section of CH3 .
+
3.2.3. e + CH4 → CH2
The CH+
2 ion is the third most abundant species in ion+
+
ization of CH4 . Unlike CH+
4 and CH3 , CH2 is produced
in many electronic states. Electron-ion coincidence measurement of Backx & Van der Wiel (1975) have estimated
−1
and (2a1 )−1
the abundance of CH+
2 produced in (1t2 )
states are ∼3% and 58%, respectively. In addition, Furuya et al. (1994) observed that a significant percentage of
CH4 excited to (2a1 )−1 (npt2 )1 states produces CH+
2 . Field
& Eland (1995) obtained a large branching ratio for production of CH+
2 from the double-hole-one-electron satellite
states, (1t2 )−2 (2t2 )1 , (1t2 )−2 (3a1 )1 , (2a1 )−1 (1t2 )−1 (2t2 )1
and (2a1 )−2 (3a1 )1 [Göthe et al. (1991)]. Finally, CH+
2 can
also be produced via doubly ionized states in terms of positive ion-pair production.
To simplify the analysis, we have subtracted the ion-pair
+
(CH+
2 , H ) cross section measured by Lindsay et al. (2001)
from the revised Straub et al. (1997) CH+
2 cross section.
In this way, contributions from excitation to doubly ionized
states and from K-shell excitation are removed. The net
production cross section of CH+
2 is expressed in five terms.
The first term, having the shape function of CH+
4 , denotes
the contribution from the (1t2 )−1 state. It has a partial oscillator strength of 0.078 and a threshold energy of 15.2 eV,
corresponding to the threshold for CH4 → CH+
2 + H2 . The
second, third and fourth terms represent the contribution
from (2a1 )−1 (3pt2 )1 , (2a1 )−1 (4pt2 )1 , (2a1 )−1 states, respectively. The collision strength parameters of the three terms
X-6
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
are identical to those of CH+
3 listed in Table 2 except the
values C0 /C7 are different (0.643 vs -0.25). The last term
denotes the contribution from the double-hole-one-electron
satellite states. Its shape function is described by equation
(3) with a threshold energy of 28.2 eV.
Table 4 lists the collision strength parameters for the five
channels of CH+
2 . Figure 1 compares the model cross sections with the measured CH+
2 cross section of Straub et al.
+
(1997) after the contribution of the (CH+
2 , H ) ion-pair
channel has been removed. The sixth and seventh columns
of Table 3 tabulate the observed and model cross sections.
The inferred CH+
2 oscillator strength, 0.5700, is significantly
larger than the photoionization oscillator strength, 0.4354,
derived from cross sections of Samson et al. (1989).
+
3.2.4. e+CH4 →CH+ , C+ , H+ and H2
+
+
All of the cross sections of CH , C , and H+
2 of Straub
et al. (1997), whether or not including positive ion-pair formation, can be approximately represented by a dipole forbidden excitation function equation (3). This fact suggests
that the oscillator strengths for producing these species are
very small and the major production channels are via excitation to ”forbidden” states. Excitation of CH4 to a number
of states can lead to the production of these ionic species
and no single state, in general, is dominant. For this reason,
accurate analysis of these species is difficult. Moreover, except for H+ , all other species can be considered to be minor
species. Only the schematic of analysis is given here. Once
again, the positive ion-pair cross section has been subtracted
to simplify the analysis.
The thermodynamic threshold for the formation of CH+
via the reaction CH4 → CH+ + H2 +H has been obtained to be 19.69 eV by Konebusch & Berkowitz (1976)
and 19.87±0.20 eV by Plessis et al. (1983). While Furuya
et al. (1994) have observed a CH+ branching ratio of 5-10%
for the (2a1 )−1 (4pt2 )1 state, the CH+ cross section remains
negligible until E≥ 22.58 eV [Samson et al. 1989]. Field &
Eland (1995) have obtained ∼10% ionization branching for
the (2a1 )−1 state and show that branching ratios for some
double-hole-one-electron satellite states are as high as 60%.
Backx & Van der Wiel (1975) have found that CH+ is 28%
of ionic species formed in the (2a1 )−1 state.
Figure 2 compares the CH+ model cross section with
the measured cross section of Straub et al. (1997). Both
cross sections exclude the contribution via doubly ionized
states. Table 5 gives the corresponding collision strength
parameters. The CH+ cross section is represented by two
components. The first represents the production via the
(2a1 )−1 state. Its shape is identical to that of the corre−1
state.
sponding CH+
2 component produced via the (2a1 )
The (2a1 )−1 component oscillator strength ratio of CH+ to
CH+
2 , 0.142/0.295, is fully consistent with the relative abundance ratio 0.28/0.58, measured by Backx & Van der Wiel
(1975). The second component gives the contribution from
double-hole-one-electron states. Similar to CH2+ , its shape
is electric dipole-forbidden. The threshold energy, Eij , has
been increased slightly, from 28.2 eV to 28.5 eV, to account
for the much higher branching ratio (≥ 60%) of CH+ near
32 eV [Field & Eland, 1995].
While the appearance potential of C+ has been determined to be 19.56±0.20 eV by Plessis et al. (1983), the
photoionization cross section is negligible below 27 eV in
the measurement of Samson et al. (1989). The production
of C+ primarily takes place by dissociation of methane in
the double-hole-one-electron satellite states and doubly ionized states. The contribution via the doubly ionized states
has been measured in the form of (C+ , H+ ) ion-pair cross
sections by Lindsay et al. (2001). The C+ excitation function via singly ionized states is given in the second column
of Table 6. The comparison of model and measured collision
strength is shown in Figure 3.
The appearance potential of H+
2 in photoionization measurements is ∼28.9 eV [Samson et al. (1989)]. The produc+
tion of H2 by electron impact is undetectable at 22.5 eV
but becomes detectable at 25 eV in the work of Straub et
al. (1997). The difference can be attributed to the small
H+
2 cross section or a different excitation-dissociation mechanism. The absence of the H+
2 signal at 22.5 eV suggests
that the H+
2 + CH2 product channel with 20.17 eV threshold is negligible. It appears that at least two production
mechanisms of H+
2 by electron impact are possible. The
first path is the formation of H+
2 + C + H2 with 23.49
eV threshold and/or H+
2 + CH + H products with 24.50
eV threshold. This path is responsible for the small cross
section at 25 eV measured by Straub et al. (1997). The
second path is the production of H+
2 + C + 2H, which has
a 27.97 eV threshold. The threshold of the second dissociation channel coincides with the energy required to excite
of double-hole-one-electron states. Samson et al. (1989)
suggest that H+
2 is primarily formed in the doubly excited
or doubly ionized states. Positive ion-pair cross sections involving H+
2 by electron impact at 10 keV have been reported
+
by Back & Van der Wiel (1975). The (H+
2 , CH2 ) ion-pair
is the major channel of H+
ion
pair
formation.
Proton
im2
pact measurements of Ben-Itzhak et al. (1993; 1994) from
1 to 12 MeV have shown that the H+
2 ion pair cross section
is about 5/8 of that of the C+ pair. The third column of
Table 6 lists the collision strength parameters of total H+
2
production by electron impact. The collision strength plots
in Figure 4 demonstrate the forbidden nature of the excitations that produce H+
2 .
Gluch et al. (2003) have shown that 1.8 to 6.4 eV in
total average kinetic energy is released in the formation of
H+ from electron impact dissociation of methane between
35 and 300 eV. The conservation of momentum and the
small mass of H+ suggest that most of protons are likely
formed with high velocity. A complete detection of protons thus can present a problem in some experimental measurements. As a result, significant differences in proton
cross sections exist among publications. The three lowest
thresholds for proton formation, by way of (H+ + CH3 ),
(H+ +H2 +CH), and (H+ +H+CH2 ) product channels, are
18.08, 22.67 and 22.81 eV, respectively, on the basis of the
most recent thermochemical data of Ruscic et al. (1999,
2000, & 2005). Early experimental studies with low energy
electrons led to the conclusion that H+ is formed through the
(2a1 )−1 state [Appell & Kubach, 1971]. Indeed, Samson et
al. (1989) failed to observe H+ formation until the photoexcitation energy reached 22.58±0.08 eV. However, a subsequent photoionization measurement by Latimer et al. (1999)
found a threshold at 21.6 eV, which was suggested to arise
from the autoionization of (2a1 )−1 (npt2 )1 Rydberg states.
