Ionisation of small molecules by state-selected Ne* (3P0, 3P2) metastable atoms in the 0.06 < E < 6 eV energy range

Chemical Physics 115 (1987) 359-379 North-Holland, Amsterdam

359

IONISATION OF SMALL MOLECULES BY STATE-SELECTED Ne * ( 3PO,3P2) METASTABLE ATOMS IN THE 0.06 < E < 6 eV ENERGY RANGE

F.T.M VAN DEN BERG *, J.H.M. SCHONENBERG Physics Department,

2 and H.C.W. BEIJERINCK

Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandr

Received 8 December 1986; in final form 29 April 1987

The velocity dependence and absolute values of the total ionisation cross section for the molecules H,, N,, O,, NO, CO, N,O, COa, and CH, by metastable Ne*(3P,,) and Ne*(‘P,) atoms at collision energies ranging from 0.06 to 6.0 eV have been measured in a crossed beam experiment. State selection of the two metastable states of Ne* was obtained by optical pumping with a cw dye laser. We observe a strongly different velocity dependence at collision energies below about 1 eV for the ionisation cross section of the systems Ne*-Hz, N,, CO, and CH,, and the systems Ne*-Oa, NO, CO1, and NsO, respectively. The first group shows an increasing cross section in this energy range, similar to the Ne * -Ar system, while the second group shows a very flat behaviour. This behaviour correlates with the difference in character (n or ob) of the orbital of the electron that is removed from the target molecule. For the molecules H,, N,, CO, and CH, an electron from a ub orbital is removed from the molecule, whereas for Os, NO, N,O, and CO2 an outer r-ortibal electron is involved. For the systems Ne*(3P,,, 3P2)-H2 we have derived the imaginary part of the optical potential by assuming a real potential similar to the theoretically calculated ground state Na-H, potential of Botschwina et al. The resonance width P(r) as a function of the internuclear distance r shows a saturation at small r (r < 2.8 A) for both the Ne*(3Pa)-H, and the Ne*(3P,)-H, interaction. This supports previous conclusions of Verheijen et al. and Kroon et al. Reliable values for the absolute value of the total ionisation cross section have been obtained by performing a careful calibration of the density-length product of the supersonic secondary beam. The results are in good agreement with the values of West et al. for experiments without state selection. The total ionisation cross sections for molecules with a-type ionisation orbitals, with their larger spatial extent, in general are larger than those for molecules with ab-type ionisation orbitals.

1. Introduction

Ionising processes involving electronically excited atoms are of fundamental and practical importance in plasma physics, astrophysics, atomic collision physics and in laser physics. The ionisation by collisions with, e.g., metastable rare gas atoms has been intensively studied since the process of Penning and associative ionisation (PI and AI) was first discovered by Penning in 1927 [l]. Since the ionisation threshold of the collision partner lies well below the electronic excitation energy of the metastable atom, such ionisation processes occur at thermal collision energies and are therefore relatively easy to study experimen’ Present address: Harshaw Chemie BV, P.O. Box 19,3454 ZG De Meem, The Netherlands. 2 Present address: Ock-Nederland BV, P.O. Box 101,590O MA Venlo, The Netherlands.

tally, both in bulk and in crossed beam experiments. In the past much attention has been paid to the investigation of the ionisation cross sections for the He*(‘S, 3S) and Ne*(3Po, 3Pz) metastable atoms in collisions with the heavier ground state rare gas atoms. A fundamental insight into the ionisation mechanism for these closed-shell atoms has been obtained from studies on the branching ratios for the different fine structure states,of the rare gas-ion product [2-51. This insight is reflected in the interaction potential of the colliding atoms and the ionisation probability during the collision [6] and the ionisation process is fully described by the complex optical potential [6,7]. The parameters of the optical potential function can uniquely be determined only if data on both the energy dependence of elastic cross sections at large scattering angles and total ionisation cross sec-

0301-0104/87/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

360

F. T. M. van den Berg et al. / Ionisation of small molecules by state-selected Ne

tions are available [8]. The total ionisation cross sections become even more valuable when absolute values are available. Elastic differential cross section measurements alone, however, do not result in a unique optical potential, as has been demonstrated by Gregor and Siska [9] and by Hausamann [lo] for the Ne*-rare gas systems. In 1972 Tang et al. [ll] have measured the velocity dependence of the ionisation cross section Q(E) for the metastable Ne*-Ar, Kr, Xe systems. Experiments on these systems have also been performed by Neynaber et al. [12-141 with the merging beam technique: West et al. [15] have measured the absolute values of the total ionisation cross sections for the rare gases and various small molecules at thermal energies with a mixed beam of Ne* atoms. State-selected cross sections for Ne* atoms have been reported for the first time by Brom et al. [16], who measured the de-excitation rate constants of Ne*(3P2) at thermal energies in a flowing afterglow experiment. Later on, Yokoyama and Hatano 1171 have published an extensive study of the de-excitation rate constants for the Ne*(3Po) and Ne*(3P2) metastable states and Ne(3Pi) short-lived states in interaction with a large number of molecules and rare gas atoms at room temperature. Despite these earlier investigations the experimental data on the velocity dependence of the total ionisation cross sections for small molecules by Ne* are still scarce. Up till now most experiments have yielded only the branching ratios for ionisation by Ne*(3P,,) and Ne*(3Pz) and for Penning to associative ionisation at thermal energies [1,15,18]. Absolute values of the ionisation cross sections obtained at room temperature are in some cases conflicting and more experiments seem to be necessary to remove the observed discrepancies. Recently, Verheijen et al. [19] have shown that the time-of-flight technique, in combination with state selection by optical pumping, is a successful method for obtaining state-selected total ionisation cross sections as a function of collision energy for the Ne * ( 3PO, 3Pz)-rare gas systems in a wide energy range (0.05-6 ev). Therefore, an extension of their experiments with small molecules seems promising. With this paper we provide accurate

data on the state-selected ionisation cross section and its velocity dependence for a number of small molecules, i.e. H,, N,, CO, CH,, O,, N,O, CO,, and NO. It is the purpose of this paper not only to report on the velocity dependence and absolute values of the cross sections but also to give a first interpretation or our results on the Ne*-H, system in terms of the optical potentials. Furthermore, the observed velocity dependence of the total ionisation cross section for the small molecules will be qualitatively discussed on the basis of a simple model for the ionisation probability, that takes into account the character of the orbital of the electron that is removed by the process of ionisation.

2. The optical potential The process of ionisation is usually described by an optical potential V(r) [6,7] given by Y(r) = vO(r) - ivim(

y,(r)

= jr(r).

(1)

The real part V,(r) describes the interaction of, e.g., a metastable rare gas atom R* with a target molecule M and determines the trajectories of the colliding particles. The spontaneous ionisation rate at a distance r of the collision partners is given by F(r)/2A, with F(r) the resonance width for ionisation. The ionisation cross sections for the system R*-M can be calculated semiclassically from a partial-wave analysis. The complex potential V(r) introduces a complex phase shift nr of the outgoing partial waves with respect to the incoming partial waves. Due to this complex phase shift, given by 7, = 5, + iS;, each partial wave with orbital angular momentum I undergoes a fractional absorption A, given by A,=l-exp(-43,),

(2)

and the total cross section Q(g) for absorption as a function of the relative velocity g is equal to:

The semiclassical

expression

for the imaginary

F. TM. van ah Berg et al. / Ionisation of small molecules by state-selected

phase shift S,, given by {*=

jq+pp2 X

cm

IG

r(r)

dr (4)

(E,,-

V,(r)

-A2(l+i)2/2pr)1’2

depends on the real and imaginary part of V(r), with E, the relative kinetic energy and rc the classical turning point. The real part of V(r) and the resonance width r(r) cannot be determined independently from each other from eq. (4). Additional information on the optical potential can be obtained from differential scattering experiments and from measurements of the total cross sections for elastic scattering. For the He * ( 3S)-Ar system Kroon et al. [8,20] have measured the energy dependence of both the total ionisation cross sections and the elastic differential cross sections at a fixed angle ela,, = $r. This approach has been very successful in unraveling the contributions of both the repulsive branch of G(r) and the resonance width F(r). Gregor and Siska [9] have performed a similar analysis for the systems Ne*-X with X = Ar, Kr, Xe. By adopting an ion-atom-Morse-Morsespline-van der Waals function (IAMMSV) for the real potential and a single exponential function for r(r), they have been able to predict the cross sections for a mixed beam of Ne* atoms that fit both their elastic differential cross sections and the energy dependence of the ionisation cross sections measured by Tang et al. [ll] and Neynaber et al. [12-141 for the Ne*-Ar, Kr, Xe systems. The absolute values of the ionisation cross section were scaled to fit 1.6 times the rate constants for the Ne*(3P2)-rare gas systems obtained by Brom et al. [16] from flowing afterglow experiments. The factor 1.6 has been introduced by Gregor and Siska in order to correct for the parabolic flow in the experiments of Brom et al. The optical potentials of Gregor and Siska yield cross sections that show a weak local maximum at moderate energies (1 eV), as has been experimentally observed. This maximum is caused by the increase in penetration depth of the potential at an internuclear distance where the ion-atom character of the interaction starts to dominate. In their paper Gregor and

