State selected total penning ionisation cross sections for the systems Ne*(3P0, 3P2) + Ar, Kr, Xe and N2 in the energy range 0.06 < E0(eV) < 8.0

255

Chemical Physics 102 (1986) 255-273 North-Holl~d, Amsterdam

STATE SELECTED TOTAL PE~NG IONISATION CROSS SECTIONS FOR THE SYSTEMS Ne*t3Po, 3P2) + Ar, Kr, Xe AND Nz IN THE ENERGY RANGE 0.06 < E,(eV) < 8.0

M.J. VERHEIJEN Physics Department,

’ and H.C.W. BEIJERINCK

Eindhoven University of Technologv, P.U. Box 513, 56Oil MB Eindhoven, The Netherlands

Received 2.5 March 1985; in final form 24 October 1985

The velocity dependence and absolute values of the total ionisation cross sections of Ar, Kr, Xe and N, by metastable Ne*(3P,) and Ney3P2) atoms have been measured in a crossed beam scattering experiment. State selection of the beam of metastable atoms has been performed by optical pumping with a cw dye laser. Our technique, which uses the UV photons released in the radiative decay following the Iaser excitation to measure the density of metastable atoms in the scattering centre, is very insensitive to details of the process of optical pumping. Systematic errors in detection efficiencies of the metastable atoms are largely eliminated in this approach. We have analysed our experimental data in terms of an optical potential, using a least-squares method to determine the potential parameters. For the real part we use an ion-atom Morse-Morse-spline-van der Waals potential VO(r) as proposed by Siska. The well area for V,(r) Q 0.1 eV is left unmodified. The energy dependence of the cross sections for the Ne*-rare gas systems points unambiguously to a pronounced “kink” in the repulsive branch at 0.1-0.2 eV. For the imaginary part, with the usual exponential behaviour, we have to introduce a saturation to a constant value at small internuclear distances r < rr,,,, with rr,,, in the range 2.1~ Q,,(A) < 2.6 which is o&y probed for energies larger than 0.15 eV. These modifications result in a satisfactory description of the data for the Ney3P,)-Ar, Kr, Xe systems. For the Ne*(3Po) systems additional modifications of the well area are necessary. By calibrating the density-length product of the secondary beam and using the available detection efficiencies for ions and UV photons of the spiraltron detector we have also determined absolute values of the total ionisation cross section. In the thermal energy range (0.06-0.16 eV) they are in fair agreement with the rate constants for the quenching of metastable atoms as measured by Brom in flowing afterglows.

1. Introduction

Ionising collisions involving metastable atoms have been studied by several techniques in the past ten years, Le. total ionisation cross section measurements, Penning ionisation electron spectroscopy, and elastic differential scattering experiments. Total ionisation cross section measurements with beams of unselected me&stable Ne*(sP*, 3P2) atoms have been performed by Tang et al. [l] (0.01-0.3 eV), Illenberger and Niehaus [Z] (0.01-0.6 ev), West et al. [3] (0.04 ev), Neynaber and Magnuson [4,5] (0.01-600 ev), Neynaber and Tang [6] (0.01-10 ev), and recently by Aguilar-

’ Present address: Philips Research Laboratories, 80000, 5600 JA Eindhoven, The Netherlands.

P.O. Box

Navarro et al. [7] (0.02-0.35 ev>. Illenberger and Niehaus have measured only the relative velocity dependence for the Ne*-Kr system in the energy region ranging from 0.015 to 0.450 eV, which shows a satisfactory agreement with the results of Tang et al. and of Neynaber and Magnuson. The absolute values given by West, Neynaber, and Tang show differences up to a factor of three. Penning ionisation electron spectroscopy [8] gives a detailed insight in the ionisation process, but is limited to only few collision energies. State selected experiments with this technique have been performed by Hotop et al. [9] with a thermal beam of metastable neon atoms with an effective temperature of 400-500 K (0.035-0.045 eV). Measurements of the differential cross section for elastic scattering have been performed by Gregor and Siska [lo] with a mixed beam of metastable neon atoms at energies of 0.03 and 0.07

0301-0104/86/$03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

256

M.J. Verheijen, H.C. W. Beijerinck / State selected total Penning ionisation cross sections

eV. For the case of a small ionisation probability, as observed for the systems studied in this paper, these measurements are rather insensitive for details of the process of ionisation. Modifications of the imaginary part of the optical potential are correlated with small changes in the real part of the potential. Gregor and Siska [lo] could even fit their data with only a real potential, i.e. assu~ng no ionisation at all. To eliminate this ambiguity they have analysed their results in combination with the total ionisation cross section measurements [l-5] in terms of optical potentials. Recently, state selected elastic differential scattering experiments have been performed in Freiburg 1111.The analysis of these data is still in progress. We have performed the first state selected measurements on the velocity dependence of the total ionisation cross section for the systems Ne*c3P,, 3P2) + Ar, Kr, Xe and N, in a wide energy range. The experiments have been performed in a crossed beam machine. High-intensity plasma sources .for the primary beam of metastable atoms and highdensity supersonic secondary beams result in an excellent statistical accuracy (section 2). State selection is obtained by optical pumping with a cw dye laser. A new technique has been developed to eliminate systematic errors due to state- or velocity-dependent detection efficiencies of the metastable atoms. The density of metastable atoms is measured directly in the scattering centre, by detecting the UV photons due to the radiative decay after excitation by the laser beam. Other systematic errors, like attenuation of the primary beam beyond the scattering centre, are also eliminated in this way. A careful1 analysis of this method is given in section 3. In section 4 we present our experimental data on both the velocity dependence and the absolute value of the total ionisation cross section, in comparison with other data available. In the thermal energy range we use Hotop’s data [9] on the ratio of the 3P0 and 3P2 cross sections as a starting point for a general discussion on the differences observed for the two states. In section 5 we analyse our data in terms of an optical potential, using the ion-atom MorseMorse-spline-van der Waals potential of Siska as

a starting point. The wide energy range proves to be of great help in dete~ing details of both the real and the imaginary part of the optical potential. Major modifications are the saturation of the imaginary part at small internuclear distances and the introduction of a more pronounced kink in the repulsive branch of the real part, together with a steeper slope of the ion-atom inner core of the IA MMSV potential. A final discussion of the modified optical potentials is given in section 6. In section 7 we give some concluding remarks on the strong evidence for an oscillatory structure in the total ionisation cross sections for the Ne*(3Po) + Ar, Kr systems.