The electron impact measurement of Locht et al. (1979)
found two lower thresholds of H+ production at 21.3±0.3
and 22.17±0.1 eV. Threshold-photoelectron photoion coincidence measurements of Furuya et al. (1994) obtained an
extrapolated proton production threshold of 22.14 eV. However, Furuya et al. (1994) failed to detect H+ formation from
the (2a1 )−1 (4pt2 )1 state and found all the protons produced
in their study were from the excitation of the (2a1 )−1 state.
In addition to the (2a1 )−1 state, Samson et al. (1989) and
Latimer et al. (1999) demonstrated that the dissociation of
the methane ion in the doubly excited satellite states and
doubly ionized states both significantly contribute to proton
production.
The results of our analysis of proton production cross section by electron impact are listed in Table 7 and shown in
Figure 5. Because the H+ cross section at 22.5 eV is below
the detection limit of Straub et al. (1997), we have neglected
the product channel 21.3±0.3 eV threshold and modeled the
allowed transitions with the (2a1 )−1 shape function listed
the third column of Table 4. The double-hole-one-electron
X-7
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
satellite states are represented with a dipole forbidden function with threshold of 27.5 eV. The positive ion-pair formation via doubly ionized states, which amount up to 12% of
the total, has once again been removed from the measured
data. Figure 5 shows that the satellite states are responsible
for most of the proton production even at 1000 eV.
3.2.5. K shell ionization
The 1a1 orbital of CH4 is considered to be entirely composed of the 1s orbital of the carbon atom. Based on the
1s transition of the isoelectronic Ne atom, the oscillator
strength of the CH4 K shell transition is expected to be near
1.67. As a matter of fact, Au et al. (1993) assumed a value
of 1.67 for the inner shell transition of methane to normalize
their valence shell photoabsorption oscillator strength.
Tawara et al. (1973) measured the X-ray emission cross
section arising from the K shell excitation in the 0.3-18 keV
range and found that the emission yield is independent of
incident electron energy. Analysis of their data produces collision strength parameters for the K shell excitation. These
parameters are listed in Table 8. In deriving the parameters,
we have used a single threshold energy Eij of 290.735 eV, the
ionization potential given by de Simone et al. (2002). Many
transitions between 1s and Rydberg states below the (1a1 )−1
state are also possible. The strongest one is the sharp 1s →
3pt2 resonance transition with a 288 eV threshold [Tronc
et al. 1979; Kivimäki et al. 1996]. Thus, X-ray emission
is possible when excitation energy is below the ionization
potential. Because of the various resonance features below
the ionization potential, the single threshold approximation
gives a poor approximation of the emission cross section
near the threshold (E <350 eV). However, when E≥350 eV,
the single threshold and collision strength parameters provide a very good representation of the K shell emission cross
section. It can be noted that the X-ray emission oscillator
strength is determined to be (5.357±0.589)×10−3 . The error limit, ±0.589×10−3 , arises from the 11% experimental
uncertainty in the emission cross section of Tawara et al.
(1973).
Application of the K shell oscillator strength, 1.6532,
and excitation collision strength parameters in Table 1
and 8 gives a maximum K shell excitation cross section of
(2.7±0.3)×10−19 cm2 , peaking near 1000 eV. The derived
emission oscillator strength, (5.357±0.589)×10−3 , leads to
an effective K shell fluorescence yield of (3.21±0.35)×10−3 .
The yield is higher than (2.69±0.39)×10−3 and 2.8×10−3
given by Tawara et al. (1973) and Krause (1979), respectively, who used an oscillator strength of 2 for the K shell
excitation. Similarly, the present K shell excitation cross is
correspondingly lower than the experimental value of Glupe
& Mehlhorn (1967) and calculated values of Santo et al.
(2003) and Uddin et al. (2005). At 888 eV, Glupe &
Mehlhorn (1967) (see also Tawara et al.) obtained a value of
3.16×10−19 cm2 while the present value is (2.7±0.3)×10−19
cm2 .
As mentioned in section 1, many investigations [Kivimäki
et al. (1996)] have shown that the principal channel of
the K shell excitation is the formation of doubly ionized
methane, which rapidly dissociates into positive ion pairs.
The total positive ion-pair cross section by electron impact
measured by Lindsay et al. (2001) has a peak value of
(5.08±0.77)×10−18 cm2 at 125 eV and decreases rapidly to
(4.33±1.34)×10−19 at 1000 eV. Since the K shell excitation
cross section peaks near 1000 eV with a value of 2.7×10−19
cm2 , it follows that positive ion-pair production by the direct excitation to doubly ionized states is a dominant channel even at 1000 eV.
Malhi et al. (1987), Knudsen et al. (1995), and BenItzhak et al. (1993, 1994) have performed extensive investigations of proton impact ionization of methane. The
positive ion-pair and ion-triplet formation cross sections by
proton impact have been measured from 1 to 12 Mev by
Ben-Itzhak et al. (1993, 1994). The ion-triplet cross section
is found to be only 0.09%-0.36% of the ion-pair cross section and is, therefore, negligible. From the data given in the
tables of Ben-Itzhak et al. (1994), the ion-pair cross section
relative to the CH+
4 cross section can be obtained. The ratio
the total positive ion-pair cross section arising from the K
shell excitation to the CH+
4 cross section, according equation
(1), is given by
ip
σ1s
σCH +
4
=
ip E
CH4+ S1s (E)
f1s
fCH + E1s SCH + (E)
4
(7)
4
where S(E) refers to either the terms enclosed by the bracket
of equation (1) or their high energy asymptotic form:
S(E) = C5 /C7 + ln(E) − ln(Eij )
(8)
The experimental positive ion-pair cross section consists
of dissociation of CH++
directly excited to the doubly ion4
ized states and indirectly via K shell excitation followed
by Auger decay. The direct excitation requires removing
two electrons simultaneously and has very a small oscillator strength. Consequently, the contribution to the positive
ion-pair formation is expected to decrease with energy faster
than that of K shell excitation. The total positive ion-pair
cross section measured by Ben-Itzhak et al. (1994) at 12
MeV is (2.22±0.39)% of the CH+
4 cross section. If C5 /C7
values listed in Tables 2 and 8 are assumed applicable to
proton impact and if the contribution from direct excitation to doubly ionized states is neglected, equations (7 &
8) give rise to an ion-pair oscillator strength of 1.83±0.32.
While the value is higher than the expected K shell oscillator strength (1.65-1.67), it agrees with expected value within
experimental error. Using the electron impact double ionization to single ionization cross section ratio at 10 keV, 0.007,
measured by Backx & Van der Wiel (1975) and assuming
direct doubly ionization is negligible, one can estimate an
ion-pair oscillator strength of 1.95 for the K shell excitation.
The contribution of direct double ionization in the high
energy region, in principle, can be estimated. The photoionization measurement of Dujardin et al (1985) yields a double ionization oscillator strength of 5.78×10−3 . The average threshold energy, estimated using equation (6) and the
Dujardin et al (1985) data, is 45.2 eV. The shape of the
excitation function for direct double ionization, however, is
not known. While Lindsay et al. (2001) have reported a
methane positive ion-pair cross section from threshold to
1000 eV, a reliable shape function can not be ascertained
because the asymptotic form of the cross section is not apparent over the measured range and possible interference
from the K-shell excitation. Nevertheless, based on the collision strength parameters obtained for the double-hole oneelectron states in Tables (4-7), it is certain that the C5 value
for the direct double ionization is positive. The double ionization oscillator strength is very small, and, therefore, the
C5 /C7 value can be very large. A minimum contribution of
direct double ionization can be obtained by setting C5 /C7
to zero. When this is done, an upper limit for the K shell
double ionization oscillator strength, 1.78±0.32, is obtained
from the 12 MeV proton impact data of Ben-Itzhak et al.
(1994). Alternatively, if the C5 /C7 value of the direct double ionization is 34, the K shell double ionization oscillator
strength would be 1.65.
The relative abundance of positive ion-pairs measured by
Ben-Itzhak et al. (1994) at 12 MeV proton impact energy
can be utilized to estimate the partial ionization oscillator
strengths of the K shell excitation. The total K shell oscillator strength can be obtained from the difference between
10 and the total valence shell oscillator strength, or 1.6532,
X-8
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
as from Table 1. The X-ray emission oscillator strength has
been determined to be 0.0054 in Table 8. The absorption
oscillator strength to the core-excited Rydberg states below
the K shell ionization potential has been calculated to be
0.01391 by Ueda et al. (1995). The decay of a small number
of Rydberg levels by the participator Auger process produces singly ionized species. Riu et al. (2003) have shown
that the single ionized methane formed by this way produces
a more complete fragmentation than the direct ionized process. Most of the Rydberg levels, however, decay by the
spectator Auger process to double-hole-one-electron satellite states. If fragmentation for the core-excited Rydberg
levels is assumed to be similar to that of the (1a1 )−1 state,
the relative positive ion-pair abundance of Ben-Itzhak et al.
