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Penning electron spectra from ionization of hydrogen atoms by He(21S) and He(23S) metastables
Volume 10, number 5
1 September 1971
CHEMICALPHYSICSLETTJZRS
PENNING ELECTRON SPECTRA FROM IONIZATION OF HYDROGEN ATOMS BY He(2*S) AND He(23S) META§TABLES H. HGTGP, E. ILLENBERGER,
H. MGRGNER and A. NiEHAUS
Phyn~kalisciresInsritut der Universitiit Phiburg Received
2 July
Germany
1971
Separate Penning election spectra were measured resulting from the ionbation of H ator& by He(Z’S) and Hc(~~S) metastables in thermal collisions. From these results potential parameters of the dhtomics .&(2’S)H(‘S) (‘C) and He(23S)-H(‘S) (7z) as well as the cross-section ratio uQinglet)/o(tripIet) are derived.
Theoretical calculations on the ionization of neutral ground state atoms in collisions with metastable excited particles have been reported only very recently and only for the simplest possible systems, He(2%, 23S)-H(ls) [l-4]. To obtain theoretical values for experimentally accessible quantities such as cross sections or electron energy distributions, the interaction potentials V*(R) and V/+(R) involved in the collision, as well as the transition probability W(R) for transitions from the incoming potential V*(R) to the outgoing potential v+(R) must be calculated, the calculations being complicated by the fact that V*(R) is a resonance state, of width r(R) = A W(R), degenerate with the continuum V+(R) + e-. The theoretical results [l-4] , concerning the potential curves V*(R) as well as the cross sections for ionization, differ strongly from one’another. The only experimental information on the He*/H systern available in the literature is a value of the dkstruction cross section for the collision pair He(23S )--H. Shaw et al: [ 51, using a flowing afterglow apparatus, obtained a value of (22 f 6) A2 at 300°K. The theoretical results of Fujii et al; [I] (ut = 36 A at 27 meV relative collision energy) and of Bell [3 J (ot = 27 A2 5 20% at 300’K) agree fairly well with the experimental value. However, this agreement has to be considered as fortuitious in view of the fact that, as we shall show in this paper, the potentials V,*(R) used in these calculations do not agree with experiment. In the case of the He(2%)-H system Fujii et al. [ 11,
performing a simple valence bond calculation, fiid a purely repulsive potential (real part of a lo& complex potential) and accordingly arrive at a small cross section (us = 0.35 A2 at 27 meV, us/at = 0.97 X 10A2). On the other hand, MiJ.ler and Schaefer [2] , cuying out a large scale CI calculation in which, however, the continuum V+ f e- was neglected, find an attractive potential of a well depth of 390 meV, resulting in a close collision cross section roughly equal to that for He(23S) + H. Adopting their simple model that each close collision leads to Penning ionization - if this transition is allowed by spin considerations - the cross section ratio us/at =Z3 at Erei = 27 meV is obtained from the extrapolated cross section curyes reported by Miller and Schaefer 121. In view of these discrepancies, ftirfher experimental information is desirable. ObviousIy, a measurement of the ratio usiut would be of particular interest with respect to the He(2&)--H system. Moreover, experimental determination of the potential cume V*(R) could help to clarify the situation; such information can be drawn, in principle, from eIastic scattering, but in the present case, this approach is complicated as a consequence of the existence of two potentials in the He(23S )--H(2S) case, 2Z and 4ZZ,and also due to the fact that the inelastic cross section is not negligible in comparison with the elastic one. A direct determination of potential parameters of l?(R) (?Z) can be obtained from the measured Perming electron energy distribution as has been &own in a recent paper from this Iaboratory [6] . 493
Volume 10, number 5
1 September 1971.
CHEMICAL PHYSICS LETTERS
k this letter we report such Penning electron distributions arising from thermal collisions (mean coljisi6n energy ~60 m;V) of ye(2lS) and He(23S) with H atoms. From these distributions - separateIy determined for collisions with He(21S) and He(23S) - we
derive (1) the cross section
ratio uS/ut, and
(2) the depth of the potentials V*(2ZZ),E: and E?, as well as the position of the classical tumg points at these potentials for central collisions,R% and RL,. The experimental method applied has been described elsewhere [6-81. Briefly: a thermal ‘beam of He metastables - containing approximately ea;uzl amounts of
,494
‘.,
.’