2. Experimental Experiments have been performed with a crossed beam technique. The primary beam of neon atoms contains a small fraction of metastable Ne*(3P,,, 3Pz) atoms. Two types of primary beam sources are used: A hollow cathode arc beam source [12] produces a high-intensity (2 x lOi s-i sr-‘) beam of metastable atoms in the supertherma1 energy range (0.5-8 eV, fraction metastable atoms 10-3). A discharge excited supersonic source [13] produces a beam of metastable atoms with 2 x 1013 s-l sr-l intensity in the thermal energy range (0.05-0.10 eV, fraction metastable atoms lo-‘). A quick interchange between the two sources is possible, without disturbing the vacuum conditions of the beam machine. The alignment of the primary beam is rigorously maintained, because both sources use the same sampling orifice (skimmer). A schematic view of the beam machine is given in fig. 1. The collimator 1301 mm downstream of the sampling orifice (73 mm upstream of the scattering center) has a diameter of 2.0 mm, resulting in a flow of metastable atoms through the scattering center of typically 4 X lo7 s-’ and 4 X 10’ s-i for the thermal and superthermal beam sources, respectively. The flight path from the time-of-flight chopper [14] to the scattering center is X60 mm. The beam of the metastable atoms can be monitored 1885 mm downstream of the scattering center, using secondary electron emission from an untreated stainless steel surface followed by an

M.J. Verheoen, H. C. W. Beijerinck / Siate selected total Penning ionisation cross sections

257

Fig. 1. Top view of the beams in the total Penning ionisation cross section experiment. (1) Primary beam source with sampling orifice at .z = - 1374.5 mm, (2) time-of-flight chopper at z = z, = - 860 mm, (3) collimator 1 at z = z1 = - 73.5 mm, (4) secondary beam at z = z, = 0 mm, (5) collimator 2 at t = .z2= 1265.5 mm with 0.3 mm diameter, (6) detector for metastable atoms at z = z, = 1884.7 mm, (7) laser beam crossing the primary beam at z = z( (- 20 < +(mm) < 5). The spiraltron is positioned in the plane perpendicular to the plane of the beams. It is oriented 45” backward with respect to the primary beam axis.

electron multiplier. We note that this detector is only used for the alignment of the laser beam and not for the calibration of the flow of metastable atoms through the scattering center in our state selected measurements (see sections 3.2 and 3.3). State selection of the primary beam has been performed by optical pumping with a cw dye laser beam 19,151.To avoid polarisation of the primary beam due to the optical pumping [16], the electrical field of the linear polarised laser beam is chosen perpendicular to an external magnetic field of = 1 gauss parallel to the primary beam axis. The laser beam (3.3 mm diameter at l/e2 intensity, 7-10 mW) intersects the primary beam at right angles with an accuracy of 0.2 mrad [17]. With a stepper motor driven flat mirror [17] the intersection point can be shifted from 20 mm upstream to 5 mm downstream of the scattering center (see sections 3.2 and 3.3). The frequency of the laser has been absolutely stabilized within 0.5 MHz at the transition under investigation [X3]. The supersonic secondary beam is double differentially pumped [19] with oil diffusion pumps and is defined by a 2 x 4 mm collimator 15 mm upstream of the scattering center. The calibrated density-length products [20] at the scattering center are 4.3, 2.5, 1.8, and 1.8 X 10” mm2 for Ar,

Kr, Xe, and N,, respectively. A schematic view of the scattering center is given in fig. 2. We use a spiraltron SEM4219 [21] with a 10 mm diameter entrance as detector for scattering products. This detector is not only sensitive to ions, but also to electrons, metastable atoms, and UV photons with wavelengths shorter than 100 nm. The count rate of “dark pulses” lies well below 1 Hz. The positive ions, produced at the scattering center can be focused onto the spiraltron (4) by a positive (400 V) voltage at the ion repeller (9) and onto the repeller by a negative voltage (-400 V). This enables us to discriminate the positive ion signal from the signal due to UV photons and metastable atoms. The contribution of elastically scattered metastable atoms from the primary beam is minimised by positioning the spiraltron in the backward position with respect to the primary beam. In this configuration the overall detection efficiency for UV photons and metastable atoms from the scattering center is $ = 5.66 x lop4 determined by the solid angle efficiency (q”, = 7.27 X 10e3), the transmission of the two grids ($+ = 0.37), and the quantum efficiency 1221 (T&, = 0.21). The overall detection efficiency for positive ions is determined by the same efficiencies, &, &, and & of which only the quantum ef-

258

M.J. Verheijen,H.C. W. Seijerinck / State selected total Penning ionisation cross sections

ficiency is known yet (n& = 0.90 [23]). With optimum field configuration the solid angle efficiency will be close to unity and the transmission of the grids will also be close to unity. In a Ne*-Ar experiment the total count rate for UV photons and metastable atoms (vi,,. rep= -400 V) is less than 0.5% of the count rate when Penning ions are included ( v,On,rep= 400 V). Ions are produced both in the secondary beam and in the residual background density along the primary beam axis. The field configuration has, to be chosen in such a way that all ions produced in the secondary beam are detected and that only a limited part of the surrounding region is seen by the detector. We can easily correct for a constant residual gas density. However, the gas load of the secondary beam causes an increase of the background density. Although this increase is only 1% of the density of the secondary beam at the scattering center, greater care has to be taken that

the acceptance length along the primary beam is well matched to the scattering length of the secondary beam. We have optimized the field configuration (i.e. with v,,,, rep and Ktield) [24] for an optima respect to signal-to-background ratio and sensitivity for signal-ions (signal: ions due to the secondary beam; background: ions due to the background density in the vacuum chamber). The optimum is reached for Vshield = 25 V and F’ion,rep = 400 V, where the signal-to-background ratio for Ne*-Ar is typically IO and the sensitivity has already reached 63% of its m~mum value. We conclude that the product && = 0.63, resulting in an overall efficiency ni = 0.56 for ion detection. 3. State selected measurements 3.1.

Method

In the state selected cross section measurements we modulate the composition of the beam of meta-

l9.0-

Fig. 2. The scattering center with the ion and UV detection system. The distances (mm) to the origin (scattering center) are indicated. (1) Collimator 1 of the primary beam with 2.0 mm diameter. The x-coordinate is fixed and the y coordinate is scanned by a stepping motor. (2) Collimator of secondary beam (2 X4 mm’}. (3) Primary beam of metastable neon atoms. (4) Spirahron SEM4219 with a cone with open area of 10 mm diameter. (5) Confining grid for secondary electrons in the cone. (6) Shielding grid. (7) Grounded shield for the high voltage leads to the spiraltron. (8) Collector. (9) Ion repeller. (10) Laser beam (position when ions are measured).

J-O

1

2

3

-*P,

Fig. 3. The energy level scheme for the neon atom. Only the first two electronic configurations are given. For the 2~~3s configuration we use the spectroscopic (L-S) notation and for the 2p53p configuration the Paschen notation. The three optical pumping transitions that we have used are indicated with solid arrows, together with the corresponding decay transitions.