361

Ne

Siska have argued that the slight “kink” at this internuclear distance is present because of the hybridization of the Ne*(3s) orbital, caused by the approach of the target rare gas atom. Recently, Verheijen et al. [19,21] have reported state-selected ionisation cross sections for the Ne*(3P,,, 3P2)-rare gas systems that show a more pronounced maximum than predicted by the optical potentials of Gregor and Siska [9]. From these experimental results Verheijen et al. have obtained a modified IAMMSV potential that shows a more pronounced “kink”. Verheijen et al. [19,21] and Kroon et al. [8,20] have also found an energy dependence of the (state-selected) ionisation cross sections for the He*, Ne*-rare gas systems at superthermal energies (l-6 eV) that could only be explained by assuming that F(r) saturates at small internuclear distances, that is to say the overlap of the wavefunctions of the relevant electron orbitals is limited to a maximum value. The function r(r) used by Kroon et al. and Verheijen et al. is defined by: fF(r> = cim exP[ =

+r(

Pi,(r/r,

-

rim)

I)]

r

>

rim,

r

<

rim,

(5)

where eim, &, and rim are parameters that Verheijen et al. and Kroon et al. have determined from their experimental ionisation cross sections.

3. Experiment 3.1. Experimental

arrangement

We have performed our measurements of the ionisation cross section in the same apparatus as has been previously used by Verheijen et al. [19,21] for their Ne*(3Po, 3P2)-rare gas experiments. In the present experiment the mixed beam of Ne* atoms is crossed at right angles by a supersonic beam of molecules. For the registration of the ions, that are produced by collisions of the Ne* atoms with the secondary beam molecules, a spiraltron electron multiplier (SEM4219) is used that is positioned at a distance of 10 mm from the scattering centre. This spiraltron looks at the scattering centre in a direction downstream of the

362

F. TM.

van den Berg et al. / Ionisationof small moleculesby state-selectedNe

primary beam in order to minimize the background signal due to backscattered Ne* atoms, which are also detected by the spiraltron. A laser beam from a Spectra Physics 580A cw dye laser crosses the primary metastable beam at right angles 14 mm upstream of the interaction region or at the interaction region. The laser beam is coupled into the beam machine by a stepping motor-driven flat mirror [22], that can be shifted parallel to the metastable beam. The laser beam is used for the modulation of the composition of the metastable states in the primary beam and for the determination of the metastable flu through the scattering centre. The latter is determined by detection of the UV photons that are released in the excitation process of the metastable atoms through a cascade decay to the ground state of Ne. 3.2. Primaly beam and state selection The primary beam of metastable atoms is produced in a hollow-cathode arc (HCA) source.[23], with a typical centre-line intensity of 1014 s-l sr-l or by a discharge excited supersonic source [24] with an intensity of 1013 s-l sr-I. The Ne* velocity distribution of the HCA source ranges from 3000 to 10000 m/s; the supersonic source produces velocities in the thermal energy range: 600-1600 m/s. The metastable beam passes a mechanical time-of-flight chopper and is detected by a CuBe electron multiplier downstream of the interaction region. As already has been pointed out by Verheijen et al. [19] the metastable beam detector is used only for aligning the laser perpendicular to the atomic beam. All experiments have been performed with the 20Ne isotope (about 10% of the Ne atoms in the primary beam are other isotopes of neon). The laser beam is tuned to a transition from one of the metastable states ‘PO or 3P2 of 20Ne to an excited {(2p),(3p)}, = {Q} level (with the index k ranging from 1 to 10 according to the Paschen notation). The UV photons, that are released in the optical pumping process through radiative cascade decay of the {(Ye} state to the ground state of Ne, are used for the determination of the time-of-flight (TOF) spectrum of the metastable atoms at the interaction region. To this end,

the primary beam is crossed by the laser beam at the scattering centre at z = 0 (the z-axis is chosen along the primary beam). An appropriate electric field is applied to suppress background ion signals. If the laser beam is tuned to a transition 3P2 + {%c; Jk}, the flux of the Ne*(3P2) atoms decreases provided that Jk = 1 or 2. The flux of Ne*( 3Po) atoms increases only if Jk = 1. This change in composition of both states in the beam in determined by (i) the efficiency dj of the laser beam to pump a Ne* atom with velocity vi and (ii) the branching ratios for the decay of the excited {Q} state to the ‘PO metastable state and the 3P1 and ‘P1 resonant states that cascade to the ground state. If fyv is the fraction of excited Ne* atoms that cascades to the ground state, the fraction (1 -fA”“) of the pumped 3P2 atoms will end up in the 3Po metastable state. Thus the flux ‘Nj (with the superscript indicating the total angular momentum J) of 3P2 atoms decreases with qf2Nj while the flux “gj of 3Po atoms increases with $(l -f,!uv)2nj. The difference between this increase and decrease is just the UV photon flux produced in the radiative decay. Therefore the metastable flux is proportional to the UV signal, that is measured with the spiraltron during one chopper period: 4”” =

Tj”vq;fy 2tij7,

(6)

where q”” is the efficiency of the spiraltron for detection of an UV photon and 7 is the duration of one time channel. 3.3. Calibration of the secondary beam The secondary beam is a supersonic expansion into a double differentially pumped system with a skimmer and a collimator in order to obtain narrow beam profiles [25]. To obtain absolute cross sections we have calibrated the density-length product (nl) for the various target gases used. The density-length product follows from the experimental centre-line intensity I,,,,(O) and the density distribution F(z) along the primary beam at the scattering region. The (nl) product at a

F. TM. van den Berg et al. / Ionisation of small molecules by state-selected Ne

363

virtual source distribution, given by

distance x from the. nozzle is given by 126,271:

(7) where u, is the final flow velocity of the secondary beam molecules and F(0) = 1. The centre-line intensity is attenuated by coliisions with the residual gas in the expansion chamber between nozzle and skimmer and in the differential stage between skimmer and collimator. This loss of intensity can be described by a transmission coefficient T, that depends on a skimmer interaction parameter f and a transparancy parameter w f25,28]. Secondly, the secondary beam source is shielded by the skimmer. This shielding effect is described by a transmission coefficient 7&, that gives the fraction of the virtual source [27] of the secondary beam seen by a storage detector positioned at the scattering centre. We write:

with Trm= exp[ -fl(l - wini)] and 15 the fiow rate of the secondary beam molecules through the nozzle. The ideal centre-line intensity ~i~~~,(0) (which gives the intensity for a skimmerless supersonic beam source) is proportional to the flow rate hi through the nozzle and depends on the peaking factor K [27]: lid&O) =

KEj/T.