(1994) can be utilized to model the partial ionization oscillator strengths of K shell excitation. The oscillator strengths
for ionic species listed in the third column of the Table 1 is
obtained by using the relative abundance and by normalizing the K shell ionization oscillator strength to 1.6478.
4. Discussion
The partial photoionization oscillator strengths for valence electrons listed in Table (1) were derived by fixing the
+
+
+
+
ionization branching ratios of CH+
4 , CH3 , CH2 , CH , C ,
H+ and H+
above
78
eV
to
27%,
29.7%,
17.7%,
7.5%,
1.9%,
2
14.5% and 1.7%, respectively. The total valence oscillator
strength at energy above 78 eV is estimated to be 0.6534.
Thus, a small deviation of branching ratios above 78 eV
from the fixed values is not expected to cause any signifi+
cant error in the partial oscillator strength of CH+
4 , CH3 ,
+
+
+
+
.
The
oscillator
strengths
of
CH
,
C
,
H
and
H
and CH+
2
2
are small, a deviations from the assumed branching ratios
will probably lead to differences in the oscillator strengths.
The e + CH4 → CH+
4 oscillator strength, derived from
the revised partial ionization cross section of Straub et al.
(1997), is 2.9916 with a standard error of 0.0716. It is about
1.0 standard error lower than the corresponding photoionization oscillator strength obtained from the experimental
data of Samson et al. (1989) and Au et al. (1993). The
difference is well within the ≤ ±5% error given by Straub et
al. (1997).
The primary error in deriving the electron impact oscillator strength from experimental data is the single threshold
approximation. The approximation is necessary due to the
lack of sufficient data on the vibrational structure of CH+
4
and reliable Frank-Condon factors. In principle, multiple
thresholds and normalized weighing factors selected from
photoabsorption and photoionization data between 12.618
and 14.323 eV can be employed to reduce the analysis uncertainty. However, such an approach will either make the
analysis appear arbitrary or produce results troublesome to
apply. The averaged single threshold by equation (6) represents a good compromise. Even so, an argument could be
made that the photoabsorption cross section, instead of photoionization cross section, should be used. It is sufficient to
point out that, in the case of ionization of H2 , where accurate
ro-vibrational levels and Franck-Condon factors are known,
Liu & Shemansky (2004) have shown that the H2 ionization oscillator strength derived from the Lindsay & Mangan (2003) data, 1.063±0.021 (one standard error), agrees
extremely well with the photoionization oscillator strength,
1.062, obtained from the Samson & Haddad (1994) measurement.
The oscillator strengths of CH+
3 production, arising from
the (1t2 )−1 state and the (1a1 )−1 (npt2 )1 Rydberg series, are
obtained to be 1.632 and 1.232, respectively. While the exact value for the (1t2 )−1 state and (1a1 )−1 (npt2 )1 Rydberg
series can have very significant errors, the total CH+
3 oscillator strength from valence shell excitation, 2.864 should be
+
reliable. The fact that the electron impact CH3 oscillator
strength differs less than 1.6% from the photoionization oscillator strength, 2.8193, also provides the confidence in the
accuracy of the value. Owing to the multiple electronic formation channels of CH+
3 , the error in oscillator strength is
expected to be higher than that of CH+
4 .
The CH+
2 oscillator strength, 0.560, obtained in the
present work is significantly larger than the photoionization
oscillator strength, 0.4354, listed in Table 1. It can be noted
that the CH+
2 photoionization cross sections measured by
Backx & Van der Wiel (1975) and Latimer et al. (1999)
are consistent with each other but both differ significantly
from the Samson et al (1989) measurement. The Backx &
Van der Wiel (1975) measurement gives a CH+
2 oscillator
strength of 0.4007 between threshold and 80 eV, whereas
the Samson et al. (1989) data yields a value of 0.3257. If
the former cross section is used between threshold and 80
eV while the value above 80 eV remains the same, the CH+
2
photoionization oscillator strength would be 0.5104. While
it is still ∼9% lower than the corresponding electron impact
oscillator strength, the difference is much more acceptable.
A higher oscillator strength for CH+
2 requires corresponding lower values of the C+ , H+ and H+
2 as the oscillator
+
+
strengths of CH+
are comparable to their
4 , CH3 , and CH
photoionization counterparts.
The oscillator strengths and collision strength parameters
of CH+ , C+ , H+ and H+
2 listed in Tables 5-7 are not uniquely
determined. They should simply be considered to be one set
of possible values that reproduce the measured cross sections
well and reflects the essential dissociative ionization paths
revealed by various experimental investigations. The uncertainty is caused by the fact that the oscillator strength
values are inherently small and many electronic states contribute the formation of these ionic species. It should be
stressed that the oscillator strengths for C+ and H+
2 , term 5
+
and H+ are set to zero because
of CH+
2 and term 2 of CH
they correspond to the excitation to the double-hole-oneelectron state and are thus expected to be small. This point
is illustrated by the almost constant collision strength plots
in the high energy region in Figures 3 and 4. However, the
oscillator strengths do not vanish because the independent
electron model is not a rigorous one for the CH4 molecule
[Kato et al. (2002); Fukuzawa et al. (2005)]. This point is
further demonstrated by the fact that C+ , H+
2 and doubly
ionized states all have small but measurable photoionization
cross sections.
The total oscillator strength for the species listed in Tables 2 and 4-7 represents that of valence shell ionization via
singly ionized states because the positive ion-pair cross sections have been subtracted from the measured cross section
of Straub et al. (1997),. The sum of electron impact oscillator strength from these tables is 6.778. The valence photoionization oscillator via the singly ionized state is 6.79760.0058, or 6.7918. The two sets of number agree within
0.3%.
It is interesting to compare the oscillator strength of
1t2 electron excitation with that of 2a1 electron excitation.
Based on the number of electrons in each orbital, the 1t2
to 2a1 oscillator strength ratio is expected to be 3. While
electron correlation will cause a small deviation from the
expected ratio, it should be close to 3. In terms of ionization, the CH+
4 oscillator strength, 2.992, the first term of the
+
CH+
3 , 1.632 and the first term of the CH2 , 0.078, is from
the removal of the 1t2 electron. The remaining ionization
oscillator strengths are attributed to the removal of the 2a1
electron. For the neutral transitions, we can simply assume
that those below 18 eV belong to 1t2 electrons while those
above belong to the 2a1 electrons. The Kameta et al. (2002)
and Chen & Wu (2004) measurements give the neutral oscillator strengths from 1t2 and 2a1 electron excitations to
be 1.5103 and 0.0388, respectively. Thus the total oscillator
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
strengths involving the 1t2 and 2a1 electron excitations are
6.21 and 2.11, respectively, leading to an 1t2 to 2a1 oscillator
strength ratio of 2.94.
Table 2 shows that the autoionization of the 2a1 → npt2
Rydberg excitations contributes about 42% of the total CH+
3
oscillator strength. The result is consistent with the suggestion by Furuya et al. (1994; 2000) that the contribution
of the Rydberg states to CH+
3 is comparable to that of the
(1t2 )−1 state. It is important to note that the CH+
3 cross
section of Straub et al. (1997) itself does not suggest any
significant contribution from the Rydberg transitions. Actually, the CH+
3 cross section can be modeled slightly better
in terms of sum of squares of residuals by assuming all the
−1
state. However, doing so
CH+
3 is produced in the (1t2 )
would not only contradict with experimental observation of
Furuya et al. (1994) but also would push the 1t2 to 2a1 electron excitation oscillator strength ratio significantly above
3. Indeed, it is impossible to obtain a reasonable ratio without a significant contribution from the 2a1 → npt2 Rydberg
transitions.
Table 3 and Figures (2 - 5) show that the model cross
section above 22.5 eV agrees with the measured cross section well within the experimental errors, which are ±5%,
+
±5%, ±6.5%, ±6.5%, ±8.5% and ±7.5% for CH+
4 , CH3 ,
+
+
+
CH+
,
CH
,
H
and
H
,
respectively.