259

i&&J.Verheijen, H. C. W. Begerinck / State se/erred total Penning ionisation crms sections

stable atoms by optical pumping with a cw dye laser beam (fig. 2) upstream of the scattering center. The modulation of the ion production at the scattering center (difference with laser off and on), which is related to the modulation of the total (“PO and 3P2) flow of metastable atoms at the scattering center, yields an experimental cross section that only depends on the optical transition used for the modulation. The modulation of the flow of metastable atoms is measured directly by registration of the UV photons produced in the optical pumping sequence (fig. 3).

sity of the beam of metastable contributions

3.2. Beam modulation

iQo(tj)=‘qrj)+odqtj)+rqtj),

For each chopper period the number of metastable atoms that arrive at the scattering center during time channel j centered at the flight time tj = L/vi, with uj the velocity of the atom corresponding to tj and L the flight path from chopper to scattering center, is given by

A$( t,) = (1 - 7g22cI( t,)

(1) where I(0) (s - * sr-*) is the center line intensity of metastable atoms, P(u) the normalised velocity distribution, Q, the solid angle determined by collimator 1, t, the open time of the chopper, and rCh the duration of one time channel. With the dye laser beam switched on the populations of the metastable states of only one isotope are modulated, because the metastable species of other isotopes do not interact with the laser beam due to the isotopic shift (1800 MHz for 20Ne-22Ne). With the laser beam one metastable state is optically pumped, and thus depleted, with a velocity dependent efficiency T$. The transmission through the laser beam for this metastable state is 1 - rlj”.A fraction f,i’ of the pumped metastable atoms cascades to the ground state, pr~ucing both a visible and an UV photon. The remaining part (1 -fz) decays to the other metastable state of the pumped isotope. This implies that the attenuation of the flow of metastable atoms amounts to fzn$. The fraction f; is fully determined by the branching ratios of the upper level of the pumping scheme, which is uniquely determined by the wavelength X of the pumped transition. We separate the inten-

I(O)P(o)

du=‘I(O)

+(u)du

atoms in three

+“I(0)oP(u)

+rIfO>*P(u) du.

du (21

The isotopes that are not modulated are denoted with a superscript r (remaining). The 3Pz and 3P,, states of the modulated isotope are indicated by their total angular momentum quantum number as superscript, i.e. J = 0 or 2. The flow of metastable atoms at the scattering center with laser off &(t,) and laser on lii,(tj) is now given by

+W(t,)

(34

+ (1 -~~)~~~(tj)

+‘&(rj),

(3b)

The contribution

“fi( tj) corresponds to the partial intensities “I(0) “P(u) du according to eq. (1). The optically pumped metastable atoms cascade to the ground state producing UV photons that can be detected with the spiraltron. With the laser beam shifted to the scattering center we can directly measure the modulation of the flow which is given by the difference ~~(tj~-~~(tj)=~~~~2~(t~).

(4)

The time-of-flight spectrum with UV photon detection is given by $y/= ~‘~~h~~f~‘&( tj),

(5)

where n” is the overall detection efficiency for a UV photon produced at the scattering center. 3.3. Experimental

ionisation cross sections

Collisions with secondary beam atoms at the scattering center will produce Penning ions. The counts from the spiraltron that are registered in time channel j for each chopper period are given by

260

M.J. Verheijen, H.C. K BeQerinck / State selected total Penning ionisation cross sections

s,:,=&.h((l -qp(li)*Ki(ti)

pumping transition with wavelength A, as given by

+[4ir(ti)+(1-fhu)l):z~(tj)]oK’(I,) +‘fi(t,)X’(r,)),

014 (6b) = [ *Ki(tj) -(l

and the modulation by "Q) s,‘.o

-

s,i,=

77’7,h17J21ir(

-j;)‘Ki(tj)]/‘j;,

(llb)

=5

014

f,)

(114 where vi is the overall detection efficiency for positive ions and Ki(tj) is the probability for a metastable atom with velocity uj to ionise a secondary beam atom. This ionisation probability is given by K+,)

= (Q;/Q;“) X (l-exP[-((gj/uj)n,l,)Q;“]),

(8)

with Q: the total cross section for an ionizing collision and Qrrf the total effective cross section which attenuates the flux of metastable atoms along the scattering center due to elastic and inelastic collisions. The effective density-length product of the secondary beam is given by (( g,/u,)n,l,), with nsls the density-length product, g, the relative velocity and 0, the primary beam velocity. There are two limiting cases for the effective attenuation. For ((g~,/~,)n,l,)Q~~” 2> 1 the flux of metastable atoms is fully attenuated and eq. (8) can be approximated by K i ( t,) = Q;./Qi”“,

(9

while for the case ((gj/uj)n,l,)Q~ff -=K1 the attenuation of the flux of metastable atoms can be neglected and we get K’(tj)

= (( gi/uj)nsls>Qj-

(10)

A first-order approximation for Q,“” is given by the hard sphere total cross section which is typically 50 A* for Ne*-Ar. We have chosen our experimental conditions such that this effective attenuation is less then 1% so eq. (10) can be used. We can now define an experimental ionisation probability ‘K’ and an experimental total ionisation cross section ‘Q’, determined fully by optical

=‘b2*Q.; +‘booQ).

(114

The superscript A is used to label the optical pumping transition. For this measuring routine it is not necessary that the modulation depth is the same for all velocities. The only requirement is that the (velocity dependent) modulation depth remains constant during one sequence of the measuring routine, with a typical duration of 15 min (see section 3.6). For an optimum signal-to-noise ratio a fraction of 75% of the maximum attainable modulation is already sufficient. This means that only moderate laser beam powers are required. A further advantage of this technique is that the flight-path for all time-of-flight spectra is equal. No flight-path transformation (including deconvolution and reconvolution) of the UV time-of-flight spectrum to the actual flux of metastable atoms at the scattering center is necessary. Moreover, all effects of attenuation of the primary beam beyond the scattering centre and velocity-dependent detection efficiencies are eliminated. Table 1 The fraction f: of the optically pumped metastable atoms, that cascades to the ground state and the composition [eq. (lld)] of the experimental cross section ‘Q’ =xb,oQi +xb,‘Q’ for three optical pumping transitions of neon metastable atoms. The branching ratios of the upper level [25] are used as numerical input Transition (upper level in Paschen notation)

Wavelength (nm)

fz

“b,

‘bo

‘p* -+ 2P2

588.2 594.5 616.3

0.66 1.00 0.71

1.51 1.0 -0.40

-0.51 0 1.40.