(91

For Ar, N,, O,, C02, CH, the peaking factors are well known experimentally [27]. Theoretically, these factors are the same for gases with the same Y. Therefore, we have assumed equal values for K for N,, NO, CO (1.20) and for CO,, N,O (1.48), respectively. The flow rate # is given by ~=f(Y)hy.q&,

(10)

with S(y) = [y/(y + 1>]“2[2/(y f l)]“+*) and cyo= (2kr,/??z) ‘I2 k the Boltzman factor and m the molecular mass. The density distribution F(z) at the interaction region (eq. (7)) can be determined from the bimodal virtual source distribution as described by Habets 1291and Beijerinck and Verster [27]. This

(with y perpendicular to the primary and secondary beam) describes the effective source at the nozzle in a plane perpendicular to the centre line. For the case of a slit skimmer and a slit collimator {with slit height > slit width) the beam profile f;(z) can easily be calculated from geometry considerations and integration over y_ For the relative populations C, of the two virtual source components and for the two source radii Ri Beijerinck and Verster [27] have proposed model functions that are described in terms of a dimensionless parameter E and six parameters q,.. The parameter Z describes the reservoir conditions and depends on (i) the ratio y of specific heats of the reservoir gas, (ii) the reservoir number density n,, (iii) the reservoir temperature T,, and (iv) the van der Waals coefficient C,. The parameters q, have been determined by Beijerinck et al. [27,30] and by Verheijen et al. 1251for the rare gases He, Ne, Ar, Kr and for the diatomic molecules N, and 0,. For the diatomic molecules NO and CO we have used the same source parameters as has been published by Beijerinck [27] for N, and 0,. The qi parameters for the molecules N,O, CO,, and CH, (y = $) have not been determined up to now. We have calculated the virtual source radii for these molecules from a scaling of the position of the last collision surface [27,31]. The C, values for N,O, CO, and CH, have been taken from Hirschfelder f32]. The parameters used for the description of the bimodal source dist~bution are su~a~zed in table 1. The parameters f and w in T,, have been determined from a measurement of the centre-line intensity as a function of the flow rate through the nozzle by means of a least-squares fit of eq. (8) to the experimental data [28]. In table 2 the results for f and w are presented together with the peaking factors K used. From the intensities in eq. (8) and the beam profiles obtained from table 2 the density-length

F. LU. van den Berg et al. / Ionisation of small molecules by state-selected Ne

364

Table 1 The virtual source parameters qi and van der Waals constants C, used in the determination of the density-length products (nl). The virtual source radii are given by R,/a(y)R,=ql (Z/100) 12 for the narrow (i =l) and broad (i = 2) source, a(5/3) = 0.806, a(7/5) = 0.591 and a(9/7) = 0.490 [27]. The population of the broad virtual source (i = 2) is equal to C, = q,(Z/lOO)+ q4 Gas

y

Virtual

1055C6/k (K m6)

5/3

0.84 4.45 >

02

NO co N2

7/3 7/3 7/3 7/3

7.39 8.32 9.42 1 6.41

co2

9/7

10.3

CH, N2O

9/7

6.84 1 30.0

Rs/a(y)R,

Rr/a(y)R,

0.28

17.6

0.17

0.22

10.1

0.42

34.0

0.41

0.08

0.44

15.87

0.562

47.61

0.652

0.0

0.583

4.40

Gas

K

10W20f (s)

lo-saw

Ar

2.07 1.98 ‘)

5.20 5.625

0.86 1.631

3.4. Ionisation cross section measurements Since the metastable atom beam consists of two different metastable states 3P0 and 3P2 in the ratio 1: 5 and since 10% of the metastable flux is of the isotopes 21Ne and 22Ne, state-selected cross sections are obtained by measurements of ion signals with the laser switched on and off, respectively. Following Verheijen et al. [19] we define an experimental ionisation probability Kj as the probability that a metastable 20Ne atom (irrespec-

Table 3 Experimental conditions of the secondary beam source for the various molecules. The (n/) products have been calculated with eqs. (7)-(10). The final flow velocities are given by ‘/2ao, with a0 = (2kT/m)‘12, To the nozzle u, = ]Y/(Y - 111 temperature and m the molecular mass

(s) Gas

Ar N2

NO co N2O co2 CH4

1.47 1.48 1.48 1.48

4.470 4.554 4.562 3.833

1.749 1.577 1.700 1.016

1.20 1.20 1.17

3.400 3.975 3.053

2.130 1.750 0.911

source (i = 2)

q4

43 q2

Table 2 The skimmer interaction parameter f and the transparancy parameter w, as determined from a least-squares analysis of the experimental central line intensity I,,,,(O) as a function of the flow rate ni [28]. The peaking factor K results from experiments by Beijerinck et al. [27]

02

virtual

41

products for the various gases can be calculated [25,28]. The results are summarized in table 3. The (nl) products presented apply to the pressures used during our cross section experiments. The corresponding fluxes calculated from eq. (10) are also given in table 3. The effective density-length products in table 3 have been used as input for the calculation of the absolute cross sections from the experimental ionisation probabilities (section 5).

H2

broad

q2

41

H2 Ar

Population

source radius

a) Due to the poor rotational relaxation of H, we expect peaking factor K close to the value for monatomic gases.

H2 N2 02

NO co N2O

a

co2 CH4

P (TOM

10-l%

lo-”

(s-r)

(mm2)

(ms

205 225

7.70 35.9

3.72 2.59

445 2601

224 211 220 469

9.59 8.37 8.88 19.75

2.31 2.24 2.23 3.15

826 772 798 826

243 219 234

8.15 7.47 13.0

1.82 1.82 1.73

141 747 1237

(nl)

24, -1

)

F. TM. van den Berg et al. / Ionisation of small molecules by state-selected Ne

tive of its metastable state) with velocity uj ion&es a target molecule. If we neglect the attenuation of the flux of metastable atoms by collisions with the target molecules, the experimental ionisation cross section is given by [19]:

KJ

Qj=(( gj/uj)nz)

for ions. The experimental K,, that we define here as TJ

(14)

s,U” ’

is independent of the pumping efficiency T$ and can be expressed in “Ki and “Kj according to

id&,.

1’K/_ f/Y

Kj=

where gj is the relative velocity of the collision partners ( gj = (ui + ~22)~‘~with u2 the mean velocity of the secondary beam molecules) and (( gj/uj)nl) is the effective density-length product of the secondary beam molecules at the scattering centre. The experimental ionisation probability Kj is determined by the ionisation probabilities OK, and ‘Kj of the Ne*(3Po) and Ne*(3P2) state, respectively, and depends on the relative population of both states in the primary beam. This population is influenced by the optical pumping of the 3Pz state to the 3Po state. The ions, produced at the scattering centre by collisions of the Ne* atoms with the secondary beam atoms, are measured with the spiraltron detector with the laser beam crossing the primary beam 14 mm upstream of the scattering centre. If the laser is switched on the contribution of the ion signal due to collisions of the Ne*( 3P2) atoms decreases with (1:. 2tij)2Kj, whereas the ‘POcontribution increases with ($(l -fy”) ‘fij)‘Kj. The difference between the ion signals with laser off and on, respectively, is equal to:

05)

fxuV

By performing two measurements at two different transitions from the 3P2 state to the {(Ye} state the unknown “Kj and 2Kj (as a function of time tj of arrival of the ions at the spiraltron) can be obtained from eq. (15). To avoid complicated expressions we write fi =fy and f2 =jy for the fraction of the atoms that cascade to the ground state by optical pumping with wavelength A, and X2, respectively. The ionisation probabilities ‘Kj and ‘Kj are then equal to “Kj =“b,Kj,l

s’~~K~,~,

2Kj=2blKj,,

+2b2Kj,2,

(16)

with

ob;=fl+f2~l_fl)~

-L ob’=-f2_fl~ Ob2=

AL_ f2_fi’

2b = fif2 l

,,;lo, = $n”V;.[2Kj - (I -~~v)oKj]2j+,

ionisation probability

uv A,yjion

K,=k-

(12)

’

365

(13)

-A

f2 -f,

2b = _ fif2 -f2 2 f2 -f1

with qion the detection efficiency of the spiraltron

OK=

’

f,(fi - 1) - fi+f2(l_f,)’

f1 2bi = fi + f,(l -f,)

’

f2(1 -fJ 2bG= f1+f2(1-f*)’

’

Table 4 The coefficients Jbi for the determination of OK, and *K, from the experimental ionisation cross sections Kj,, and Kj,*. The first pumping transition is a 3P2 + {a,; Jk = 2) transition, with X, = 594.5 nm for k = 4 and fAy=l. The ratio of rms errors o(‘K)/o(*K) shows that the 3P2 -t { ns; J = 1) transition at X2 = 597.6 nm results in the highest signal-to-noise ratio for OK Transition

a)

“V x2

(na

fhl

%

*b2

‘b,

‘4.

fJ(OK

3P2-(a71

588.2 597.6 621.7

0.66 0.48 0.77

1 1 1

0 0 0

2.94 1.92 4.35

-1.94 - 0.92 - 3.35

4.3 2.9 6.3

3pO-(a21 3Po-(a51 ‘%(a,)

616.3 626.6 653.2

0.72 0.86 0.85

1 1 1

0 0 0

0.28 0.14 0.15

0.72 0.86 0.85

5.7 5.7 5.7

3P2-{%) ‘P2-{a51

a) All states

k = 2, 5 and 7 have Jk = 1.