Below
22.5
eV,
usu2
2
ally at the first two or three measurable points, however,
the difference between the two sets of cross sections exceeds
the experimental errors. On the experimental side, the uncertainty in electron energy calibration is ±1 eV Lindsay
& Mangan (2003). The calibration uncertainty, along with
the finite energy width of the electrons, can cause significant error near the threshold region where cross section
increases rapidly with the energy. Indeed, a shift of a few
tenths of eV in energy is more than sufficient to remove the
difference between the two sets of cross sections. Even for
the 17% difference between the model and observed CH+
3
cross section at 20 eV, an upward shift of 0.65 eV is enough
to remove the difference completely. Moreover, since many
vibrational excitation channels are opened or closed with a
small change of excitation energy in the threshold region, the
single threshold approximation used by the present model
obviously becomes a very poor approximation. These two
factors are sufficient to account for all of the differences in
the two sets of cross sections below 22.5 eV.
All the single excitation processes involved the 1t2 and
2a1 electrons are essentially described by two excitation
shape functions. Ionic species produced in (1t2 )−1 state
+
such as CH+
4 and Term 1 of CH3 in Tables 2 as well as the
+
Term 1 of the CH2 in Table 5 all have identical shape functions (with different thresholds and oscillator strengths).
+
The terms 2, 3 and 4 of CH+
2 in Table 4, term 1 of CH
in Table 5, and term 1 of H+ in Table 7, all describing the
single excitation of the 2a1 electrons, have another common shape functions. CH+
3 , which is essentially formed in
the (1t2 )−1 and (2a1 )−1 (npt2 )1 Rydberg states, is described
by both shape functions. However, we have to adjust the
C0 /C7 coefficient of the 2a1 shape function of CH+
3 slightly
to achieve better agreement with the cross section of Straub
et al. (1997) in the low energy region. Even with the adjustment, the difference between the model and measured
cross sections at 20 eV is 17%.
The neutral and ionization oscillator strengths of
methane are about 15% and 85% of the total. In a uniform white photon radiation field, the ionization would be
the dominant process of methane photochemistry. Likewise,
ionization process would be more important than neutral
dissociation in the presence of large number of high energy
electrons. Solar photons and photoelectrons in planetary atmospheres are mostly low energy, which makes both neutral
dissociation and ionization significant. From threshold to
30 eV, the electron impact ionization cross section of Straub
X-9
et al. (1997), as revised by Lindsay & Mangan (2003), are
significantly larger than those obtained by other measurements. Thus, the use of the revised Straub et al. cross section may significantly change previous estimates of methane
ionization by electrons.
In conclusion, we have obtained excitation functions
and oscillator strengths for dissociative and non-dissociative
electron impact ionization of methane. The partial oscillator
+
strengths of CH+
4 and CH3 and total valence shell ionization
oscillator strength are in very good agreement with values
derived from photoionization measurements. The excitation
functions not only are consistent with qualitative physical
features of dissociative ionization channels but also capable
of quantitatively reproducing the partial cross sections of
each ionic species.
Acknowledgments. We would like to thank Dr. C.Y.R. Wu
and Dr. N. Kouchi for providing their photoabsorption data in
digital format. This work is supported by the National Science
Foundation ATM-0131210, and the Cassini UVIS contract with
the University of Colorado.
References
Aart, J. F. M., C. I. M. Beenakker, and F. J. De Heer, Radiation
from CH4 and C2 H4 produced by electron impact, Phys., 53,
32-44, 1971
Adamczyk, B., J. H. Boerboom, B. L. Schram, and J. Kistemaker,
Partial ionization cross sections of He, Ne, H2 and CH4 for
electrons from 20 to 500 eV, J. Chem. Phys., 44, 4640-4642,
1966
Appell, J., and C. Kubach, On the formation of energetic protons by electron impact on methane, Chem. Phys. Lett., 11,
486-490, 1971
Arents, J, and L. C. Allen, Ab Initio study of the geometries,
Jahn-Teller distortions, and electronic charge distribution in
the CH+
4 ion, J. Chem. Phys., 53, 73-78, 1970
Au, J. W., G. Cooper, G. R. Burton, T. N. Olney, and C. E.
Brion, The valence shell photoabsorption of the linear alkanes, Cn H2n+2 : absolute oscillator strengths (7-220 eV), Chem.
Phys., 173, 209-239, 1993
Backx. C. and M. J. Van der Wiel, Electron-ion coincidence measurements of CH4 , J. Phys. B., 18, 3020-3033, 1975
Backx. C., G. R. Wight, R. R. Tol, and M. J. Van der Wiel,
Electron-electron coincidence measurements of CH4 , J. Phys.
B., 18, 3007-3019, 1975
Banaszkiewicz, M., and J. C. Zarnecki, Interaction of solar flare
X-rays with atmosphere of Titan, Planet. Space Sci., 47, 3544, 1999
Banaszkiewicz, M., L. M. Lara, R. Rodrigo, J. J. Lopez-Moreno,
and G. J. Molina-Cuberos, A coupled model of Titan’s atmosphere and ionosphere, Icarus, 147, 386-404, 2000
Braunstein, M., V. McKoy, L. E. Machado, L. M. Brescansin,
L.M. and M. A. P. Lima, Studies of the photoionization cross
sections of CH4 , J. Chem. Phys., 89, 2998-3001, 1988
Ben-Itzhak, I., K. D. Carnes, S. G. Gither, D. T. Johnson, P.
J. Norris, and O. L. Weaver, Fragmentation of CH4 by fastproton impact, Phys. Rev. A, 47, 3748-3757, 1993
Ben-Itzhak, I., K. D. Carnes, D. T. Johnson, P. J. Norris, and O.
L. Weaver, Velocity dependence of ionization and fragmentation of methane caused by fast-proton impact, Phys. Rev. A,
49, 881-888, 1994
Berkowitz, J., Atomic and molecular photoabsorption : absolute
total cross sections (Academic Press, San Diego, 2002)
Boyd, R. J., K. V. Darvesh, and P. D. Fricker, Energy component
analysis of Jahn-Teller effect in the methane, J. Chem. Phys.,
94, 8083-8088, 1991
Chatham, H., D. Hils, R. Robertson, and A. Gallagher, Total and
partial electron collisional ionization cross sections for CH4 ,
C2 H6 , SiH4 , and Si2 H6 , J. Chem. Phys., 81, 1770-1777, 1984
Chen, F. Z. and C. Y. R. Wu, Temperature-dependent photoabsorption cross sections in the VUV-UV region. I. methane and
ethane, J. Quant. Spectrosc. Rad. Trans, 85, 195-209, 2004
X - 10
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
Cravens, T. E., J. Vann, J. Clark, J. Yu, C. N. Keller, and C.
Brull, The ionosphere of Titan: an updated theoretical model,
Adv. in Space Res., 33, 212-215, 2004
de Simone, M., M. Coreno, M. Alagia, R. Richter, and K.
C. Prince, Inner shell excitation spectroscopy of tetrahedral
molecules CX4 (X=H, F, Cl), J. Phys. B., 35, 61-75, 2002
Denne D. R., Measurements of the ultrasoft x-ray absorption of
Ar, Ne, N2 , O2 , CH4 , He and H2 , J. Phys. D, 3, 1392-1398,
1970
Deutsch, H., K. Becker, S. Matt and T. D. Märk, Theoretical
determination of absolute electron-impact ionization cross sections of molecules Int. J. Mass Spectrom., 197, 37-69, 2000
Dixon, R. N., On the Jahn-Teller distortion of CH+
4 , Mol. Phys.,
20, 113-126, 1970
Duric, N., I. Cadez, and M. Kurepa, Electron impact total ionization cross-sections for methane, ethane and propane, Int. J.
Mass. Spectrom. Ion Proc., 108, R1-10, 1991
Dujardin, G., D. Winkoun, and S. Leach, Double photoionization
of methane, Phys. Rev. A, 31, 3027-3038, 1985
Dutuit, O, M. Ait-Kaci, J. Lemaire and M. Richard-Viard, Dissociative photoionization of methane and its deuterated compounds in the A state region, Phys. Scr., T31, 223-226, 1990
Fainelli, E., F. Maracci, L. Avaldi, Triple coincidence experiments
to study the fragmentation of core ionized molecules by electron impact, J. Elec. Spectrosc. Rel. Phen., 123, 277-286, 2002
Field, T. A. and J. H. D. Eland, The fragmentation of CH+
4 ions
from photoionization between 12 and 40 eV, J. Elect. Spectrosc. Rel. Pheno., 73, 209-216, 1995
Fournier, P. G., J. Fournier, F. Salama, P. J. Richardson, and
J. H. D. Eland, Formation and dissociation of doubly ionized
methane, J. Chem. Phys., 83, 241-246, 1985
Fox, J. L., and R. V. Yelle, Hydrocarbon ions in the ionosphere
of Titan, Geophys. Res. Lett., 24, 2179-2182, 1997
Frey, R. F. and E. R. Davidson, Potential energy surfaces of CH+
4 ,
J. Chem. Phys., 88, 1175-1185, 1988
Fukuzawa, H., T. Odagiri, T. Nakazato, M. Murata, H. Miyagi,
and N. Kouchi, Doubly excited states of methane produced
by photon and electron interactions, J. Phys. B, 38, 565-578,
2005
Furuya, K., K. Kimura, Y. Sakai, T. Takayangi, and N. Yonekura,
2
Dissociation dynamics of CH+
4 core ion in the A1 state, J.