‘P24P-a

‘PO --f 2Pz

M.J. Verheijen, H.C. W. Beijerinck / State selected total Penning ionisation cross sections

These experimental cross sections are a result of an experiment at a single optical pumping transition. A second experiment at another transition with a different fraction ft is necessary to obtain the state resolved cross sections ‘Q’ and ‘Qi. For each optical pumping transition the fraction f; is fully determined by the upper state of the optical pumping scheme. The values for fc and the coefficients ‘bO,2 for the composition of the experimental cross sections, eq. (lle), are given in table 1 for the three transitions we have used. For an optical pumping transition between the 3Pz (J = 2) state and an upper state with J = 2, the fraction fz = 1 (fig. 3) and this single measurement directly gives the state resolved total cross section 2Qi. This is not possible for the 3Po (J = 0) state since, due to the selection rules, each allowed upper level has .I = 1, which will (partially) decay to the 3P2 (J = 2) state. 3.4. Correction for background density The measured ion signals S$ have to be corrected for contributions of the background gas before evaluating the cross sections according to eqs. (lla) and (11~). This correction can be performed by a measurement of ,!$ with secondary beam switched off. However, in that case there will only be collisions with normal background gas, while with secondary beam on, there will also be collisions with the extra background gas due to the gas load of the secondary beam on the vacuum chamber. A better procedure is to measure the ion signal while the secondary beam is switched off, but with an auxiliary gas flow through a side flange to the vacuum chamber which is equal to the gas load of the secondary beam. As a check we have performed some measurements for the Ne*-Ar system without secondary beam, both with and without an auxiliary gas flow. The ratio of the ion signals, due to the normal background gas and due to the normal and extra back~ound gas, respectively, shows no velocity dependence and is within 20% equal to the ratio of the pressures in the vacuum chamber, measured with an ionisation gauge in the vicinity of the scattering center. The total cross section now can be determined by a correction of the experimental

261

data via a me~~ement without gas load multiplied with the ratio of the pressures in the vacuum chamber with secondary beam on and off. The contribution of this correction to the accuracy of the absolute value of the total cross section is only 2% when the total correction is 10% of the signal. The contribution to the accuracy of the velocity dependence of the cross section is even smaller. 3.5. Experimental

conditions

The time-of-flight spectrum of UV photons gives the modulation of the beam of metastable atoms by the laser beam and is measured with the laser beam intersecting the atomic beam at the scattering center, secondary beam off and the ion repeller on (YIXI, rep= -400 V). The four ion time-of-flight spectra (laser on and off, secondary beam on and off) are measured with the ion repeller off (vion,rep= 400 V) and with the intersection of laser beam and secondary beam 14 mm upstream of the scattering center (fig. 2), in order to avoid that UV photons produced in the optical pumping process are registered by the spiraltron. For each system all measurements have been performed on a single day in the mixed sequence: the X = 594 run transition thermal and superthermal, followed by the A = 616 nm transition superthermal and thermal.

Fig. 4. The UV photon signal relative to the m~ulation of the total beam of metastable atoms as a function of the position of the laser beam along the atomic beam axis zc. Negative values of I( correspond to a position between scattering center and beam source. The solid line is an approximation for the solid angle acceptance of the spiraltron. The dashed line marks the position from where half the open area of the spiraltron can be seen tbrougb the aperture in the grohnded shield.

262

M.J. Verheijen, H.C. W. Begerinck / State selected total Penning ionisation cross sections

Fig. 4 gives the UV signal as measured with the spiraltron (relative to the modulation of the total beam of metastable atoms as measured with the detector for metastable atoms) as a function of the position of the laser beam along the atomic beam axis. Moving up-stream of the scattering center (negative z direction) the UV signal first increases slightly due to the decreasing distance between the production center of UV photons and the spiraltron. The dashed line marks the position of the laser beam where half the open area of the spiraltron can be seen through the aperture (with shielding grid) in the grounded shield (fig. 2). This position is in good agreement with the data points. At a position 14 mm upstream of the scattering center the total count rate of UV photons is significantly less than 1% of the ion count rate with both secondary beam and laser beam on. We cannot go further upstream because of mechanical reasons. 3.6. Measuring routine Each measurement consists of five time-of-flight spectra. Firstly two ion time-of-flight spectra are measured with secondary beam off, the first one with laser on and the second one with laser off. Next the laser beam is moved to the scattering center with the computer controlled flat mirror (fig. 1) and the UV time-of-flight spectrum is measured with laser on and secondary beam off. Finally two ion time-of-flight spectra are measured with the laser beam back to its original position and secondary beam on, the first one with laser on and the second one with laser off. During one measurement this sequence is repeated ten or more times, each sequence taking typically 15 min. During the registration of the ion flight-time spectra the background density in the vacuum chamber is measured with a vacuum gauge in the vicinity of the scattering center once every two seconds. Measurements in both energy ranges are all performed on a single day, with the measurements in the thermal energy range sandwiched between two measurements in the superthermal energy range. Drift of the apparatus can thus be detected directly. In this way a reliable scaling of the data from both sources is obtained. The only exception

is the elapsed ranges. scaling

Ne*-Kr measurement, where two days between the measurements in both energy The procedure used to obtain a reliable in this case is described in section 4.2.

4. Total ionisation cross sections 4.1. Velocity dependence

Fig. 5 gives the experimental total ionisation cross se&ion ‘Q’ for three modulation transitions (X = 588.2, 594.5, and 616.4 nm) for the Ne*-Ar system. Fig. 6 gives the total ionisation cross sections *Q’ and ‘Q’ for the 3P2 and 3Po state, respectively, derived from the experimental cross sections of fig. 5 according to eq. (11). The cross section *Qi is equal to 594Qi because f$j4= 1 (table 1). When we combine the 594Qi cross section with the 588Qi and 616Qi cross sections, respectively, we obtain two independent values for the ‘Q’ cross section. There is a perfect agreement between the two ‘Q’ cross sections measured with the 616 nm modulation transition (which attenuates the 3Po population and enhances the 3P2 population) and with the 588 nm modulation transition (which enhances the 3Po population and attenuates the 3P2 population). This proves that there are no

EoCeV) Fig. 5. The experimental total ionisation cross section ‘Q’ for three modulation transitions (wavelength. h) for the Ne*-Ar system as a function of the collision energy in the superthermal energy range, obtained with the hollow cathode arc beam

263

M.J. Verhegert, fi. C. W. Be~erin~k / State selected total Penning ionis~i~n cross sections

E, teV1

E,(eV)

I.0

10

Fig. 6. The state selected total ionisation cross sections 2Qi and ‘Q’ for the Net-Ar system in the supertbermal energy range. The cross section for the 3Pz state (‘Q’) is equal to the expe~ment~ cross section ‘%Qi of fig. 5. The full symbols for ‘Q’ are derived from the 6r6Qi and ‘%Qi experimental cross sections and the open symbols from the ‘“8Qi and the 594Qi experimental cross sections of fig. 5.

systematic errors introduced by the detection of UV photons and the optical pumping for the different transitions. We have performed the same check for the Ne*-Kr system which shows also a perfect agreement between the two ‘Q’ cross sections. Figs. 7-10 give the experimental results for the state selected total ionisation cross section for the four systems investigated. For all systems the 3P,, -+ 2p, (Paschen, h = 616 nm) and the 3Pz -+ 2p, (Paschen, h = 594 nm) transitions have been used. All systems show larger cross sections for the 3P0 state than for the 3Pz state. The absolute scaling is discussed in section 5.2. To represent these measurements in a way that they can be .used in a multiproperty analysis with future results of state selected experiments with different techniques, e.g. Penning ionisation electron spectroscopy, differential cross section measurements, we describe the cross sections for each system with four polynomials. The two cross sections in the thermal energy range are described by a second-order polynomial and the two cross sections in the superthermal energy range by a polynomial of order four. The coefficients are determined by a least-squares anal-

Fig. 7. The state selected total ionisation cross sections for the system Ne*-Ar as a function of the collision energy E,. The m~rern~ts have been scaled so that the 3Pz results agree with the predictions of the optical potential of Gregor and Siska at Es = 0.1 eV (table 3). Tire solid lines correspond to the curve fits of the modified potentials to these results. The residues after these curve fits are given separately. The dashed tine corresponds to the optical potential as proposed by Gregor and Siska. Open symbols refer to ‘Q’ C3Po system) and closed symbols to ‘Qi ( 3P2 system).

ysis with the model functions 2Qi(&)

=2~~~~(~~~)~(~o),

oQi&,)

=2Q~~,(E,,)[oPi(E,,)/2Qi(~~~~)~ XOf(Eo),

02a>

(W

264

M.J.