)/4*K

)

366

F. T.M. oan den Berg et al. / Ionisation of small molecules by state-selected Ne

For completeness we have also given the coefficients Jbi that refer to the situation of pumping the 3PZ state at X, and pumping the 3Po state at X,. In table 4 the values for f2 and the corresponding “bj are given for the various transitions at wavelength A,. The transition at X, corresponds to a value fi = 1, The fi values have been calculated from the branching ratios reported by Kandela [33]. The wavelength X, has been chosen such that fi = 1 by taking an upper state with Jk = 2, in our case the 3P2-{ IY~1 transition. In that case ‘Kj in eq. (16) is simply given by ‘Kj = Kj,,. The second transition at wavelength X, has been chosen on the basis of calculations of the statistical errors in 2K. and OK. caused by the errors in the experim&al ioniiation probabilities Kj,l and Ki,2. The experimental errors in Kj,i depend on the errors in the measured ion signals and UV signals as can be seen from eq. (14). We note here that the errors in these signals are interdependent since a small difference ion signal due to a small fyv is accompanied by a low production of UV photons. The results of the calculations are shown in table 4. The errors in “Kj are expressed in the statistical error in 2Kj, that is mainly determined by the available measuring time. In contrast to Verheijen et al. [19], who have pumped the 3Po state through the transition 3Po + ( (Ye} at wavelength A,, we have used the transition 3P2 --B( a5 }. This produces a factor of two smaller statistical errors in OK in comparison with ‘K. We point out that the f2 value for the transition 3Po-(as} (X, = 616.3 nm) used by Verheijen et al. and calculated from the branching ratios reported by Wiese et al. [34] deviates from the fi values calculated from the branching ratios published by Kandela [33]. As a consequence our state-selected cross sections calculated from eq. (16) can only be compared adequately with the results of Verheijen et al. if the cross sections are corrected for the differences in the fi values used. All the measurements for obtaining the stateselected cross sections for one particular Ne*molecule system are performed within twelve hours. Since the Ne*-Ar ionisation cross sections have been measured by different groups with different techniques [9,11,12,15-181 we have used

this system for our calibration meas~ements. We started our me~~ements with the HCA source and with Ar as secondary beam target, followed by a measurement with the molecule under investigation as target. The modulation of the primary beam was obtained with the laser at wavelength Xi. At the same wavelength a measurement with the thermal energy source was performed. Subsequently, the laser was tuned to the second transition at X, and the same series of measurements were done in reversed order. All the TOF measurements were corrected for background signals as has been described by Verheijen et al. [19]. From the Ar results the state-selected cross section in the superthermal energy range was evaluated and compared with the earlier results of Verheijen et al. [19]_ In this way any drift in detection efficiencies could be established and corrections, if necessary, could be made.

4. Energy dependence of the total ionisation cross s&ion “Q

The experimental results of the state-selected total ionisation cross sections for the systems Ne*(3Po, 3Pz)-M (M= H,, N,, O,, CO, NO, CO,, N,O, CH,) as a function of the relative collision energy E are shown in fig. 1. In this figure the state-selected cross sections *Q(E) for Ne*(3Pz)-M are normalized to unity at a reference energy E,,, = 0.1 eV. The cross sections ‘Q(E) for Ne*(3Po)-M relative to 2Q(E), i.e. the ratios o~(E)/2~(~), do not depend on the detection efficiencies @” and ?I”” and the (nl) products of the secondary beam molecules at the scattering centre. Therefore, the data points for ‘Q(E) in fig. 1 are obtained from the experimental values of the ratio ‘Q( E)/‘Q( E). For the presentation of the experimental data we introduce, in analogy with Verheijen et al. 1191, two model functions “f(E) and ‘f(E) that describe the energy dependence of the state-selected cross sections “Q(E) and 2Q(E). We have normalized ‘f(E) and 'f(E)to unity at E = E,,. The absolute values of the cross sections ‘Q(E) and

F. TM. van den Berg et al. / Ionisation of small molecules by state-selected Ne

361

Table 5 The coefficients ‘an and 2a, in the polynomial representations ‘f(E) and *f(E) (eq. (17)) of the state-selected total ionization cross sections, normalized to Jf(E,r) =1 at E,, = 0.1 eV. All Ja, values (except for ‘aI) are multiplied by a factor equal to 10 in this table. The representation is only valid within the range E,, < E < E_ of collision energies Group II

Group I

Rare gas Ar

H,

N,

co

CH,

02

co2

N2O

NO

10 ‘a2 10 ‘as

0.9117 - 6.387 1.452

0.6767 - 2.189 0.1800

0.5815 - 2.120 0.1872

0.4117 - 0.7343 0.0840

-0.1497 - 0.8698 - 0.2521

-0.1379 0.5953 - 0.1559

- 0.1494 0.6394 - 0.1724

0.1465 - 0.6768 - 0.0070

0.4158 - 1.484 0.1075

10 *a, 10 *a2 10 *a3

5.087 - 3.842 1.038

5.756 - 1.812 0.1263

5.712 - 2.287 0.2326

- 4.677 - 1.878 0.1556

- 0.4139 - 0.1424 - 0.0737

- 0.7978 - 0.3071 -0.1120

- 1.141 - 0.6546 - 0.2006

- 3.023 0.0250 -0.1046

3.044 - 1.496 0.1288

‘01

E,, E,

(meV) (ev)

70 0.84

78 4.96

‘Q(E) can be calculated according to

78 5.38

99 3.81

from these functions

“Q(E) =‘Q(E,,)[‘Q(E,,)/‘Q(E,,)]

of(Eh 07)

Table 6 The experimental values of the ratio ‘Q(E)/*Q(E) at E,, = 100 meV, calculated with different available values of the branching ratios for radiative decay. For comparison we also give the experimental results of Yokoyama et al. [17] at E = 25 meV and Hotop [18] at E = 50 meV Gas

This work E,, = 0.1 eV a) b) C)

Ref. [17] E= 25 meV

Ref. [18] E= 50 meV

Ar

1.311 1.324 ‘)

1.295 1.327 d,

1.394 1.325 d,

1.15

1.23kO.12

1.477 1.335 1.339 1.203

1.453 1.318 1.321 1.193

1.608 1.425 1.430 1.257

1.0 1.03 1.41

1.580 1.056 1.361 1.271

1.550 1.053 1.342 1.257

1.741 1.070 1.458 1.343

1.19 0.93 1.18 0.88

N2

co CH, 02

NO co2

N,O

a) Calculated with the branching ratios of Kandela [33]. b, Calculated with the branching ratios of Hartmetz and Schmoranzer [35]. ‘) Calculated with the branching ratios of Wiese et al. (341. d, These values have been derived from the OQ(E,r)/ 2Q(E),r) value reported by Verheijen et al. 1191,who have used the transition probabilities of Wiese et al. [34].

84 5.94

84 6.33

78 5.28

67 5.65

with Jf(E)

‘Q(E) =2Q(~re,) 2f(E),

H2

77 5.26

= exp( c Ju, ln(E/E,,)“), ”

J= 0,2.

The scaling cross section 2Q(E,,r) will be discussed in section 5. The choice of this analytical form of the model functions Jf(E) is based on the observation that a plot of the experimental cross section in the superthermal energy range shows an energy dependence that is linear on a double logarithmic scale. The values of the coefficients Ja, have been obtained from a least-squares analysis of the experimental data and are given in table 5. The coefficients Ja, for Ne*( 3PJ)-Ar, not presented in fig. 1, are also given in table 5. In fig. 1 the full curves through the experimental points are the calculated “best-fit” functions given by eq. (17) with 2Q(E,,r) = 1. The gap in experimental data in fig. 1 between 0.1 and 0.6 eV originates from the non-overlapping velocity distributions of the metastable atoms emerging from the two sources used. We note that the experimental cross sections measured with the two types of metastable sources have not been scaled to each other in fig. 1. In contrast to Verheijen et al. [19], who had to describe their state-selected cross sections in the thermal and superthermal energy range by two different model functions, our model functions “f(E) and 2f(E) smoothly connect the experimental data in the thermal and superthermal energy range. The energy range for which our model function is valid,

F. TM. oan den Berg et al. / Ionisation of small molecules by state-selected Ne

368

0.5 t

H2

0.1

1

10

EkV)

Fig. 1. Experimental results for the energy dependence of the total ionisation cross section JQ(E) for the two fine structure states with J = 0 and J = 2, normalized to the scaling value ‘Q,=r = *Q (E,, = 0.1 eV). The solid lines represent the curve fit with the model functions of eq. (17), with the parameters given in table 5 and the ratios oQ(E,,r)/2Q(E,,r) given in table 6. On basis of the observed energy dependence the molecules can be classified in two distinct groups: H,, N,, CO and CH, in group I and O,, NO, CO, and N,O in group II, correlating with eb- and n-type ionisation orbitals, respectively.