Chem. Phys., 101, 2720-2728, 1994
Furuya, K., K. Ishikawa, and T. Ogawa, Mass analysis of polyatomic high-Rydberg fragments produced by electron impact
on methane, Chem. Phys. Lett., 319, 335-340, 2000
Glupe, G., and W. Mehlhorn, A new method for measuring electron impact ionization cross section of inner shells, Phys. Lett.,
25A,274-275, 1967
Gluch, K., P. Scheier, W. Schustereder, T. Tepnual, L. Feketeova,
C. Mair, S. Matt-Leubner, A. Stamatovic, and T. D. Märk,
Cross sections and ion kinetic energies fro electron impact ionization of CH4 , Int. J. Mass. Spectrom., 228, 307-320, 2003
Göthe, M. C., B. Wannberg, L. Karlsson, S. Svensson, P. Baltzer,
F. T. Chau and M.-Y. Adam, X-ray, ultraviolet, and synchrotron radiation excited inner-valence photoelectron spectra
of CH4 , J. Chem. Phys., 94, 2536-2542, 1991
Hatherly, P. A., M. Stankiewicz, L. J. Frasinski, K. Codling, and
M. A. MacDonald, Double Photoionization of methane studied by triple coincidence (PEPIPCO) technique, Chem. Phys.
Lett., 159, 355-360, 1989
Kameta, K., N. Kouchi, M. Ukai, and Y. Hatano, Photoabsorption, photoionization, and neutral-dissociation cross sections
of simple hydrocarbons in the vacuum ultraviolet range, J.
Elect. Spectrosc. Rel. Pheno., 123, 225-238, 2002
Kato, M., K. Kameta, T. Odagiri, N. Kouchi, and Y. Hatano,
Single-hole one-electron superexcited states and doubly excited states of methane in the vacuum ultraviolet range as
studied by disperse fluorescence spectroscopy, J. Phys. B, 35,
4383-4400, 2002
Khare, S. P. , M. K. Sharma and S. Tomar, Electron impact
ionization of methane, J. Phys. B, 32, 3147-3156, 1999
Kivimäki, A., M. Neeb, B. Kempgens, H. M. Köppe, and A.
M. Bradshaw, The C 1s Auger decay spectrum of the CH4
molecule: the effects of vibrational fine structure, double excitations and shake-up transitions, J. Phys. B, 29, 2701-2709,
1996
Köppe, H. M., S. Itchkawitz, A. L. D., Kilcoyne, J. Feldhaus,
B. Kempgens, A. Kivimäki, M. Neeb, and A. M. Bradshaw,
High-resolution C 1s photoelectron spectra of methane, Phys.
Rev. A, 53, 4120-4126, 1996
Knigt, L. B., J. Steadman, D. Feller, and E. R. Davidson, Experimental evidence for a C2v (2 B1 ) ground-state structure of the
methane cation radical: ESR and ab initio CI investigations of
+
methane cation radicals (CH+
4 and CD2 H2 ) in neon matrixes
at 4 K, J. Am. Chem. Soc., 106, 3700-3701, 1984
Knudsen, H., U. Mikkelsen, K. Paludan, K. Kirsebom, S. P.
Moller, E. Uggerhoj, J. Slevin, M. Charlton and E. Morenzoni,
Non-dissociative and dissociative ionization of N2 , CO, CO2 ,
and CH4 by impact of 50-6000 keV protons and antiprotons,
J. Phys. B, 28, 3569-3592, 1995
Krause, M. O, Atomic Radiative and Radiationless Yields for K
and L Shells, J. Phys. Chem. Ref. Data, 8, 307-327, 1979
Kronebusch, P. L., and J. Berkowitz, Photodissociative ionization
in the 21-41 eV region: O2 , N2 , CO, NO, CO2 , H2 O, NH3 and
CH4 , Int. J. Mass Spectrom. Ion Phys., 22, 283-306, 1976
Kukk, E., J. R. Riu, M. Stankiewicz, P. A. Hatherly, P. Erman,
E. Rachlew, P. Winiarczyk, M. Huttula, and S. Asela, Dissociation of deuteromethane following carbon 1s core ionization,
Phys. Rev. A, 66, 012704-10, 2002
Lara, L. M., M. Banaszkiewicz, R. Rodrigo, and J. J. LopezMoreno, Icarus, 158, 191-198, 2002
Latimer, C. J., R. A. Mackie, A. M. Sands, N. Kouchi, and K.
F. Dunn, The dissociative photoionization of methane in the
VUV, J. Phys. B., 32, 2667-2676, 1999
Lee, L. C., R. W. Carlson, D. L. Judge, and M. Ogawa, The absorption cross sections of N2 , O2 , CO, NO, CO2 , N2 O, CH4 ,
C2 H4 , C2 H6 , and C4 H1 0 from 180 to 700 Å, J. Quant. Spectrosc. Radiat. Transfer, 13, 1023-1031, 1973
Lee, L. C., and C. C. Chiang, Fluorescence yield from photodissociation of CH4 at 1060-1420 Å, J. Chem. Phys., 78, 688-691,
1983
Lee, L. C., E. Phillips, and D. L. Judge, Photoabsorption cross
sections of CH4 , CF4 , CF3 Cl, SF6 , and C2 F6 from 175 to 770
Å, J. Chem. Phys., 67, 1237-1246, 1977
Liu, X., D.E. Shemansky, H. Abgrall, E. Roueff, S. M. Ahmed,
and J. M. Ajello, Electron impact excitation of H2 : resonance
excitation of B 1 Σ+
u (Jj =2, vj =0) and effective excitation function of EF 1 Σ+
g , J. Phys. B., 36, 173-196, 2003
Liu, X., and D.E. Shemansky, Ionization of molecular hydrogen,
Astrophys. J., 614, 1132-1142, 2004
Liu, X., D. E. Shemansky, Y. Yung, Titan solar reflection and
emission properties in the EUV/FUV, American Geophysical
Union, Fall Meeting 2004, abstract # P53A-1455
Lindsay, B.G., and M. A. Mangan, Cross sections for ion production by electron collision with molecules, in Landolt-Börnstein,
Photon- and electron-interaction with molecules: Ionization
and dissociation New Series Vol. I/17C, edited by Y. Itikawa,
pp. 5-1−5-77 (Springer-Verlag, Berlin-Heidelberg, 2003)
Lindsay, B. G., R. Rejoub, and R. F. Stebbing, Production of positive ion pairs by electron-impact ionization of CH4 , J. Chem.
Phys., 114, 10225-10226, 2001
Locht,R., J. L. Olivier and J. Momigny, Dissociative autoionization as a mechanism for the proton formation from methane
and methane-d4 by low energy electron impact, Chem. Phys.,
43, 425-432, 1979
Luna, H., E. G. Cavalcanti, J. Nickles, G. M. Sigaud, and E. C.