VerheGen, ff. C. W! Be~erinck / State selected total Penning ionisation cross sections

% ._

d

E,(eV)

Ne*?P 2 I-Kr

Fig. 9. The total ionisation cross sections for the system Ne*-Xe. See also caption of fig. 7. Only the residue of the 3Pz system is given. Fig. 8. The total ionisation cross sections for the system Ne*-Kr. See also caption of fig. 7. Only the residue of the 3Pz system is given.

where E,_ is the upper bound of the energy range used for the least-squares analysis. In this representation we separate the absolute scaling, as given by the total ionisation cross section ‘Qref of the 3Pz from the velocity depenstate at energy E. = Erref, dence “f and ‘f and the ratio oQ’/2Qi at the same reference energy. The absolute scaling depends directly on detector efficiencies for ions and UV photons, which cannot be determined in our apparatus, resulting in a limited accuracy. In contrast to the absolute scaling the functions “f, ‘f and the ratio ‘Q’/‘Q’ have been determined with a very high accuracy.

The coefficients a, are given in table 2, together with the energy range used in the least-squares analysis. Within this energy range the numerical representation of eq. (12d) gives an excellent de-

0-

7

6r

!

0.01

1

,

I1~1ll11 0.1

I

,

,

,

E,,leV)

I ,

I,

1.0

’

,

#

,

I

,

I

,

,

10

Fig. 10. The total ionisation cross sections for the system Ne*-N,.

M.J.

Verheijen, H. C. W. Be~eri~ck

/ State selected total Penning ~onis~t~~n cross sections

26.5

Table 2 The coefficients a, (eV-“) of the polynomial f(E) of eq. (12) with f( E,,r)=l, describing the velocity dependence of the total ionisation cross sections “Q i and *Q i for *‘Ne together with the ratio *Q( E,r)/‘Q( &) which describes the relative scaling of the ‘f(E) and “j(E) curves. The power of ten is given in parentheses behind the number System

oQi(E,,) ‘Q’fEr,,)

Emin Ema WI (W

State

0.06

0.1522

0.64

5.838

3Pa ‘P2 3Pc 3PZ

0.05

0.1724

0.77

7.273

0.05

0.1662

0.82

7.830

0.05

0.1082

0.41

3.667

no

04

&v-t,

&2)

&--‘)

1.1082 I.0458 8.6580( - 1) 6.1414( - 1)

1.3472 2.9111(-l) -15422(-l) - 5.2878( - 2)

- 1.3900 (1) - 1.1227 (1) - 5.1461( - 2) -8.1473(-3)

- 1.2992( - 2) - 3.197q - 3)

- 8.7013( - 4) 1.0271( - 5)

‘Pa ‘PZ ‘Pa 3PZ

1.1752 1.0847 1.0454 7.2226( - 1)

2.1965 1.1082 3.0487( - 2) 2.8891( - 2)

- 3.0845 - 8.4750( - 1) 6.3494( - 2) 4.6592( - 2)

1.224q - 2) 9.6148( - 3)

9.5728( - 4) 8.8379( - 4)

3Pa 3P2 3Pa 3PZ

1.1910 1.0313 1.0582 7.7777( - 1)

4.0937 - 6.4363( - 1) -1.4%6(-l) 4.5378( - 2)

1.8245 - 1.6873 - 3.0165( 3.8736(

(1) (1) - 2) - 2)

- 9.2673( - 3) 6.0068( - 3)

-7.1415(-4) 4.3895( - 4)

3P0 3P* 3P0 ‘PZ

1.0518 1.0376 7.0493( -1) 8.5698( - 1)

6.7111 4.8779 - 2.7211( - 1) -1.8933(-l)

4.8066 3.5929 - 2.4625( - 1.6695(

(1) (1) - 1) - 1)

- 1.3698( - 1) - 1.0699( - 1)

-2.0.519(

(eV4)

at E_-. = 0.1 eV s..

Ne*-Ar

Ne*-Kr

Ne*-Xe

Ne*-N,

1.325

1.468

1.240

1.484

Scription of the energy dependence, but it should not be used for extrapolation outside this range. As a reference energy we have chosen E, = 0.10 eV, for an easy comparison with the large amount of data in the thermal energy range. The ratio ‘Q’( Er~,)/2Q’(Er~f) is also given in table 2.

-

-2)

- 1.7344( - 2)

4.2. Absolute values Absolute values of the total ionisation cross section have been derived from our me~urements [eq (ll)] by inserting the value 77J7li = 1.0 X 10S3 for the detection efficiencies and using the values

Table 3 Experimental results for the absolute values of the total ionisation cross section for the Ne*( ‘Ps) state at Erel = 0.1 eV, in comparison with values derived by Gregor and Siska [lo] from flowing after glow measurements of Brom et al. 126). The errors in the experimental result are due to the calibration error in the density-length product of the supersonic secondary beam. Systematic errors in the detection efficiencies for ions and UV photons have not been taken into account System

Experimental result 2

Q

i

(A;’ Ne*(3P2)-Ar Ne*(3P2)-Kr Ne*( 3 P,)-Xe Ne*(3P2)+N2

34f3 22+3 17&S 32+3

Scaling values for least-squares analysis *Q’(Ne*-gas)

*Q’(Ne*-Ar) 1.00 0.66+0.11 0.51 kO.16 0.94f0.12

2

i

Qrer

(A2) 148”’ 16:7 ” 17.5 a’ 18 s’

*Q’(Ne*-gas) *Q’(Ne*-Ar) 1.00 1.13+0.17 E, 1 .18fO .18 ‘) 1.22+0.18 ‘)

a> Best experimental results according to Gregor and Siska [lo] at E, = 43 meV. Calculated values at E, =lOO meV only differ siightly from these values. ‘) Brom et al. [26]. ‘) Error due to 15% error in rate constants of Brom et al. (261. Systematic errors in the correction factor 1.6, as calculated by Gregor and Siska [lo], have not been taken into account.