F. TM. van den Berg et al. / Ionisation of small molecules by state-selected Ne

is given in table 5 by E,,,in -C E < E,,,,. The ratios ‘Q(E,,,)/*Q( EIer) in eq. (17) are obtained from our experimental cross section data with high accuracy (better than 2%), since the ratios are independent of the experimental conditions. The ratios obtained are still dependent on the transition probabilities of the applied excitation scheme. The results for ‘Q(E)/*Q(E) at a reference energy E,,, = 0.1 eV for the various systems are presented in table 6. The results apply to the transition probabilities reported by Kandela [33], Wiese et al. [34] and Hartmetz and Schmoranzer [35]. In table 6 we have also given the ratios obtained by Yokoyama and Hatano [17] for comparison. For all Ne*-molecule systems we have found a ratio ‘Q/*Q larger than unity, in contrast to Yokoyama and Hatano [17], who have obtained ratios smaller than unity for N,O and NO. On the basis of the observed energy dependence of the ionisation cross section we have separated the molecules investigated in two classes: in the first class the cross sections show a maximum at intermediate energies (N,, CO, CH,, H,); in the second class the cross sections are practically constant in the thermal energy range (O,, CO,, N,O, NO). 4.2. The Ne*(3P0, ‘P2)-Ar

cross section: a test case

The Ne*(3Po, 3P2)-Ar cross sections are pre-

369

sented in fig. 2 and have been obtained from one of the calibration measurements that we have performed during each experiment on a particular Ne*-molecule system. We have not observed any significant deviation between the cross sections for Ne*-Ar given in fig. 2. and the other calibration measurements. This indicates that the detection efficiencies have not changed during our experiments. In fig. 2 the experimental results of ‘Q and *Q for Ne*-Ar as published by Verheijen et al. [19] are compared with our Ne*-Ar results. The cross

Fig. 2. Experimental results for the energy dependence of the total ionisation cross section “Q(E) for the Ne *( J = 0, 2)-Ar system (solid line is curve-fit according to eq. (17)) in comparison with the results of Verheijen et al. [19] (dashed line).

370

F.T.M. oan den Berg et al. / Ionisation of small molecules by state-selected Ne

sections shown are obtained from the least-squares fits to the experimental data as given by eq. (17) and reported by Verheijen et al. [19]. The slight difference in energy dependence in the thermal energy range is partly due to the gj/vj factor in the calculation of the ionisation cross sections from the ionisation probabilities Kj, which by mistake was not taken into account by Verheijen et al. Nevertheless, the ratio ‘Q/‘Q is not influenced by this factor. Verheijen et al. have obtained a ‘Q/*Q ratio at 0.1 eV equal to 1.325 using the branching ratios from Wiese et al. [34] in the calculation of fyv. In order to compare this result with our ‘Q/*Q value we have recalculated ‘Q/*Q obtained by Verheijen et al. by taking the f2 value obtained from the transition probabilities published by Kandela [33], Hartmetz and Schmoranzer [35] and Wiese et al. [34]. The ‘Q/*Q values obtained in this work and from the data published by Verheijen et al. [19] for Ne*-Ar are summarized in table 6. It is obvious from table 6 that the transition probabilities published by Wiese et al. 1341 yield ‘Q/*Q ratios that do not give consistent results for the data published by Verheijen et al. and our work, respectively. In view of the large differences in branching ratios this is not rather surprising. The data of both Kandela [33] and Schmoranzer et al. [35] have a much better accuracy and have our preference. We note that our ratio at Eref = 0.1 eV is in fair agreement with the ratio obtained by Hotop et al. [18] at thermal energies. Yokoyama and Hatano [17] have obtained the ‘Q/*Q ratio for Ne*-Ar from a pulsed radiolysis method, resulting in a quite low value of this ratio.

(Is) orbital, whereas the N, C and 0 atoms have filled (ls)* and (2s)* orbitals and one or more filled and/or half-filled (2~) orbitals. If we denote the electron orbitals belonging to atom A (B) by index a (b) we can write the different molecular states formed by the atomic orbitals in zero-order approximation as [36]:

‘k((ls)tJI,

‘k( csb) = 2-l’* [ ~((lsh)

+

*b3

- ~((l&>l,

= 2-1’2[~(ohJ

*k(G) =

2-“*[wPz),)

+ *k((2PZ)tJl,

*k(c,*) = 2-“‘[‘k((2PZ)J

- *k((2PZ)LJl,

~mPx)lJl~ WC) =2-“*[*k((2PxLJ- ‘k((2PX)J~ ?I+?)

= 2-“*[%2PXLJ

+

~(~yb)=2-l’*[ ‘k(@P,)J+ ‘k@P,),)]? qb!.) =2-l’*[ 42~~)~) - *((2p,),)].

(18)

The superscript b in the wavefunction Ik indicates a bonding molecular state and the superscript * an anti-bonding state. The internuclear axis of the diatomic molecule AB has been chosen as z-axis. In fig. 3 the electron densities of the states (u,“), bonding

anti - bonding

I

4.3. Molecular orbitals and ionisation probabikties Since the overlap of the electron orbitals of the molecules with the 2p vacancy in the core of the excited Ne* atom plays a dominant role in the ionisation process, a knowledge of these molecular orbitals will contribute to a better understanding of the energy dependence of the ionisation cross sections presented in section 4.1. The molecular orbitals are linear combinations of the electron orbitals of the separated atoms that form the molecule. The H atom has a half-filled

0

Fig. 3. Schematic representation of the electron densities of the bonding and anti-bonding molecular orbitals IJ,“, o:, T,” and US*>ox*, TX* >respectively.

F.T.M. van den Berg et al. / Ionisation of small molecules by state-selected

Ne

371

Table 7 Electronic configuration of the ground state of the target molecules and the ionisation energy and ionisation orbitals of the accessible ionic states. The electronic energy of the Ne* states is E * = 16.617 and 16.713 eV for the 3P2 and 3P0 state, respectively Target gas M

Ground state M electronic configuration ‘)

Ionic state M+

b2

HZ

(ab)2(a*)2(7r6 I s

co

ionisation energy ‘) (eV)

ionisation orbital ‘)

x

15.426 15.581 14.014 16.665 12.99

IJb

lx+

X2$

~~b;‘(~~)‘(T~,)~(0~)2

N2

spectroscopic notation ‘)

X.Y

)4(ob)2

x

.?

23

CH, b,

(%b)2(&2($)2(~:)2

AZHi ii ‘A,

02

(4)2(~~)2(~,Py)4(%b)2(~~)(q)

x

211g

a 4HUi NO

co, b, N,O b,

(%b)2(~,*)2($,Y)4(%b)2(cY)

x

lx+

(e,“)2(e;c)2(%!,y)4(?&)4

a 3Z+ b3H X2H

(o)2(c)2(T)4(n)4

x

2s

A%+

12.071 16.092 9.264 15.667 16.567 13.769 12.89 16.42

b 9

b

9

b %Y

eb $Y “X;Y “XGY ?rXdY

e* CY

71 cl

a) The r-axis has been chosen along the internuclear axis for the diatomic and linear triatomic molecules. For CH, the origin of the coordinate system coincides with the central C atom. b, Ref. [37]. ‘) Ref. [38].

(a,*), (a:), (a=*), (lr,“) and (n,*) are shown schematically. We observe that the electrons belonging to the ub states have a large probability to be found between the nuclei of the two atoms. In contrast, this probability is small for the antibonding states. In table 7 the electron configurations for the molecules H,, N,, CO, CH, (group I, defined in section 4.1) and O,, NO, CO,, N,O group I: up

group II: rtx,y

ionising orbital

ionising

N2/C0

orbital

02

Fig. 4. Schematic three-dimensional representation of the electron densities of a group I molecule N, (equal to CO) with a ezb-type ionisation orbital and a group II molecule 0, with a ?rxTy-typeionisation orbital.