Montenegro, CH4 ionization and dissociation by proton and
electron impact, J. Phys. B, 36, 4717-4729, 2003
Ma, G., M. Suto, and L. C. Lee, Fluorescence from excitation
of CH4 , CH3 OH, and CH3 SH by extreme vacuum ultraviolet
radiation, J. Quant. Spectrosc. Radiat. Transfer, 44, 379-391,
1990
Malhi, N. B., I. Ben-Itzhak, T. J. Gray, J. C. Legg, V. Needham, K. Carnes, and J. H. McGuire, Fragmentation of CH4 in
collisions with fast highly charged ions, J. Chem. Phys., 87,
6502-6506, 1987
McCulloh, K. E., T. E. Sharp, and H. M. Rosenstock, Direct Observation of the Decomposition of Multiply Charged Ions into
Singly Charged Fragments, J. Chem. Phys., 42, 3501-3509,
1964
Mitsuke, K., S. Suzuki, T. Imamura, and I. Koyano, Negative ion
mass spectrometric study of ion-pair formation in the vacuum
− + CD+ ,
ultraviolet. IV. CH4 → H− + CH+
3
3 and CD4 → D
J. Chem. Phys., 94, 6003-6006, 1991
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
Mitsuke, K., H. Hattori, and H. Yoshida, Ion-pair formation from
saturated hydrocarbons through photoexcitation of an innervalence electron, J. Chem. Phys., 99, 6642-6652, 1993
Molina-Cuberos, G. J., H. Lammer, W. Stumptner, H. O. Rucker,
J. J. Lopez-Moreno, R. Rodrigo, and T. Tokano, Ionospheric
layer induced by meteoric ionization in Titan’s atmosphere,
Planet. Space, Sci., 49, 143-153, 2000
Motohashi, K., H. Soshi, M. Ukai and S. Tsurubuchi, Dissociative
excitation of CH4 by electron impact: Emission cross sections
for the fragment species, Chem. Phys., 213, 369-384, 1996
Nishimura, H., and H. Tawara, Total electron impact ionization
cross sections for simple hydrocarbon molecules, J. Phys. B,
27, 2063-2074, 1994
Orient, O. J., and S. K. Srivastava, Electron impact ionization of
H2 O, CO, CO2 and CH4 , J. Phys. B, 20, 3923-3936, 1987
Paddon-Row, M. N.,D. J. Forx, J. A. Pople, K. N. Houk, and
D. W. Pratt, Dynamic Jahn-Teller effect in methane radical cation. Location of the transition structures for hydrogen
scrambling and inversion J. Am. Chem. Soc., 107, 7696-7700,
1985
Pang, K.D., J. M. Ajello, B. Franklin and D. E. Shemansky, Electron impact excitation cross section studies of methane and
acetylene, J. Chem. Phys., 86, 2750-2764, 1987
Plessis, P., P. Marmet, and R. Dutil, Ionization and appearance
potentials of CH4 by electron impact, J. Phys. B, 16, 12831294, 1983
Probst, M., H. Deutsch, K. Becker, and T. D. Märk, Calculations of absolute electron-impact ionization cross sections for
molecules of technological relevance using the DM formalism,
Int. J. Mass Spectrom., 206, 13-25, 2001
Rabalais, J. W., T. P. Debies, J. L. Berkowsky, J.-T. J. Huang,
and F. O. Ellison, Calculated photoionization cross sections
and relative experimental photoionization intensities for a selection of small molecules, J. Chem. Phys., 61, 516-528, 1974
Rapp D., and P. Englander-Golden, Total Cross Sections for Ionization and Attachment in Gases by Electron Impact. I. Positive Ionization, J. Chem. Phys., 43, 1464-1479, 1965
Riu, J. R., E. M. Garcia, A. Ruiz, P. Erman, P. Hatherly, E.
Rachlew, and M. Stankiewicz, Core-excitation-dissociation in
CD4 after participator Auger decay, Phys. Rev. A, 68, 022715,
2003
Ruscic, B., M. Litorja, and R. L. Asher, Ionization Energy of
Methylene Revisited: Improved Values for the Enthalpy of Formation of CH2 and the Bond Dissociation Energy of CH3 via
Simultaneous Solution of the Local Thermochemical Network,
J. Phys. Chem., 103, 8625-8633, 1999
Ruscic, B., M. Litorja, and R. L. Asher, Additions and Corrections, J. Phys. Chem., 104, 8600-8600, 2000
Ruscic, B., J. E. Boggs, A. Burcat, A. G. Csaszar, J. Demaison,
R. Janoschek, J. M. L. Martin, M. L. Morton, M. Rossi., J. F.
Stanton, P. G. Szalay, P. R. Westmoreland, F. Zabel, and T.
Berces, IUPAC critical evaluation of thermochemical properties of selected radicals. Part I, J. Phys. Chem. Ref. Data, 34,
573-656, 2005
Sasic, O., G. Molovic, A. Strinic, Z. Nikitovic, and Z. Lj Petrovic,
Excitation coefficients and cross sections for electron swarms
in methane, New J. Phys., 6, 74, 2004
Samson, J. A. R., G. N. Haddad, T. Masuoka, P. N. Pareek, and
D. A. L. Kilcoyne, Ionization yields, total absorption, and dissociative photoionization cross sections of CH4 from 110-950
Å, J. Chem. Phys., 90, 6925-6932, 1989
Samson, J. A. R. and G. N. Haddad, Total photoabsorption cross
sections of H2 from 18 to 113 eV, J. Opt. Soc. Am. B, 11,
277-279, 1994
Samson, J. A. R. and L. Yin, Precision measurements of photoabsorption cross sections of Ar, Kr, Xe, and selected molecules
at 58.4, 73.6, and 74.4 nm, J. Opt. Soc. Am. B, 6, 2326-2333,
1989
Schram, B. L., J. van der Wiel, F. J. de Heer, and H. R. Moustafa,
Absolute Gross Ionization Cross Sections for Electrons (0.6-12
keV) in Hydrocarbons, J. Chem. Phys, 44, 49-54, 1966
Seabra, G. M., I. G. Kaplan, V. G. Zakrzewski, and J. V. Ortiz,
Electron propagator theory calculations of molecular photoionization cross sections: The first-row hydrides, J. Chem. Phys.,
121, 4143-4155, 2004
Shemansky, D. E., J. M. Ajello, and D. T. Hall, Electron impact excitation of H2 : Rydberg band systems and benchmark
dissociative cross section for H Lyman α, Astrophys. J., 296,
765–773, 1985a.
X - 11
Shemansky D E, J. M. Ajello, D. T., Hall, and B. Franklin, Vacuum ultraviolet studies of electron impact of helium: excitation of He n 1 P0 Rydberg series and ionization-excitation of
He+ (n`) Rydberg series, Astrophys. J., 296 774-783, 1985b
Signorell, R. and F. Merkt, The first rotationally resolved spectrum of CH+
4 , J. Chem. Phys., 110, 2309-2311, 1999
Signorell, R. and F. Merkt, PFI-ZEKE photoelectron spectra of
the methane cation and the dynamic Jahn-Teller effect, Faraday Discuss., 115, 205-208, 2000
Signorell, R., and M. Sommavilla, CH+
4 : a fluxional ion? J.
Electr. Spectrosc. Rel. Pheno., 108, 169-176, 2000
Signorell, R., M. Sommavilla, and F. Merkt, Jahn-Teller distortion in CD2 H+
2 from rotationally resolved photoelectron spectrum, Chem. Phys. Lett., 312, 139-148, 1999
Song, Y., X. -M. Qian, K. -C. Lau and C. Y. Ng, A pulsed field
ionization study of the dissociative photoionization reaction
−
CD4 +hν →CD+
3 + D+ e , Chem. Phys. Lett., 347, 51-58,
2001
Sorensen, S. L., A. Karawajczyk, C. Strmholm and M. Kirm, Dissociative photoexcitation of CH4 and CD4 , Chem. Phys. Lett.,
232, 554-560, 1995
Stano, M., S. Matejcik, J. D. Skalny, and T. D. Märk, Electron
impact ionization of CH4 : ionization energies and temperature
effects, J. Phys. B, 36, 261-271, 2003
Stebbings, R. F., and B. G. Lindsay, Comment on the accuracy of absolute electron-impact ionization cross sections for
molecules, J. Chem. Phys., 114, 4741-4743, 2001
Stener, M., G. Fronzoni, D. Toffoli, and P. Decleva, Timedependent density functional photoionization of CH4 , NH3 ,
H2 O, and HF, Chem. Phys., 282, 337-351, 2002
Stockbauer, R., Threshold electron-photoion coincidence mass
spectrometric study of CH4 CD4 , C2 H6 and C2 D6 , J. Chem.
Phys., 58, 3800-3815, 1973
Straub, H. C., P. Renault, B. G. Lindsay, K. A. Smith, and
R. F. Stebbings, Absolute partial and total cross sections for
electron-impact ionization of argon from threshold to 1000 eV,
Phys. Rev. A, 52, 1115-1124, 1995
Straub, H. C., D. Lin, B. G. Lindsay, K. A. Smith, and R. F.