266

M.J. Verheiien, H. C. W. Beijerinck / State selected total Penning ionisation cross sections

for the density-length product (n,) of the secondary beam as given in section 2. Table 3 gives the results for ‘Q:.,(&,,) at E,,, = 0.1 eV, in comparison with the values calculated with the optical potentials of Gregor and Siska [lo]. These optical potentials were constrained to fit the quenching rate constants of Ne*( 3P2) + Ar, Kr, and Xe at 300 K measured by Brom et al. [26] in a flowing afterglow experiment. Gregor and Siska have modified the quenching rate constants of Brom et al. with a factor of 1.6 to correct for parabolic flow instead of plug flow as was assumed by Brom et al. These cross sections for Ne*-Ar derived from quenching rate constants are accepted as the most reliable ones. Our experimental total cross sections are in reasonable agreement with these reference values, especially when we consider that other beam measurements of total ionisation cross sections show mutual differences of a factor two to three [27]. We observed a decreasing cross section going from Ar to Xe while the quenching rate constants of Brom et al. show the opposite. However, the error of 15% in their rate constants is larger than the differences between the three rate constants. The accuracy of our experimental results in table 3 is determined by the density-length product of the secondary beam which we know within 10% for the calibrated Ar, Kr and N, secondary beams [20]. For Xe the error may be larger (up to 25%) because we have estimated the attenuation parameters of the secondary beam [20]. Other sources of systematic errors may be the overall detection efficiencies for ions and UV photons which we have not calibrated. We have used the quantum efficiency for Ar+ detection as measured by Potter and Mauersberger [23] for all our systems. The comparison of the detection system for UV photons with the metastable atom detection system and the detection system for photons in the visible part of the spectrum [24,28] shows that the theoretically expected overall detection efficiency for UV photons is reliable within lo%,, but these measurements do not give a real calibration. For the analysis of the energy dependence of our data we did not use our own absolute values, ybut we have scaled our measurements so that the

3P2 results agree with the optical potential of Gregor and Siska at Erer = 0.1 eV (table 3). These scaled experimental results are shown in figs. 7-9. For all systems the same normalisation constant was used for the thermal and superthermal 3P0 and 3P2 data. The only exception is the Ne*-Kr system, where the superthermal cross sections were measured two days later than the thermal data. In order to obtain reasonable potential parameters we have multiplied the superthermal Ne*-Kr cross sections with an extra factor 0.85. This correction of 15% corresponds to the increase of the experimental Ne*-Ar cross sections that we measured as a reference before and after these Ne*-Kr measurements. This is probably due to a change in the absolute detection efficiencies. 4.3. Ratios of the state selected total ionisation cross sections Fig. 11 gives the ratio 2Qi/oQi of the total ionisation cross sections for the four systems. The reference values of Hotop et al. [9] are in good agreement with our results in the thermal energy range. For the Ne*-rare gas systems we see a decreasing ratio with increasing collision energy. This effect is most pronounced in the thermal energy range and saturates to = 0.5 in the superthermal energy range. For the Ne*-N, system we see an almost constant ratio of 0.70 in the thermal energy range and a slow increase in the superthermal energy range. An interpretation of these results in terms of the interaction potential is difficult because we have to deal with two independent parts, i.e. the real potential curve (particle trajectory) and the imaginary potential curve (absorption). Firstly we discuss the observed behaviour with the assumption that the shape (and not the absolute value) of the imaginary part of the potential is identical for the 3Po and 3P2 states. The energy dependence of the ratio for the Ne*-rare gas systems is then fully due to the difference V,( 3Po) - V,( 3P2) in the repulsive branch of the real part of the potentials. The measurements indicate that the onset of this different behaviour of the repulsive branches is in the thermal energy range or even at lower energies. This is in fair agreement

M. J. Verheoen, If. C. W. Beijerinck / State selected total Penning ionisaiion cross sections

267

Ne*-Ar

Ne’- Xe i

i

l* l*

Y$----

,

. .

,II,

. . .

-

~ 10

E. leVl

E. (eV)

Fig. 11. The ratios ‘Q’/‘Q’ of the state selected cross section for the four systems. The open square gives the result of Hotop et al. [9] measured with a thermal beam with an effective temperature of 370 K (0.05 ev). The solid lines have been calculated with the curve fit of eq. (12) to the experimental data (coefficients of table 2) as input.

with the potential curves for the Ne*-Ar and Ne*-Xe system as calculated by Morgner [29] and Gregor and Siska [lo], respectively. Secondly we discuss the observed behaviour under the assumption of identical real parts of the optical potential, as proposed by Morgner [29]. In this approach the different behaviour of the two metastable states is fully explained by symmetry effects, which result in different absolute values of the imaginary part of the 3P0 and 3P2 optical potentials. Within this frame work Morgner [30] can fully explain the measured value ‘Q’( ~~)/‘Qi( E,) = 0.80 at E. = 50meV of Hotop et al. [9]. One should now expect that the ratio has

a limit of 0.80 in the low collision energy range. However, our results in the thermal range indicate that the limit is reached for E. -C 50 meV and the asymptotic value presumably is higher than 0.80. This means that the repulsive parts of the potentials for the 3P0 and 3P2 systems are different for collision energies below 50 meV and the ratio of 0.80 at 50 meV is not only due to different absolute values of the imaginary part of the potentials. Measurements at lower collision energies will be necessary to support this conclusion. The energy dependence of the ratio for the Ne*-N, system is much less than for the Ne*-rare gas systems, with even an increasing ratio at higher

268

M.J. Verheijen, H. C. W. Beijerinck / State selected total Penning ionisation cross sections

energies. As yet, we have no explanation for this different behaviour. An extensive study of ionisation of small molecules (N2, 9, CH,, COz, CO, NO, N,O, H,) is in progress in our group to obtain insight in these molecular systems ]31].

5. Optical potential analysis of experimental cross sections

The switch-over function f(r) by f(r)=

v,(r)

= [I

-ml

Y+(r)-t.fW~*G-)t

03)

with V,(r) an atom-atom (Ne*-rare gas) potential represented by a Morse-Morse-spline-Van der Waals (MMSV) function P*(r) = &*Z(z - 2), z = exp[ -&(r/rz o
(14a) - l)],

(w

my

z = ew[ -&(r/G

- I)],

r; < r < t-1;

(144

V,( r ) = cubic spline polynomial, r, < r < r, ; V,(r)

= - C,/r6

(144 - C8/r8 - C,,/r’O,

r2 < r,

We)

and V+(r) a core ion-atom (Ne+-rare tial, represented by a Morse-spline-van function V+(r)

= E+z(~ - 2),

z=exp[-#3+(r/r,+

@a>

-l)],

O
gas) potender Waals

(15b)

( r ) = cubic spline polynomial, r, < r < r2 ;

V+(r)

054

= - C4/r4,

r, < r.

(154

{l+exp[(r,-r)/d]}-I.