(group II) are given, together with the ionisation energy and the orbital from which the electron is removed for the accessible ionic states of the target molecules. We note that the molecules in group I have ub orbitals that ionise to the ionic ground state, whereas the molecules from group II have 71 orbitals that ionise to the ionic ground state. Although in our experiment we cannot distinguish between ions in their ground state and ions in excited states we first discuss our results only in terms of the character of the ionising orbital of the ionic ground state. In section 4.6 we will discuss the influence of the excited ionic states on our general conclusions. The electron orbitals for the molecules N2 (CO) and O,, that belong to the two different groups I and II, are drawn schematically in fig. 4. From these electron density plots it is obvious that the Ne* atom has to penetrate the molecule N, deeper in order to get a sufficient overlap of the 2p vacancy of Ne* with the ionising orbital than in the case of the qv ionising orbitals of, e.g., 0,. Therefore, it is expected that the ionisation cross sections for group I are smaller than for group II. Regarding the shape of the ub orbitals in fig. 3

372

i? T.M. oan den Berg et al. / Ionisation of small molecules by state-selected

Ne

I’(r) a small decrease in the pre-exponential factor, resulting in r’(r,),G < r(r,)/fi, can easily be compensated for by a slightly smaller value r,’ < r, with the net result r’(r,l)/tz = r(r,)/A, i.e. the same ionisation rate. This demonstrates the large correlation between the real part of the optical potential, which determines rC, and the imaginary part. Differences in the observed energy dependence of “Q can thus be explained by assuming different shapes for either the real or the imaginary part of the optical potential. The observed behaviour of group I molecules with a ab-type ionisation orbital is very similar to the energy dependence of the total ionisation cross section for the Ne*-Ar system (fig. 2). Both exhibit the increase of “Q in the thermal energy range to a local maximum and a decrease at higher energies. For the Ne*-Ar system this is attributed to the existence of a “kink” in the repulsive branch of the intermolecular potential [9], i.e. a localised region where the repulsive region is less steep (fig. 5). In this energy range the classical turning point r, thus decreases more rapidly with increasing collision energy. The resulting increase in the ionisation rate T(r,)/A is

we expect that the overlap integral of the ‘2p vacancy of Ne* with the eb orbital will increase more rapidly with decreasing internuclear distance at small r than at large r, resulting in a bi-exponential shape of the resonance width’ r(r). For the interaction of the Ne* atom with molecules with ITSy ionising orbitals, we expect that the usual single exponential behaviour is a rather good approximation. 4.4. Optical potentials and molecular orbitals To support these suggestions for a different shape of r(r) to explain the observed differences in the energy dependence of the total ionisation cross section for molecules with eb- or T-type ionisation orbitals we have to investigate the influence of the real and the imaginary part of the optical potential. Ionisation occurs preferentially close to the classical turning point rC of a trajectory and is proportional to the product of the ionisation rate r(r,)/tt (s-l) at the classical turning point and the residence time in this region. With the usual assumption of a single exponential function for I

I

I

I

16'

i\l

1d2 Id3

104,

2

4

r(1)

r(I)

q

16’ I#

0.1

1

E IeVl

rkink

IO3

16 o

Fig. 5. Schematic representation of two optical Ne* -molecule systems of group I (Hz, N,, CO, the intermolecular potential in combination with section Q(E) as an undisturbed

2 r(A)

4

potentials that lead to the energy dependence of JQ(E) typical for Ne*-Ar and CH,). A “kink” at internuclear distance r = rkk with a value v(rr,,,) = E,, of a single exponential function T(r) leads to the same shape of the ionisation cross intermolecular potential V(r) with a bi-exponential function r(r).

F. TX.

uan den Berg et al. / Ionisation

larger than the decrease in residence time, with the net result of an increasing cross section with increasing energy. For higher cofhsion energies the decrease of the residence time is again the dominating factor, resulting in a decreasing ionisation cross section with increasing energy, Moreover* for the Ne*-Ar system it is necessary to introduce a saturation of r(r) to a constant value for small internuclear distances r < rim (= 2.5 A), because the overlap of the relevant wavefunctions of projectile and target does not increase infinitely. The existence of a “kir@ is justified ]9] as a transition of the interaction with an atom-atom character at large internuclear distances to an iteration with a dominant ion-atom character at small intemu~le~ distances, where the influence of the valence electron is less pronounced. Due to the correlation of real and imaginary part of the optical potentia1 the observed energy dependent behaviour can also be explained by assuming a repulsive branch without a “kink” in combination with a bi-exponential shape of f(r). The second, steeper exponential branch of r(r) at small internu~l~ distance r -Krk (see fig. 5) then emulates the influence of the decreasing value of the classical turning point in the former case of an inte~ole~~~ potential with a “kink”‘. If we assume an optical potential without a ‘Gkink” in the real part and only a single exponential function for the imaginary part we observe a flat behaviour of “Q in the thermal energy range, with at higher energies the characteristic decrease of the crass section due to the decreasing residence time. This type of energy dependence is typical for the group II molecules with a T-type ion&at&n orbital. Based on the preceding infu~ati~n we have to make a choice for a ~h~acte~stie optical potenti~ for each group. If we assume intermolecular potentials without a “kink”, the consequence is a bi-exponential function for I’(r) for group I molecules ( ab-ionisation orbital) and a single exponential function for r(r) for group II (+ionisation orbital). The alternative is a single exponential function for r(r) for both groups and an intermolecular potential w;h “kink” for group I and wj~~~u~“kink’” for group II.

of smallmolecules by state-selected Ne

373

In our opinion -there is no solid reason to assume systematic differences in the repulsive branch of the ~termolecular potenti~s of group I and II molecules. Large differences in the attractive branch and the well region are also rather unlikely. For the heteronuclear No*-Ar, Kr, Xe systems the we11 depth ranges from 5.45, to 12.5 meV, respectively, at a position rm = 5 A for all target gases [9]. For molecules with polarisabilities comparable to the heavy rare gases similar values are to be expected. In conclusion we state that the simple picture of different shapes for I’(r) to describe the ~ffere~t energy dependence of molecules with eb- or v-type ion&&on orbitals has our preference. This Gon~lu~o~ is in agreement with the result of Penning ionisation of unsaturated hydrocarbons ]39,40] and heterocyclic molecules [41] by collisions with He*f3S) ]39,41] and Ne*f3Fz) ]40] metastable atoms. In these experiments the real part of the optical potential is fixed, because it concerns the same molecule, but the imaginary part is determined by the overlap with the different molecular orbitals. The ‘I; bands in the Penning electron spectra are always enhaneed relative to the u bands in comparison with the photoeiectron spectra. The latter can be unde~tood directly if we real&e that the photons are undisturbed by the repulsive forces that prohibit further penetration of the metastable atoms at thermal energies. 4.5. Fine structure dependence Until now we have only discussed the overall characteristic behaviour of both fine structure states. In fig. 6 we have plotted the energy dependence of the ratio ‘Q~~~~~~~) for all molecules of both group I and group II. ~thou~ the aver= age value of the ratio ‘~~~~/‘~~~) of the group I molecules seems to be slightly larger than for the group II molecules, we do not observe a characteristic behaviour of molecules of either group. The overall behaviour is quite different from the results for, e.g., the Ne*-Ar system, as reported by Hotop [18] and Verheijen et al. [19]. In this case a rapid decrease is observed from a value “Q(E)/ ‘%J(E) = 0.85 at thermal energies to a. constant value 0.5 for E :, 2 eV_ However, it is not clear

Fig. 6. The ratios zQ(~)~Q(~) for the @sup I molecules (dashed lines) and the group II molecules (solid lines).

what causes these differences for the two fine structure states, even for the well studied Ne*-Ar system. Hotop [18] and Morgner [4,5] attribute this behaviour to differences in I’(r), while Verheijen et al. [19] assume differences both in the repulsive branch of the intermol~ul~ potential and in F(r). In a recent analysis of elastic differential cross section measurements by Hausamann [lo] it was assumed that the intermolecular potentials only differ in the well position rm, with a 3% smaller value for the 3P0 fine structure state. In our opinion the latter assumption also is most likely for the Ne*-molecule systems. However, state-selected measurements of the total cross section or the differential cross section for elastic scattering of the Ne*-molecule systems will have to help in deciding on the the relevant differences.