Stebbings, Absolute partial cross sections for electron-impact
ionization of CH4 from threshold to 1000 eV, J. Chem. Phys.,
106, 4430-4435, 1997
Tawara, H., K. G. Harrison, and F. J. De Heer, X-ray emission cross sections and fluorescence yields for light atoms and
molecules by electron impact, Physica, 63 351-367, 1973
Takeshita, K., A theoretical analysis of the Jahn-Teller effect in
the photoelectron spectrum of methane, 86, 329-338, 1985
Tarnovsky, V., A. Levin, H. Deutschm, and K. Becker, Electron
impact ionization of CDx ( x = 1 - 4), J. Phys. B., 29, 139-152,
1996
Tian C., and C. R. Vidal, Electron impact dissociative ionization
and the subsequent ion-molecule reactions in a methane beam,
Chem. Phys., 222, 105-112, 1997
Tian, C., and C. R. Vidal, Electron impact ionization of N2 and
O2 : contribution from different dissociation channels of multiply ionized molecules, J. Phys. B, 31, 5369-5381, 1998
Tronc, M., G. C. King, and F. H. Read, Carbon K-shell excitation in small molecules by high-resolution electron impact, J.
Phys. B, 12, 137-157, 1979
Yung, Y. L., M. Allen, and J. P. Pinto, Photochemistry of the
atmosphere of Titan, Astrophys. J. Suppl., 55, 465-506, 1984
Uddin, M. A., A. K. F. Haque, M. M. Blliah, A. K. Basak, K. R.
Karim, and B. C. Saha, Computation of electron-impact Kshell ionization cross section of atoms, Phys. Rev., 71, 032715,
2005
Ueda, K., M. Okunishi, H. Chiba, Y. Shimizu, K. Ohmori, Y.
Sato, E. Shigemasa, and N. Kosugi, Rydberg-valence mixing
in the C 1s excited states of CH4 probed by electron spectroscopy, Chem. Phys. Lett., 236, 311-317, 1995
Vager, Z, E. P. Kanter, G. Both, P. J. Cooney, A. Faibis, W.
Koenig, B. J. Zabransky, and D. Zajfman, Direct determination of the stereochemical structure of CH+
4 , Phys. Rev. Lett.,
57, 2793-2795, 1986
Van der Wiel, M. J., W. Stoll, A. Hamnett, and C. E. Brion, Partial oscillator strengths (25-50 eV) of the one-electron states of
CH+
4 measured in an (e, 2e) experiment, Chem. Phys. Lett.,
37, 240-242, 1976
X - 12
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
Van Dishoeck, E. F., W. J. Van Der Hart, and M. Van Hemert,
Ab initio studies of the photodissociation processes in positive
hydrocarbon ions I. the methane ion, Chem. Phys., 50, 45-62,
1980
Wantanabe, T., and S. Nishikawa, Molecular dissociation processes caused by ionization and excitation of CH4 and CD4 ,
Chem. Phys. Lett., 11, 49-56, 1975
Wang, P., and C. R. Vidal, Dissociation of multiply ionized alkanes from methane to n-butane due to electron impact, Chem.
Phys., 280, 309-329, 2002
Weitzel, K.-M., M. Malow, G. K. Javis, T. Baer, Y. Song and C.
Y. Ng, High-resolution pulsed field ionization photoelectronphotoion coincidence study of CH4 : accurate 0 K dissociation
threshold for CH+
3 , J. Chem. Phys., 111, 8267-8270, 1999
Wilson, E. H., and S. K. Atreya, Current state of modeling
the photochemistry of Titan’s mutually dependent atmosphere
and ionosphere, J. Geophys. Res., 109, E06002, 2004
Wu, C. Y. R., and D. L. Judge, Lyman-α fluorescence from hydrogen photofragments of CH4 and H2 O, J. Chem. Phys., 75,
172-178, 1981
Xianming Liu and Donald E. Shemansky, Planetary and Space
Science Division, Space Environment Technologies, 320 North
Halstead, Pasadena, CA 91107, USA. xliu@spacenvironment.net,
dshemansky@spacenvironment.net
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
Table 1. Partial photoionization oscillator strengths of CH4
Valence Shell K Shellc Total
Ions
CH+
4
CH+
3
CH+
2
CH+
C+
H+
H+
2
C+
2
Double ionizationa
Net valence ionization
Total Neutral
Total Valence Shell
X-ray Emission
3.0638
2.8193
0.4354
0.1487
0.0316
0.2759
0.0287
0.166
0.331
0.190
0.130
0.744
0.081
0.005
3.0638
2.985
0.767
0.339
0.161
1.020
0.110
0.005
0.0058
6.7976
1.5492b
8.3468
0.005
a
Derived from experimental measurement of Dujardin et
al.(1985)
b Derived from measurement of Kameta et al. (2002) and
Chen & Wu (2004)
c The K shell oscillator strength is assumed to be 1.6532,
or 10 minus the valence shell oscillator strength. The partial ionization K shell oscillator strengths are derived from
12 MeV proton impact relative ion-pair cross section of BenItzhak(1994) by neglecting difference in fragmentation of the
single ionization Auger decay channels. See section 3.2.5
Table 2. Collision strength parameters for e + CH4 → CH+
4
and CH+
3
Parametera
C0 /C7
C1 /C7
C2 /C7
C3 /C7
C4 /C7
C5 /C7
C6 /C7
C8
fij
Eij (eV)
CH+
4
CH+
3 Term 1
CH+
3 Term 2
-0.323351901
-0.23667982
0.977207808
-2.93095812
3.56563333
-0.878823599
0.878823599
0.25472016
2.99164b
13.844
-0.323351901
-0.23667982
0.977207808
-2.93095812
3.56563333
-0.878823599
0.878823599
0.25472016
1.63240
14.323c
0.64272222
-0.61479404
2.6111285
-9.8782976
10.909956
-0.35528176
0.35528176
0.47268153
1.23146
19.89 & 21.11d
a See equations (1-4) for definition of the collision strength
parameters.
b The standard error is 0.071611
c 0 K dissociation threshold of CH+ measured by Weitzel
3
et al.(1999)
d Thresholds of v =0 level of the 2a →3pt and 4pt
1
2
2
j
obtained by Wu & Judge (1981). The oscillator strength,
−3
1.23146, is partitioned according to the (n*)
relation with
n*=2.34 and 3.24 for 3pt2 and 4pt2
X - 25
X - 26
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
+
+ ionization cross
Table 3. e+CH4 → CH+
4 , CH3 , and CH
sections (unit:10−18 cm2 )
E(eV)
12.7
12.8
13
13.2
13.5
13.7
14
14.2
14.5
14.8
15
17.5
20
22.5
25
30
35
40
45
50
60
70
80
90
100
110
125
150
175
200
250
300
400
500
600
700
800
900
1000
1500
2000
2500
3000
3500
4000
5000
6000
7000
8000
9000
10000
11000
12000
CH+
4
Modelb
CH+
3
Obs.a Model
3.26E-05
5.49E-04
1.09E-02
0.063
0.402
0.987
2.70
4.54
8.36
12.68
15.73
51.34
82.15
103.82
118.33
134.41
142.11
146.57
149.68
152.06
155.12
156.13
155.50
153.75
151.36
148.67
144.47
137.66
131.25
125.17
113.93
104.06
88.35
76.89
68.27
61.57
56.18
51.76
48.04
35.80
28.86
24.34
21.13
18.73
16.86
14.11
12.19
10.76
9.65
8.76
8.03
7.42
6.91
0.8452
2.49
3.71
21.86
39.18
68.67
86.80
103.61
110.91
115.41
118.88
121.68
125.47
127.02
126.89
125.72
123.97
121.94
118.71
113.30
108.03
102.95
93.51
85.26
72.27
62.84
55.77
50.28
45.87
42.24
39.20
29.19
23.52
19.83
17.21
15.25
13.73
11.49
9.92
8.75
7.85
7.13
6.53
6.04
5.62
Obs.a
18.2
47.9
82.5
103.0
120.0
136.0
141.0
145.0
150.0
153.0
155.0
156.0
155.0
154.0
152.0
149.0
144.0
138.0
131.0
125.0
113.0
104.0
89.1
77.8
68.6
62.2
55.2
51.6
47.6
3.5
22.0
47.4
68.5
85.7
105.0
111.0
114.0
119.0
122.0
126.0
127.0
126.0
126.0
124.0
122.0
119.0
113.0
108.0
103.0
93.4
85.5
71.9
63.8
56.0
50.7
45.4
42.0
38.5
CH+
2
Obs.a,cModel
0.50
1.57
2.64
5.19
13.10
20.30
24.80
27.90
28.80
29.57
29.55
29.76
28.45
28.13
27.39
25.85
24.17
22.23
21.24
18.19
16.28
12.78
10.96
9.61
8.40
7.54
6.90
6.33
0.61
1.36
2.85
5.17
12.70
20.95
24.94
27.16
28.48
29.72
29.89
29.49
28.81
28.01
27.19
25.98
24.12
22.45
20.93
18.30
16.14
12.98
10.88
9.42
8.36
7.54
6.90
6.38
4.71
3.79
3.20
2.78
2.46
2.21
1.85
1.60
1.41
1.26
1.15
1.05
0.97
0.90
a Observed cross sections are from revised Straub et al.