7
65
0
He(&) and He(Z3S) - is produced by a hot cathode He discharge. An almost pure He(2%) beam [less than 1% He(2lS)] is formedh< quenching the He(2lS) atoms by irradiation by light from another He discharge [g-1011 The H atoms, produced from Hz in an rf discharge, effiise from a g!ass tube into the scattering chamber which is crossed by the He* beam. Penning electrons arising from the collision of He* with H are andysed in a plane retarding potential electron spectrometer. The integra! electron stopping curve is stored in a multichannel anaIyser and the electron energy distribution is obtained by numerical differentiation with respect to energy. The energy resolution - full width at half.intensiQ, of the differentiated curve for monochromatic electrons - was about 60 mV in these measurements. Energy calibration was achieved by measuring Penning electrons from a mixture of H atoms and Ar atoms [7-g]. The determination of the distribution for the He(23S)/H system is complicated by the fact that the low energy part of the very broad distribution overlape with the distribution from ionization of H2, which is also present in the scattering center, and that the high energy part overlaps with electrons from ionization df H by He(21.5) atoms which have not been quenched. The pure He(23S)/H distribution is obtained by subtracting these contributidns, which are determined in separate measurements. A minor uncertainty is introduced due to the f&t that the H2 contribution is assumed to arise from unexcited H2 molecules; yhile, with the rf power on, some ,of the H2 may be vibrationally excited. No complication arises in the case of th$ He(2%)/H &z&urn because +Slesmall contribution from the He(23S)/H spectrum in this energy.range is e&ly car-
7.5
Ed(cv)
E&l
lip.
1
6
7
1. Measured enerB
distributions.
E1;&bv)
2
4
5
D
o-o, electron energy
distribution for ionization of H by (2lS) and He(Z3S); distribution of relative kinetic energy obtained
from the D+-encrgy distribution -, and from the H+-energy distribution -.-.-.- . The two dotted vertical lines show position and width of an electron energy distribution obtained for the potentials calc&ted by Miller and Schaefer III [ 21 using their simple model for collisions at relative kinetic energy of 60 meV.
rected for. The distributions obtained in this way are shown in fig. 1. Eo .m_arksthe electron energy Eel = iT0 = V’(m) -
V’(-).
Due to energy EL
energy conservation the relative kinetic of the heavy particle system in the outgoing channel is connected to the electron energy by
in the center of mass system. Therefore to the electron distribution P(E,,) corresponds a distribution of Ei, P(-E;, +Ek), which is equal in shape for Et > 0. This distribution can be obtained in a simple way from the measured laboratory ion energy distribution for EL S f&. Wehave performed this measurement, using the electron spectrometer with reversed potentials, for ionization of H and D atoms. The result is shOwn in frg. 1 where p(--Ei:Ek) is plotted against -/Ye, with -EL + Ek = 0 atEo. The shift pfP(rEk+Ek), at the edge of the distributions, .with respect toP(E,$ is believed to be not an experimental effect. A pbssible explanation & that thk ions,rcacl@g the detector are pre-. dominantly decelerated by the iecoil from the ejected. :
1 Septembrr 1971
CHEMICAL PHYSICS LETTERS
Volume 10, number 5
TabIe I Comparison of experimental data with theory. Rcl = classical turning point at Y*(R) for 60 mV wUision energy; em = [V*(m) - V*(Rm)] - [V*(m) - V+(Rm)] (see text); E* = depth of v*(R); ut,-,t = total ionization cross section at relative collision energies (temperatures) given in brackets. Experiments are performed using FA = flowing afterglow technique or PES = Penning electron spectroscopy
System
Author
Method
He(21S)-H(1’S)
this work
exp. PES
‘z (V,*)
Miller et al. [ 21 Fujiiet al. [l]
theory
Hc(2%)-H(l’S) ‘z
this work
Shaw et al. [5]
3.4 i 0.2 3.6 ==6
exp. FA exp. PES
BeU[3]
Fujiietat
e*[eV]
%3t[~’
I
0.46 * 0.05
0.46 + 0.05
=33
(60 mV) a)
0.380
0.390 repuIsive
120 (27 mW 0.35 (27 mV)
2.18 r 0.15
3.44 -c 0.2
1.77
1.91 1.15
43 27
<300°K)
1.16
36
(27 mV)
22 c 6 (300°K)
2.15 2 0.1
Miller et al. [ 21 wg
EmIN
R&o1
2.3 theory
1.36
(11
-0.5
1.34
0.55
(27 mm b)
a) Value obtained using our ratio u$ut and ut from ref. [ 5 1. b) Close collision v;ilues (extrapolated from fires published, ref. [2] ).
electron - this recoil has been neglected so far - , while electrons detected have excess energy because they are ejected from systems moving towards the de-
our data, is the one calculated by MiLIerand Schaefer [2] . On the other hand, as mentioned above, the
tector. Such an effect is possible if ion- and electron angular distributions are strongly correlated. The effect should be smaller for the He(23S)/D system, for which, however, only the ion distribution was measured. This is actually found as shown in fig. 1. The quantities eel and em are connected to the potentials by the following relations [6] :
agree grossly, both, for the He(23S)/H as well as for
‘rn
= V*(==)
-
V*(R,)
- [v+(m) - V+(R,)]
.