(16)

For the imaginary part of the potential we use an exponentially increasing function which saturates abruptly to a constant value for internuclear distances smaller than rim: V,,(r)

We describe our total Penning ionisation cross sections with an ion-atom Morse-Morse-splinevan der Waals (IA MMSV) potential for the real part of the optical potential. The IA MMSV potential is given by

in eq. (13) is given

= EImexp[ -Ph(r/r,

r > rIm; Gtl(~)

- I)] y (174

= GnkInJ~

O
(17b)

Although the two Ne*-N, systems have more than one Q-potential curve and the Ne*( 3P2)-rare gas systems have three Q-potential curves, we use a single potential curve for each system. In a least-squares analysis we can only determine a selected number of parameters to which our experiment is sensitive. For the remaining parameters we have used the values of Gregor and Siska [lo]. A general guide in choosing suitable parameters to vary is that we are not allowed to modify the potential in the region below 70 meV because this part is well determined by Gregor and Siska. For the real potential we have treated the V, parameters, /3’ and r,, and the switch position r, as free parameters. We have always adjusted the V, parameters E* and & to make our new potential equal to the potential of Gregor and Siska at two internuclear distances, r = r,,, and r = 0.64 rm. In doing so, our new potential is nearly equal to the potential proposed by Gregor and Siska in the region up to 70 meV. Remaining small deviations can be neglected, especially with regard to their influence on the total ionisation cross section. For the imaginairy part of the potential it is allowed to vary all three parameters. When we treat all these six parameters (erm, &,,,, rim, /?+, r,, and r,‘) as free, the final results become rather unrealistic. Therefore we have fixed rim, r,, and + at reasonable values and determined only &rm, I;;i,,,, and /?’ by a least-squares analysis. The partial wave expansion with JWKB complex phase shifts is used to evaluate total ionisation cross sections [32,33]. The real and the imaginary part of

M.J. Verheijen, H.C. W. BeQerinck / State selected total Penning ionisation cross sections

the phase shift are treated uncoupled. For the magnitude of the ionisation cross sections as observed for the systems studied in this paper, this approach is fully justified [33]. We have used the criterion Y,,(r)< 0.1 [&J u&,(r)] suggested by Micha [32], with .L+~~(T)the radial velocity, to determine the range Sr of r-values near the classical turning point where this uncoupled treatment only has a limited validity, resulting in a relative width &r/r, of the order of 10m3. The relative contribution of this region to the imaginary phase shift Se is typically limited by &/&< 0.1. Assuming an error of 10% in the calculation of St, we conclude that the overall accuracy of & and thus Q’ is of the order of 1% [24]. To save calculation time we only use five and seven characteristic data points in the thermal and superthermal energy range, respectively, during the first trial and error curve fits. These points are chosen at log-equidistant collision energies and are given by the polynomial fits. After the least-squares analysis with these characteristic data points, all with the same weighting factors, a final &i-square value is calculated for all experimental data points. Finally a least-squares analysis is performed with all experimental data points. This last step resulted in only a negligible improvement of x’/(N - M) = 1.14 to 1.12, with N the number of data points (typically seventy) and M the number of free parameters in the least-squares curve fit (typically six). The results of all systems refer to the final least-squares analysis with all experimental data points. The dashed lines in figs. 7-9 are calculated with the optical potentials proposed by Gregor and Siska for mixed systems. They have performed a multi-property analysis of their own differential scattering data at two energies for each Ne*-rare gas system, of quenching rate-constant measurements [26], and of the energy dependence of the total ionisation cross section measurements of Tang et al. [I] and of Neynaber et al. 14-61. All the beam data (cross sections) were measured without state selection. Compared to this reference our experimental results for the 3P2 systems show a more pronounced maximum located at a larger collision energy (appro~ately a factor 8). The same feature, however less pronounced, is seen when we

269

compare the experimental ionisation cross sections that Gregor and Siska have used in their fits with the predictions of their potentials (figs. 7-9 in ref. [lo]). This is caused by the fact that they only have used the data points between 8 and 80 meV to determine their potentials. This shape of the ionisation cross section indicates that there will be a pronounced “kink” in the repulsive branch of the real potentials between 0.1 and 1.0 eV. Such a pronounced kink, which has also been observed for the He*(%) + Ar system [34,35], can be obtained by a modification of the V, potential and the switch-over function. The decrease of the ionisation cross section at high ( > 1 eV) collision energies is due to the decreasing collision times. The slope in this region is governed by the slope of the repulsive branch of the real potential. We observed a rather steep slope in the cross section. It was not sufficient to use a V, potential with a steeper repulsive branch but we also had to introduce a saturation of the imaginary part of the potential for small internuclear distances (eq. (18), ref. [36]).

6. Discussion The solid lines in figs. 7-9 correspond to the best-fit total ionisation cross sections. In the same figure the residues after the least-squares analysis are shown for all 3P2 systems and for the Ne*( 3Po)-Ar system. The corresponding real parts of the optical potentials are shown in fig. 12. The optical potential parameters obtained are listed in tables 4 and 5. 6.1. The cross sections for the Ne*(3P2)-rare systems

gas

Our Ne*(‘P,) measurements are well described by the IA MMSV potentials as proposed by Gregor and Siska for the Ne*-rare gas systems, after modification with a pronounced kink in the repulsive branch and the introduction of a saturation of the imaginary part at small internuclear distances. This kink lies well above the region that is probed in the scattering experiments of Gregor and Siska. The residues of the Ne*(3P,)-Ar and

M.J. Verheijen, H. C. W. Beijerinck / State selected total Penning ionisation cross sections

270

I

Ne*-A r

103-

-

s

zEIOO-

4

20 Kl608200

I

6

Fig. 12. The real parts of the optical potentials for the systems (a) Ne*-Ar, (b) Kr, and (c) Xe. The solid lines give the Ney3P2) systems and the dotted lines the Ne*(‘P,) systems. The dashed lines are the potentials as proposed by Gregor and Siska [lo]. (d) Comparison of the modified Ne*(3P,) potentials of the three rare gas (Ar, Kr and Xe) systems.