The relative importance of io~sation to excited ionic states depends on the bracing ratios to these states and the character of the electron orbitals involved. The accessible excited states and the orbitals involved are given in table 7. Data on the branching ratio for Penning ionisation to the different excited ionic states are scarce. The existing photoelectron spectroscopy data cannot be used, because the process of io~sation by UV photons is not hindered by the repulsive forces encountered in the process of ionisation by excited atoms. This is clearly demonstrated by the com-

parison of photoelectron and Penning-electron data in the paper of Hotop et al. [42], describing the Pen~g-el~tron spectra for io~sation of N2, NO, O,, N,O and CO, by collisions with metastable He*(2 3S). For this reason only the data on Penning ionisation optical spectroscopy (PIOS) and Penning ionisation electron spectroscopy (PIES) can be used for determining branching ratios. However, nearly all available data concern collisions with He * (2 *S, 2 3S) and very little information on Ne*(3Po, 3Pz) is available in this field for molecular targets. With these notations we will discuss the influence of excited ionic states on our results. For H,, N, and CH, of group I with a a-ionisation orbital no excited ionic states are involved. For CO, the fourth molecule of group I, the only excited state that can be reached is CO+(A211i) with a $,- ionisation orbital. Emission from this state has been observed by Bruno and Krenos [43] for collisions with Ne*( 3P0, 3Pz) in a crossed mol~ular beam experiments, without state selection for the Ne* beam. Their obse~ations are consistent with an ionisation cross section for the lowest-lying vibrational state which is independent of collision energy. Considering the ~-io~satio~ orbital of the CO+(A) state {table 7), this is in full agreement with the conclusions of this paper. Because they do not give absolute values for their cross sections, it is not possible to derive a branching ratio from their work. In view of fig. lc, which shows an energy dependence of the total ionisation cross section typical for a ab-ionisation orbital, we conclude that the ~ont~bution of the CO+(A) state is quite small. In group II the target molecules 0, and CO, are expected to have an energy dependence of the total ionisation cross section in agreement with a n-ion&&on orbital: for C& because the only accessible excited ionic state also concerns a oforbital and for CO, because no excited ionic states are involved. For the NO molecule only the NO*(b 3H) state has a o-ionisation orbital. The origin of this band lies only 50 meV below the Ne*( 3Pz> state and the effect will be most important for the Ne*(3Po) state. A close look at the experimental results for J = 0 in fig. 1 (NO} indeed shows an increasing

F. TM. van den Berg et al. / Ionisation of small molecules by state-selected

behaviour in the thermal energy range typical for a a-ionisation orbital. From the 20% increase of ‘Q in the thermal energy range we estimate a branching fraction of approximately 0.20 for ionisation to the NO+(b) state. For N,O the origin of the N,O+(A*Z+) band lies 0.2 and 0.3 eV below the electronic energy of the Ne*(3P2) and (3Po) states, and we do not expect a very different behaviour for both fine structure states. Fig. 1 (N,O) indeed shows a very similar behaviour for the energy dependence consistent with a T-ionisation orbital, which leads us to the conclusion that the contribution of the excited ionic state to the experimental ionisation cross section is quite small.

5. Absolute values of ionisation cross sections “Q The absolute values have been calculated from the experimentally obtained ionisation probabilities OK and *K using eqs. (12) (14) and (16). The detection efficiency for ions has been taken equal to $0” = 1. Verheijen et al. [19,21] have obtained an ion detection efficiency equal to qio” = 0.56, which yields ionisation cross sections for Ar that are too large with respect to the Ne*(3Po, 3P2)-Ar results reported by Gregor and Siska [9]. Therefore, vion can be regarded as a parameter that has to be determined from a comparison with other cross section data published. The detection efficiency 17 “’ for UV photons is determined by the solid angle of acceptance of the spiraltron, by the quantum efficiency and by the transmission coefficient of the grids used [19,21]. We have adopted the value 77“v = 5.66 X 1O-4 obtained by Verheijen et al. The (nl) products for the various molecules have been taken from table 4. Stebbings and co-workers [15] have measured the absolute total ionisation cross sections for various molecules by metastable Ne* atoms at thermal energies ina crossed beam experiment. Brom et al. [16] have obtained the quenching rate constants for Ne*(3P2) metastable atoms in a flowing afterglow experiment at room temperature. Yokoyama and Hatano [17] have used the pulsed radiolysis method for the determination of de-excitation rate constants of Ne*(3Po, 3P2) by

375

Ne

molecules. In the comparison of our experimental data with the cross section data published by these authors we must take into account the energy dependence of the ionisation cross sections. We have found that the group II molecules O,, NO, CO, and N,O yield nearly constant cross sections at thermal energies for both the 3Po and 3Pz metastable states (see section 4.3). In table 8 we give our results of the total ionisation cross section data for Ne*(3Po, 3P2)-0,, NO, CO,, and N,O at E,,= 0.1 eV. From our state-selected results we have obtained effective total ionisation cross sections Q, for a mixed Ne*(3Po, 3Pz) beam, assuming that in the metastable atom beam the ratio of the 3Po, 3Pz state fluxes is 1 to 5. The cross section data for O,, NO, CO,, and N,O obtained by West et al. [15] have also been presented in table 8. They have reported an effective temperature T,,= 435 K, independent of the target molecule used in their crossed beam experiments. We have calculated the relative kinetic energies from the velocity distributions of the primary and secondary beam reported in an earlier paper [44]. The source temperature of the secondary beam is equal to 300 K. For the temperature of the primary metastable atom beam we have assumed a value of 300 K. Theuws [23] has shown that the temperature of the metastable beam is not affected by the excitation process if this excitation is supplied by electron impact. It turned out that the mean relative kinetic energies calculated from the velocity distributions are equal to E = 43 meV for all Table 8 Comparison of our state-selected ionisation cross sections at E,, = 0.1 eV for the Ne*(3P,,. 3P2)-02, NO, CO2 and N,O systems (T-type ionisation orbital) with the mixed-beam cross sections ewes, obtained by West et al. [15] at E = 45 meV. For the detection efficiencies for UV photons and ions we have used the values vu”= 5.66X 10e4 and q’O”=l, respectively. The effective cross section for mixed beams is Qmix = OQ/6 + 5 X =Q/6

Gas

02

NO co, N2O

‘Q

=Q Qmix Q,, (A=) (A=) 63 (A=)

Q,/ Qwes,

38.6 24.1 48.0 30.0

1.05 1.08 1.01 1.00

24.5 22.9 33.3 23.6

26.9 23.1 37.4 24.7

25.5 21.4 37.1 24.8

F. TM. van den Berg et al. / Ionisation of small molecules by state-selected Ne

316

target gases used (except for H,: E = 35 mev>. These values are outside the energy range that we have investigated. From fig. 1 it can be seen that our experimental cross sections for N,O, CO,, 0, and NO at E,,= 0.1 eV can be compared with the results of West et al. [15] at E = 43 meV without introducing significant errors caused by the energy dependence of the cross sections. The ratio of our “absolute” values and the cross section data of West et al. [15] is nearly constant for the molecules N,O, CO,, 0, and NO. The mean value QmJQWest= 1.035 + 0.03. This moleculeindependent ratio indicates that we only have to adjust the ratio nuv/n io” in the calculations of the ionisation cross sections to obtain absolute values in agreement with the results of West et al. [15]. Therefore, we present in table 8 the absolute cross sections ‘Q and ‘Q at reference energy E,,= 0.1 eV for all systems investigated, calculated with the corrected n”‘#‘” ratio. Our *Q(E,,,) values in table 9 may be used for the calculation of 'Q(E) and *Q(E)with eq. (11). In table 9 we have also given the cross sections obtained by Brom et al. 1161 and by Yokoyama and Hatano [19]. When comparing the data of Yokoyama and Hatano with our results one should keep in mind that their cross sections are total quenching cross sections, which are always larger or equal to the total ionisation cross section. The given values of Yokoyama and Hatano are thus upper limits for

is

our value. This effect can improve the comparison for the gases NO, CO2 and N,O, but the discrepancy for O2 can still not be explained. The data of Brom et al. [16] are corrected for the parabolic flow by a factor 1.6 as has been discussed by Gregor and Siska [9]. We see from table 8 that for the systems Ne *-CO and Ne*-N, the cross sections are nearly equal. This is not surprising in view of the electron-orbital discussion, given in section 4.3. In contrast, the cross sections for the similar systems Ne*-CO, and Ne*-N,O differ by a factor 1.55 + 0.05, which cannot be explained by the relatively simple orbital considerations. For the absolute total ionisation cross section *Q of Ne*-Ar Verheijen et al. [19] obtained *Q( Eref = 0.1 eV) = 34 f 3 A2 assuming an ion detection efficiency nion = 0.56. If the detection efficiency used had been equal to $“’ = 1 this cross section, corrected with a factor of 1.035 obtained from the comparison with the data reported by West et al. [15], would be 18.4 &-1.6 A2 which is in good agreement with our value *Q( E,,_) = 18.3 A2 in table 9. For the Ne*-N, system this approach of correcting the ion detection efficiencies of Verheijen is unsuccessful. The corrected results of Verheijen [20] are ‘Q( E,,)= 26.7 A2 and *Q( Erer) = 17.9 A2 = 0.1 eV, which show a pronounced disat Eref agreement with our data. In our opinion this