(2)
Here we have neglected ‘the fact that V*(R) has a fmite width. R,, is the classical turning point for central collisions. R, is the separation at which [V*(R) - V+(R)] attains its minimal value in the range R,l GR
that either of the distributions
The potential V*(R) is welI known from experiment [ 121 as well as from theoretical calculations [2, 13-151. The potential which we use to evaluate
recent theoretical calculations El-31 of V’*(R) disthe He(2%)/H system [1,2,4] and we shall theret’ore use our results - in conjunction with reIations (1) and (2) - to obtain information OR these potentials. The most direct information is obtained from relation (l), namely the turning point Rd at V*(R). These experimental v&es RE, and REr for singlet and triplet potentials are given in tabIe 1 and compared with the values predicted by theory. Tfie agreement with the values of MiLler and Schaefer III [2] is excellent, showing that the repuIsive part (R = Rcl) of the potentials V*(R) is c&&ted accurately. The deviation from the other caIcuIated vdues [I, 31 is much larger than the pos.siXe error of the experimental value. Information on the depth of V*(R), E* = V*(W) - V*(R,), can be derived from relation (2). In the case of the singlet potential Rk (R& > R;) is large enough so that V*(m) - Vf(Rg) = 0, within the error of ek. Therefore RS = RX and es = e: to a very good approximation. Cmparison of %i s value e: with the theoretical values in tabIe I shows again agreement with the value of Milk et al. [Z] , whiIe the other theoretical potential [I, 4] shows no attraction at all. In the case of the triplet potential the determination 49s -.
Volume 10, number 5
CHEMICALPHYSICS~LBTTBRS
ofer.from the‘measured quantity EL is not quite so straightforward as in the singlet case, since here the turn&g point Ri lies’at a much smaller separation arrd .the corit+ution of the potentiai V+(Rj in-relation (2) cannot be neglected. Therefore we compare in tabIe 1 the experimental EL directly with the corresponding values taken from the theoretical potentials. A’good estimate on’e,* c-an be obtained in the foliowing way: Inspection of known potentials of a similar type as V*(lZ) for He(23S)/H, namely those for Li/HilZ) and Li/aikah(lZ), shows that tht equilibrium distance R, Ii& at approximately R, % 1.5 K, where R, is the zero of the potential. Since R, T Rcl we expect for the He(23S)/H(2Z) potential R, 53 1.5 RL. At this separation v*(R) is still slowly varying so that the minimum of Y+(R)- P+(R) is R& * Ri. In this way, replacing R, in relation (2) by RE m 1.5 R& we obtain
1 Septembir 1971
-.
ter of V*(R) has been neglected. The simplified model for Penning ionkation, proposed by Miller and Schaefer [2] ‘f in which the’transiticn probability I’(R)/h for transitions V*(R) + V+(R) is approximated by.a S-function of R at the classical turning points of the,respective trajectories, is not able to predict the actual electron distribution. This is shown’by the.dotted lines in fig. 1, which inark width and position of the‘distribution obtained by the model?. Au electrons arising from transitions close to the minimum of V*(R) are missing in this distribution. The cross.section ratio cs/ut for ionization of H by I-ie(2lS) and He(23S) can be obtained from the measured step heights of the integral electron stopping curves when H and Ar atoms are ionized using the same metastable beam. A preliminary evaluation leads to a value of c&Jt = 1.5~50%.