(1997) (see also Lindsay and Mangan(2003)).
b Model cross section for CH+ below or equal to 15 eV
4
are calculated with collision strength parameters in table 2
and multiple thresholds and weighing factors derived from the
Kameta et al. (2002) data. Other model entries are calculated
from single threshold and parameters listed in table 2.
c The (H+ , CH+ ) ion-pair cross section reported Lindsay
2
et al. (2001) has been subtracted from the measured CH+
2
cross section.
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
Table 4. Collision strength parameters for e + CH4 → CH+
2
a
Term 1
C0 /C7
-0.323351901
C1 /C7
-0.23667982
C2 /C7
0.977207808
C3 /C7
-2.93095812
C4 /C7
3.56563333
C5 /C7
-0.878823599
C6 /C7
0.878823599
C8
0.25472016
fij
0.078
Eij (eV)
15.2
Terms 2, 3, & 4
-0.25c
b
C0
C1
C2
C3
C4
C5
C6
C8
fij
Eij
-0.61479404
2.6111285
-9.8782976
10.909956
-0.35528176
0.35528176
0.47268153
0.49201d
d
Term 5
1.2111104
0.23437743
0.46255677
-0.93829647
1.255228
0.0025
-0.0025
0.15104086
0
28.2e
a See equations (1-2) for definition of the collision strength
parameters.
b See equation (3) for definition of the collision strength
parameters.
c Fixed
d Thresholds for terms 2, 3, and 4 are 19.89, 21.11 and 22.41
eV, corresponding to those of vj =0 levels of the 2a1 →3pt2 and
4pt2 obtained by Wu & Judge (1981) and (2a1 )−1 obtained by
Göthe et al. (1991). The partial oscillator strengths for 3pt2 ,
4pt2 and (2a1 )−1 are 0.1429, 0.0539, and 0.2952, respectively.
Once again the oscillator strength of the 3pt2 , 4pt2 is fixed
according to the (n*)−3 relation with n*=2.34 and 3.24 for
3pt2 and 4pt2 .
e The center binding energy of (1t )−2 (2t )1 given by
2
2
Göthe et al. (1991) is 29.2 eV with FWHM of ∼4 eV.
Table 5. Collision strength parameters for e + CH4 → CH+
Parametera
C0 /C7
C1 /C7
C2 /C7
C3 /C7
C4 /C7
C5 /C7
C6 /C7
C8
fij
Eij (eV)
Term 1
-0.25
-0.61479404
2.6111285
-9.8782976
10.909956
-0.35528176
0.35528176
0.47268153
0.142
22.6
Parameterb
C0
C1
C2
C3
C4
C5
C6
C8
fij
Eij (eV)
Term 2
-0.059284681
0.28504427
-0.52895674
1.6821527
-1.9517868
0.9629438
-0.9629438
0.22202841
0
28.5
a See equations (1-2) for definition of the collision strength
parameters.
b See equation (3) for definition of the collision strength
parameters.
Table 6. Collision strength parameters for e + CH4 → C+
and H+
2
Parametera
C0
C1
C2
C3
C4
C5
C6
C8
fij
Eij (eV)
C+
H+
2
-0.54797238
0.14599324
-0.23137839
-0.63278286
0.55232757
0.64698388
-0.64698388
0.26618235
0
27
-0.40077442
0.08372811
-0.41572575
1.0551294
-0.82806278
0.39291539
-0.39291539
0.10433324
0
23.53 & 28.9a
a See equation (3) for definition of the collision strength
parameters.
b The weight factors for E =23.53 and 28.9 eV channels
ij
are 11% and 89%, respectively
X - 27
X - 28
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
Table 7. Collision strength parameters for e + CH4 → H+
parametera
C0 /C7
C1 /C7
C2 /C7
C3 /C7
C4 /C7
C5 /C7
C6 /C7
C8
fij
Eij (eV)
Term 1
-0.25
-0.61479404
2.6111285
-9.8782976
10.909956
-0.35528176
0.35528176
0.47268153
0.21c
22.7
parameterb
C0
C1
C2
C3
C4
C5
C6
C8
fij
Eij (eV)
Term 2
-0.2057316
1.5145956
-9.1077259
22.191013
-29.420589
3.8882288
-3.8882288
0.305c
0
27.5
a See equations (1-2) for definition of the collision strength
parameters.
b See equation (3) for definition of the collision strength
parameters.
c Fixed
Table 8.
excitation
Collision strength parameters for CH4 K shell
Parameter
Value
C0 /C7
C1 /C7
C2 /C7
C3 /C7
C4 /C7
C5 /C7
C6 /C7
C8
em b
fij
Eij (eV)
4.8117638
0.3947709
-7.96414218
28.8399006
-54.3939722
-0.860019837
0.860019837
0.5a
0.0053567
290.737
a
b
Fixed
Emission oscillator strength
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
e+CH4 (X 1A1) -> CH2+
30
Measured - Ion Pair
(1t2)-1,3pt2 & 4pt2 & (2a2)-1
2 hole 1 particle
Model Total
σ(unit: 10-18 cm2 )
25
20
15
10
5
0
0
100
200
300
400
500
600
700
800
900
1000
E(eV)
Figure 1. Comparison of experimental (solid circle)
and model (solid diamond) ionization cross sections for
e+CH4 → CH+
2 . The experimental cross section is from
the revised values of Straub et al. (1997), subtract+
ing (CH+
2 , H ) ion-pair cross section of Lindsay et al.
(2001). Model cross section via dipole allowed transitions
[(1t2 )−1 , (2a1 )−1 (npt2 )1 , and (2a1 )−1 ] and dipole forbidden transitions (double-hole-one-electron satellite states)
are shown in solid triangle and square, respectively.
e+CH4 (X 1A1) -> CH+
16
Measured - Ion Pair
Model (2a2)-1
Model (2 hole 1 particle)
Model Total
14
σ(unit: 10-18 cm2 )
12
10
8
6
4
2
0
0
100
200
300
400
500
600
700
800
900
1000
E(eV)
Figure 2. Comparison of experimental (solid circle)
and model (solid diamond) ionization cross sections for
e+CH4 → CH+ . The experimental cross section is from
the revised values of Straub et al. (1997), after subtraction of the (CH+ , H+ ) ion-pair cross section of Lindsay
et al. (2001). Model cross section via the (2a1 )−1 state
and dipole forbidden transition via the double-hole-oneelectron satellite states are shown in solid triangle and
square, respectively.
X - 29
X - 30
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
e+CH4 (X 1A1) -> C+
900
800
Ω(unit: 10-18 cm2 eV )
700
600
500
Measured - Ion Pair
Model (2-hole-1-particle)
400
300
200
100
0
0
100
200
300
400
500
600
700
800
900
1000
E(eV)
Figure 3. Comparison of experimental (solid circle) and
model (solid diamond) ionization collision strength for
e+CH4 → C+ . The experimental cross section is from
the revised value of Straub et al. (1997), after subtraction
of the (CH+ , H+ ) ion-pair cross section of Lindsay et al.
(2001).
e+CH4 (X 1A1) -> H2+
600
Ω(unit: 10-18 cm2 eV )
500
400
Measured
Model
300
200
100
0
0
100
200
300
400
500
600
700
800
900
1000
E(eV)
Figure 4. Comparison of experimental (solid circle) and
model (solid diamond) ionization collision strength for
e+CH4 → H+
2 . The experimental cross section is from
the revised value of Straub et al. (1997).
LIU ET AL.: IONIZATION PROPERTIES OF e+CH4
e+CH4 (X 1A1) -> H+
7000
Ω(unit: 10-18 cm2 eV )
6000
5000
4000
Measured - Ion Pair
Model
Model (2a1)-1
Model 2-hole-1-electron
3000
2000
1000
0
0
100
200
300
400
500
600
700
800
900
1000
E(eV)
Figure 5. Comparison of experimental (solid circle) and
model (solid diamond) ionization collision strength for
e+CH4 → H+ . The experimental cross section is from
the revised values of Straub et al. (1997), after subtraction of the H+ ion-pair cross section of Lindsay et
al. (2001). Model cross section via the (2a1 )−1 state
and dipole forbidden transition via the double-hole-oneelectron satellite states are shown in solid triangle and
square, respectively.
X - 31