M.J. Verheijen, H. C. W. Beijerinck / State selected total Penning ionisation cross sections

271

Table 4 The optical potential parameters of Gregor and Siska [lo], that we did not modify Parameter

Ne*-Ar

Ne*-Kr

Ne*-Xe

Ne*-N,

12.50 5.0

5.45 5.0

unit meV A

IA MMSV IW. (13)l

e %

5.45 5.0

8.33 5.0

atom-atom [es. V4)l

a2

5.333 5.229 1.436 0.955 0.831 0.8 1.6

5.389 5.230 1.407 0.934 0.806 0.8 1.6

5.220 5.241 1.491 0.978 0.846 0.8 1.6

5.333 5.229 1.436 0.955 0.831 0.8 1.6

e+

1.284 0.8 2.0 187

1.272 0.8 2.0 239

1.381 0.8 2.0 288

1.284 0.8 2.0 187

d

0.69

0.69

0.69

0.69

G

War: c*/sr: cta/erZ - V+(Ws* r2ifG

ion-atom [es. (15)I

C4/e+(r,1Y -V+trt+)/e+ r2+/4

switch-over [eq. (WI

A

meV A

Table 5 The optical potential parameters that we have modified. The values of Gregor and Siska are given for comparison. The parameters marked + were obtained by fitting (@+, et,,,, &,,) and by modification of the parameters of Gregor and Siska (re, rz, ru,,). The errors of the three parameters obtained by curve-fitting are given in parentheses. In some cases these errors are rather large due to correlation of the parameters, e.g. for the case of &, and et,,,. The error in 8” is large due to the low sensitivity of Qi, for this parameter for the ease of a steep repulsive branch of the real part of the potential. The parameters marked + were adjusted in order to leave the Gregor and Siska potential unmodified at r = 0.64 r,,, and r = r,,,, resulting in an almost unmodified potential for V,(r) < 70 meV Contribution to IA MMSV potential [es. (1311

Ne*-Ar parameter

4- e*

atom-atom 1%. (14)l

+-Bl

ion-atom [eq. (IS)]

--i r,’ -8’

switch-over [eq. (16)l

-,

imaginary part [es. (17)l

-+ EPA

‘0

-a$ -+ rtm

Ne*-Kr ‘PO

‘Pz

ref. ‘)

3P0

Ne*-Xe ‘Pr

ref.@

‘Pa

Unit 3P2

ref. ‘)

5.62 3.75

5.62 3.75

4.17 5.98

8.58 3.55

8.57 3.58

6.55 5.85

12.94 3.46

12.93 3.50

9.89 5.75

meV

2.04 34.4 (4.1)

2.04 (E)

2.65 4.83

1.54 25.4

2.04 16.0 (8.2)

2.77 4.80

1.54 25.4

2.04 17.26 (9.6)

2.92 4.82

A

1.14

1.14

3.6

0.86

1.14

3.60

0.86

1.14

3.60

A

4.54 (0.9) 16.32 (0.7) 2.6

20.87 (0.3) 9.24 (0.07) 2.1

30.27

12.54 (5.7) 14.6 (1.5) 2.6

17.51 (1.0) 10.98 (0.2) 2.6

31.06

12.90 (13 ) 14.6 (3.5) 2.6

19.16 (0.8) 11.3 (0.2) 2.6

34.80

7.35 -

8.21 -

PeV

8.24 -

a) Ref. [lo]. b) Gregor and Siska [lo] use Vt,,, = ;T(r) = 0.5 (kcal mol-‘) exp[ - a(r - p)], resulting in E,,,, = 0.5 (kcal mol-‘)exp(ap)exp( and fit,,,= er,,, with (Yand p given in table 2 of ref. [lo].

A - &)

272

M.J. Verheijen, H. C. W. Beijerinck / State selected iota1 Penning ionisation cross sections

Ne*(‘P,)-Xe data are almost free of structure. The residue of the Ne*(3P2)-Kr data, however, shows a clear structure, but this is most likely due to a remaining error in our renormalisation of the superthermal data (see section 4.2). The characteristic lengths p,-,’ of the imaginary parts of our optical potentials for the rare gas systems are 25-40% smaller than those of the Gregor and Siska potentials. However, the relative scaling of these values, i.e. almost equal characteristic lengths for Kr and Xe and a larger one for Ar, is in agreement with the results of Gregor and Siska. Due to the scaling of our cross sections to the same reference values as used by Gregor and Siska these smaller values for PC,’ result in smaller values for &im,because the value of the imaginary part Vi, should be approximately the same in the region 2.8 Q r(A) < 4.0 on internuclear distances probed at E = 0.1 eV. We can thus be fairly confident that our optical potential gives a fair description of the differential scattering data of Gregor and Siska. 6.2. The cross sections for the Ne*(%)-rare systems

gas

The description of the Ne*(3Po) data by only a modification of the repulsive branch above 70 meV of the real part of the optical potential of Gregor and Siska and of the imaginary part clearly fails up till now. This can be seen in the analysis of the Ne*(3Po) data in figs. 7-9. A better fit needs an unrealistic small radius of the repulsive branch. This failure is most likely due to a different shape of the real part of the optical potential for I$( r) < 70 meV. These modifications are allowed for the Ne*( 3P0) systems, because the optical potentials given by Gregor and Siska are obtained with mixed beams of 3P, and 3P2 metastable atoms, with statistical weight of = 1 : 5. A multi-property analysis of state selected large angle differential cross section measurements as performed at Freiburg [ll], of quenching rate constants [26], and of our accurate total ionisation cross section measurements will be necessary to obtain the optical potentials for the ‘PO systems. It is likely that the real parts of the optical potentials for the 3P0 systems differ from the 3P2 systems at lower en-

ergies than generally expected. This is supported by the fact that the long-range C, coefficients, as calculated by Gregor and Siska [lo] already show differences up to 10%.

7. Concluding remarks Careful1 inspection of the residue of Ne*( 3P,,)Ar ionisation cross sections (figs. 6 and 7) shows a slight oscillatory structure in the superthermal energy range, which is not seen in the 3P2 ionisation cross sections. These oscillations are visible in all our measurements on the Ne*-Ar and Ne*-Kr systems. They are also observed in the Ne*( 3Po)-Ar, Kr ionisation cross sections evaluated from the 588Qi and 594Qi experimental data, where in both experiments the 3P2 state is optically pumped with the laser beam, as shown in fig. 6. The extrema are in first approximation equidistant in the inverse relative velocity. As yet we have no explanation for this effect. Future experiments with a better statistical accuracy will have to decide if this effect is real or an artifact of the measurements in this paper. Only the Ne*(3P,,)-rare gas systems have a single potential, the other systems that we have investigated consist of three potentials. The effect of these multiple potential curves has to be considered carefully in a multiproperty analysis. Penning ionisation will occur most likely on the potential with the most inward situated repulsive branch, while large-angle differential scattering will occur most likely on the potential with the most outward repulsive branch. The effect of these features will even be enhanced due to the symmetry effects in Penning ionisation [30]. These effects give the 52= 0 potential the largest imaginary part and this potential happens to have the most inward repulsive branch [10,29]. These symmetry effects have to be verified by future experiments with a beam of polarised 3Pz metastable atoms. A multi-property analysis for the Ne*( 3P0, 3P2) + rare gas systems is in progress in Freiburg, using state selected differential elastic scattering cross sections [ll] and the total ionisation cross section as input. Together with state selected measurements of the total cross section for elastic scatter-

M.J. Verhegen, H.C. W. Beijerinck / State selected total Penning ionisation cross sections

ing [37] it will be finally possible to determine accurate potentials for these systems.

Referemxs

VI S.Y. Tang, A.B. Marcus and E.E. Muschlitz Jr., J. Chem. Phys. 56 (1972) 566.

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