This value is compared in table 1 with the theoretical binding energies. All experimental values shown in table 1 definitely favor the calculations of Miller and Schaefer [2], especially so in the case of the He(2%)/H potentia!, where,Nakamura et al. [I,, 41 predict a repulsive inter.action. But also the position (Rk = RL), and the depth (et*) of the triplet potential, as given in refs. [.I, 33, are obviously not correct, In the quantum mechanical formulation given by Miller [I l] the width of the low energy “edge” of the distributions is closely connected to the curvature of the potential difference V*(R) V+(R) at R a R,$ , and can be evaluated to give the curvature df Z’*(R) at R =R,. A preliminary evaluation gives approximate agreement with the potentials calculated by Miller and Schaefer [2] . An additional test of the approximate consistency of our results,with the potentials calculated by Miller and Schaefer [2] can be achieved by computing the electron distributions from these potentials using the method described by us (H. Hotop and A. Niehaus),,in ,a recent publication [6]. IF. this wzy information on r(R) is ako’obtained. 4 detaiIed discussion will be given in a forthcoming paper C.omparison of computed and measured distributions, ‘aswell as the vaiues of table 1 seem-to indicate to& the interaction as calculated in ref. [2], both _m the singlet ,and,in the triplet case,. is not strong en+&. Thiamay be due to,the fact that the resonance charac.’
Tire deviation of the value of Miller and Schaefer [2], %l% = 3, from our result is to be expected because
the ionization probability per close collision should be smaUer in the singlet case than in the triplet case due io a larger value of Rz, instead of being equal (= l), as was assumed in the simple model. Assuming that the long range part of the potentials V*(R) has been calculated correctly by Miller and Schaefer [2], comparison of their close collision cross section with the experimental value of ut of Shaw et al. [S] leads in the triplet case to an ionization efficiency per close collision (averaged) of ‘I, m 0.50 (at E,, = 27 .meV) ; comparison of the cross-section ratio derived from the resuits in xef. [2] , with our experimental value then leads, for the singlet case, to the corresponding approximate ionization efficiency of 7/s * 0.25 f 50%. We would like to thank W. Frobin, E. Hierholzer, and C. Schmidt for helpful discussions concerning the rf cIis&rge used for production’of H atoms. t Hsre g discrete relativb collision energy of 60 meV was u&d. If in&&a maxwslliar’distibution were’as&ed, t5e ac-
tuaKy me&u& .&ctru?n would kill be very differ&if from ,.thecala$atedgne~~ . ..
.-.:. ,, . . ‘..
., ;
Volume10. number 5
CHEMICAL PHYSICS LEmRS
References [l] H.Fujii, H.Nakamun and M.Mori, J. Phys. Sot. Japan 29 (1970) 1030. [2] W.H.Milier and H.F.Schaefer III, J. Chem. Phys. 53 (1970) 1421. [3] K.L.Beil, J. Phys. B3 (1970) 1308. [4] H.Nakamura, J. Phys. Sot. Japan 31 (1971). to be published_ [S] M.J.Shaw, R.C.Boiden, R.S.Hemsworth and N.D.Twiddy, Chem. Phys. Letters 8 (1971) 148. [S] H.Hotop and A.Niehaus, 2. Phyjik 238 (1970) 452. [7] H.Hotop and A.Niehaus, 2. Physik 228 (1969) 68.
1
September 1971
[B] H.Hotop and A.Niehaus, I. h&s Spectry. Ion Phys 5 (1970) 415. [9] H.Hotop and A.Niehaus, Chem. Phys. Letters 3 (1969) 687; H.Hotop, A.Niehaus and A.L.SchmeItekopf, Z. Physik 229 (1969) 1. [lo] E.S.Fry &d W.L.Wiiams, Rev. Sci. Instr. 40 (1969) 1141. 1111 W.H.MilIer. J. Chem. Phys. 52 EL97Gj 3563. [12] H.P.Weise, A.V.Mittmarm, A.Dingand A.Henglein, Z. Nahuforsch., to tre published. [ 131 L.Wolniewicz, J. Chem. Phys 43 (1965) 1087. 1141 H.H.Michels, J. Chem. Phys 44 (1966) 3834. [IS] SPeyerimhoff, J. Chem. Phys. 43 (1965) 998.
1 September 1971
CHEMICALPHYSICSLETTJZRS
PENNING ELECTRON SPECTRA FROM IONIZATION OF HYDROGEN ATOMS BY He(2*S) AND He(23S) META§TABLES H. HGTGP, E. ILLENBERGER,
H. MGRGNER and A. NiEHAUS
Phyn~kalisciresInsritut der Universitiit Phiburg Received
2 July
Germany
1971
Separate Penning election spectra were measured resulting from the ionbation of H ator& by He(Z’S) and Hc(~~S) metastables in thermal collisions. From these results potential parameters of the dhtomics .&(2’S)H(‘S) (‘C) and He(23S)-H(‘S) (7z) as well as the cross-section ratio uQinglet)/o(tripIet) are derived.