Table 9 Absolute values for ‘Q(E) and *Q(E) at Erof = 0.1 eV. For the ratio of the detection efficiencies n”” and via” we have adopted the value that makes our mixed-beam cross sections Q,, for 0,, N,O, CO, and NO equal to the cross sections at E = 45 meV measured by West et al. [15]. The average value is Qmix/Qwes, = 1.035 + 0.030 (table 8) Gas

E,,

= 100 meV this work

'Q(A*)

*Q6*2,

E=45meV West [15]

Brom [16]

Qwest (A21

'Q@*',

Yokoyama

[17]

'Q(A*)

*Q@*2)

Ar

24.0

18.3

14.7

16

16

14

H2

11.8 18.0 17.4 19.2

7.9 13.5 13.0 16.0

2.65 10.4 11.2

4.3 17.6 11.8

3.5 8.9 14

3.5 8.6 10

37.3 23.3 46.4 29.0

23.7 22.1 34.1 22.8

25.5 21.4 37.1 24.8

51.2

25 27 54 43

21 29 46 49

N2

co C% 0, NO co2 N2O

F. TM. van den Berg et al. / Ionisation of small molecules by state-selected Ne

difference is due to an incorrect estimate for the (nl) product of the secondary beam. This is not really surprising, because Verheijen [20] did not perform any calibration of his N, secondary beam.

6. The optical potentials for the system Ne*cPO, 3P2)-H2 We have analysed the experimental ionisation cross sections ‘Q(E) and 2Q(E) for the systems Ne*CPo, 3Po)-H2 in terms of optical potentials. Until now only the absolute ionisation cross section at thermal energies had been measured. An earlier investigation of the deactivation cross settions in an aferglow plasma already indicated a strong energy dependence in the thermal energy range [45]. Our results, presented in fig. 1, confirm this strong energy dependence. Furthermore, we find a saturation of the ionisation cross section in the superthermal energy range. West et al. [15] have measured the absolute ionisation cross section for H, at 435 K with a mixed beam of Ne* atoms. Recently, Bussert et al. [46] have measured the state-selected cross sections at 300 K, which are slightly smaller than the state-selected data-reported by Yokoyama and Hatano [19]. A comparison of these data with our results is not straightforward, due to the different energies used. Although our absolute cross section data at E,,, = 0.1 eV, given in table 9, are a factor of 3 larger than the results of Busset et al., an extrapolation of our experimental values to lower energies will yield cross sections comparable with the thermal energy data reported previously. In contrast with our discussion in sections 4.3-4.5 we have analysed our data for the Ne * (3PO, 3P2)-H2 system with the same real potential for both fine structure states and without a bi-exponential function for the imaginary part of the optical potential. This approach is mainly due to the lack of state-selected data on elastic scattering for this system. The results for r(r) are thus only a first approximation for the actual ionisation width. State-selected measurements of the velocity dependence of t.he elastic total cross section are planned in Eindhoven in the near future. The results of these measurements are necessary to

371

introduce fine structure dependent modifications of the existing real potential for the Na-H, system. For the real part of the optical potential we have adopted the ground state potential curves of the Na(3s)-H, system calculated by Botschwina and Meyer [47]. Apart from small differences in the repulsive branch due to the empty 2p orbital in the core, these curves are expected to be similar to the Ne*(3s)-H, potential curves. The potential curves for the C,, symmetry calculated by Botschwina are only slightly dependent on the internuclear distance r of the two H atoms. These curves have purely repulsive shapes without a well. Due to this potential shape the ionisation cross section will rise steeply with increasing energy. In that case the decrease in interaction time is compensated by a stronger increase in ionisation probability r(r) as a function of intermolecular distance r, as happens in the well-known He*(3S)-Ar system [8]. We have varied the parameters bi,, ri, and cim of the imaginary part of the optical potential (given in eq. (5)) until satisfactory agreement was found between the calculated and experimental cross sections, both with respect to the energy dependence and to the absolute values at Erer = 0.1 eV. The “best-fit” functions T(r)/2 for the Ne* (3PJ)-H, system are given by: J= 0:

r(r)/2=3.5exp[-lB(r/r,--l)]

(PeV)

r’ ri,, r(r)/2 ‘im

= 9.63 meV =2.8&

r G r,,,

r,=S.Oz&

J = 2:

r( r)/2

= 10.4 exp[ - 13( r/rm - l)]

( PeV)

r ’ rirn, r(r)/2 rim

= 3.17 meV =2.8&

r < rim,

r,=s.oi,

(19)

with r,,, a scaling length of the potential. In fig. 7 the state-selected ionisation cross sections for Ne*(3Po, 3P2)-H2 are shown together with the calculated best-fit functions obtained with the r(r)

378

F. TM. oan den Berg et al. / Ionisation of small molecules by state-selected Ne

E(eV) Fig. 7. Experimental results for the total ionisation cross section ‘Q(E) in comparison with a best-fit optical potential, using the predictions of the intermolecular potential for Na(3s)-H, of Botschwina [43] for the real part and the single exponential (saturated for r < 2.8 A) function of eq. (19) for the imaginary part.

for J = 0, 2 in eq. (19). In our opinion the, discrepancy between experiment and calculations at energies E > 2 eV can be removed if we use a bi-exponential form for the F(r) as shown in fig. 5. By the larger increase in F(r) at small internuclear distances, only attainable at high energies, the calculated cross sections will show a more constant energy dependence at high collision energies, comparable with the experimental results. We note that the best-fit functions F(r) depend on the shape of the real potential. Since this function contributes to the ionisation cross sections only significantly at small internuclear distances r, a measurement of elastic scattering cross sections in backward direction will uniquely yield the correct imaginary part of the optical potential

PI. 7. Concluding remarks Measurements of elastic scattering, with their sensitivity to the real part of the potential, are required to support the major conclusions of this paper. Firstly, we have to find additional support for our conclusion that the optical potential for molecules with eb- and T-type ionising orbitals mainly differ in the shape of the imaginary part.

Secondly, we have to explain the physical background of the different behaviour of the two fine structure states, both for atoms and molecules as a scattering partner. Our idea that the major differences have to be found in the real part of the optical potential is still rather speculative and only based on preliminary conclusions of Hausamann [lo] for the Ne*-Ar system. At this moment we are in the process of planning a series of measurements of the total cross section for elastic scattering of the systems studied in this paper (except H,, due to the cryoexpansion chamber of the secondary beam in the crossed beam apparatus used), again using state-selected Ne*(3P0, 3P2) beams. Both the energy dependence and the absolute value of the total cross section will be measured, resulting in information on the well region from the position of the glory extrema and information on the long-range attractive forces. From the latter we can determine both the absolute value of the van der Waals constant C, and the first higher-order term C,, due to induced-dipole-induced-quadrupole interaction. Previous measurements on the Ar *-rare gas and Kr *-rare gas systems [48,49] are a good reference for the interpretation of these measurements. With this additional information it will finally be possible to perform a full analysis of the data in terms of an optical potential. However, the preliminary conclusions already give a good insight in the process of ionisation with molecular targets. By investigating the energy dependence of the process of ionisation to excited electronic states of the molecular ion, which involves the removal of an electron from an orbital with a different character, we have an extra check on the influence of the orbital on the shape of F(r). In these experiments the real part of the optical potential is exactly the same for all different final states. All differences in the total ionisation cross section are thus only due to the imaginary part, i.e. the dynamics of the process of ionisation. This type of experiment can be performed both by PIES [39-411 (Penning ionisation electron spectroscopy) and PIOS (Penning ionisation optical spectroscopy). PIOS experiments with Ne* on these small molecules are in progress in our laboratory,

F.TX. van den Berg et al. / Ionisation ofsmallmolecules by state-selectedNe

and will be used for supplying additional information and for comparison with the He*-molecule systems. The latter is important in view of the conflicting results on the branching to the NO+ (b) state with a (I orbital. In the m~surements of Hotop [42] at thermal energies more than 60% of the ions in the X, a and b states go to the b state, while we only estimate a contribution of the order of 20%. References [l] F.M. Penning, Naturwissenschaften

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