Theoretical calculations on the ionization of neutral ground state atoms in collisions with metastable excited particles have been reported only very recently and only for the simplest possible systems, He(2%, 23S)-H(ls) [l-4]. To obtain theoretical values for experimentally accessible quantities such as cross sections or electron energy distributions, the interaction potentials V*(R) and V/+(R) involved in the collision, as well as the transition probability W(R) for transitions from the incoming potential V*(R) to the outgoing potential v+(R) must be calculated, the calculations being complicated by the fact that V*(R) is a resonance state, of width r(R) = A W(R), degenerate with the continuum V+(R) + e-. The theoretical results [l-4] , concerning the potential curves V*(R) as well as the cross sections for ionization, differ strongly from one’another. The only experimental information on the He*/H systern available in the literature is a value of the dkstruction cross section for the collision pair He(23S )--H. Shaw et al: [ 51, using a flowing afterglow apparatus, obtained a value of (22 f 6) A2 at 300°K. The theoretical results of Fujii et al; [I] (ut = 36 A at 27 meV relative collision energy) and of Bell [3 J (ot = 27 A2 5 20% at 300’K) agree fairly well with the experimental value. However, this agreement has to be considered as fortuitious in view of the fact that, as we shall show in this paper, the potentials V,*(R) used in these calculations do not agree with experiment. In the case of the He(2%)-H system Fujii et al. [ 11,
performing a simple valence bond calculation, fiid a purely repulsive potential (real part of a lo& complex potential) and accordingly arrive at a small cross section (us = 0.35 A2 at 27 meV, us/at = 0.97 X 10A2). On the other hand, MiJ.ler and Schaefer [2] , cuying out a large scale CI calculation in which, however, the continuum V+ f e- was neglected, find an attractive potential of a well depth of 390 meV, resulting in a close collision cross section roughly equal to that for He(23S) + H. Adopting their simple model that each close collision leads to Penning ionization - if this transition is allowed by spin considerations - the cross section ratio us/at =Z3 at Erei = 27 meV is obtained from the extrapolated cross section curyes reported by Miller and Schaefer 121. In view of these discrepancies, ftirfher experimental information is desirable. ObviousIy, a measurement of the ratio usiut would be of particular interest with respect to the He(2&)--H system. Moreover, experimental determination of the potential cume V*(R) could help to clarify the situation; such information can be drawn, in principle, from eIastic scattering, but in the present case, this approach is complicated as a consequence of the existence of two potentials in the He(23S )--H(2S) case, 2Z and 4ZZ,and also due to the fact that the inelastic cross section is not negligible in comparison with the elastic one. A direct determination of potential parameters of l?(R) (?Z) can be obtained from the measured Perming electron energy distribution as has been &own in a recent paper from this Iaboratory [6] . 493
Volume 10, number 5
1 September 1971.
CHEMICAL PHYSICS LETTERS
k this letter we report such Penning electron distributions arising from thermal collisions (mean coljisi6n energy ~60 m;V) of ye(2lS) and He(23S) with H atoms. From these distributions - separateIy determined for collisions with He(21S) and He(23S) - we
derive (1) the cross section
ratio uS/ut, and
(2) the depth of the potentials V*(2ZZ),E: and E?, as well as the position of the classical tumg points at these potentials for central collisions,R% and RL,. The experimental method applied has been described elsewhere [6-81. Briefly: a thermal ‘beam of He metastables - containing approximately ea;uzl amounts of
,494
‘.,
.’
7
65
0
He(&) and He(Z3S) - is produced by a hot cathode He discharge. An almost pure He(2%) beam [less than 1% He(2lS)] is formedh< quenching the He(2lS) atoms by irradiation by light from another He discharge [g-1011 The H atoms, produced from Hz in an rf discharge, effiise from a g!ass tube into the scattering chamber which is crossed by the He* beam. Penning electrons arising from the collision of He* with H are andysed in a plane retarding potential electron spectrometer. The integra! electron stopping curve is stored in a multichannel anaIyser and the electron energy distribution is obtained by numerical differentiation with respect to energy. The energy resolution - full width at half.intensiQ, of the differentiated curve for monochromatic electrons - was about 60 mV in these measurements. Energy calibration was achieved by measuring Penning electrons from a mixture of H atoms and Ar atoms [7-g]. The determination of the distribution for the He(23S)/H system is complicated by the fact that the low energy part of the very broad distribution overlape with the distribution from ionization of H2, which is also present in the scattering center, and that the high energy part overlaps with electrons from ionization df H by He(21.5) atoms which have not been quenched. The pure He(23S)/H distribution is obtained by subtracting these contributidns, which are determined in separate measurements. A minor uncertainty is introduced due to the f&t that the H2 contribution is assumed to arise from unexcited H2 molecules; yhile, with the rf power on, some ,of the H2 may be vibrationally excited. No complication arises in the case of th$ He(2%)/H &z&urn because +Slesmall contribution from the He(23S)/H spectrum in this energy.range is e&ly car-
7.5
Ed(cv)
E&l
lip.
1
6
7
1. Measured enerB
distributions.
E1;&bv)
2
4
5
D
o-o, electron energy
distribution for ionization of H by (2lS) and He(Z3S); distribution of relative kinetic energy obtained
from the D+-encrgy distribution -, and from the H+-energy distribution -.-.-.- . The two dotted vertical lines show position and width of an electron energy distribution obtained for the potentials calc&ted by Miller and Schaefer III [ 21 using their simple model for collisions at relative kinetic energy of 60 meV.
rected for. The distributions obtained in this way are shown in fig. 1. Eo .m_arksthe electron energy Eel = iT0 = V’(m) -
V’(-).
Due to energy EL
energy conservation the relative kinetic of the heavy particle system in the outgoing channel is connected to the electron energy by
in the center of mass system. Therefore to the electron distribution P(E,,) corresponds a distribution of Ei, P(-E;, +Ek), which is equal in shape for Et > 0. This distribution can be obtained in a simple way from the measured laboratory ion energy distribution for EL S f&. Wehave performed this measurement, using the electron spectrometer with reversed potentials, for ionization of H and D atoms. The result is shOwn in frg. 1 where p(--Ei:Ek) is plotted against -/Ye, with -EL + Ek = 0 atEo. The shift pfP(rEk+Ek), at the edge of the distributions, .with respect toP(E,$ is believed to be not an experimental effect. A pbssible explanation & that thk ions,rcacl@g the detector are pre-. dominantly decelerated by the iecoil from the ejected. :
1 Septembrr 1971
CHEMICAL PHYSICS LETTERS
Volume 10, number 5
TabIe I Comparison of experimental data with theory. Rcl = classical turning point at Y*(R) for 60 mV wUision energy; em = [V*(m) - V*(Rm)] - [V*(m) - V+(Rm)] (see text); E* = depth of v*(R); ut,-,t = total ionization cross section at relative collision energies (temperatures) given in brackets. Experiments are performed using FA = flowing afterglow technique or PES = Penning electron spectroscopy
System
Author
Method
He(21S)-H(1’S)
this work
exp. PES
‘z (V,*)
Miller et al. [ 21 Fujiiet al. [l]
theory
Hc(2%)-H(l’S) ‘z
this work
Shaw et al. [5]
3.4 i 0.2 3.6 ==6
exp. FA exp. PES
BeU[3]
Fujiietat
e*[eV]
%3t[~’
I
0.46 * 0.05
0.46 + 0.05
=33
(60 mV) a)
0.380
0.390 repuIsive
120 (27 mW 0.35 (27 mV)
2.18 r 0.15
3.44 -c 0.2
1.77
1.91 1.15
43 27
<300°K)
1.16
36
(27 mV)
22 c 6 (300°K)
2.15 2 0.1
Miller et al. [ 21 wg
EmIN
R&o1
2.3 theory
1.36
(11
-0.5
1.34
0.55
(27 mm b)
a) Value obtained using our ratio u$ut and ut from ref. [ 5 1. b) Close collision v;ilues (extrapolated from fires published, ref. [2] ).
electron - this recoil has been neglected so far - , while electrons detected have excess energy because they are ejected from systems moving towards the de-
our data, is the one calculated by MiLIerand Schaefer [2] . On the other hand, as mentioned above, the
tector. Such an effect is possible if ion- and electron angular distributions are strongly correlated. The effect should be smaller for the He(23S)/D system, for which, however, only the ion distribution was measured. This is actually found as shown in fig. 1. The quantities eel and em are connected to the potentials by the following relations [6] :
agree grossly, both, for the He(23S)/H as well as for
‘rn
= V*(==)
-
V*(R,)
- [v+(m) - V+(R,)]
.
(2)
Here we have neglected ‘the fact that V*(R) has a fmite width. R,, is the classical turning point for central collisions. R, is the separation at which [V*(R) - V+(R)] attains its minimal value in the range R,l GR
that either of the distributions
The potential V*(R) is welI known from experiment [ 121 as well as from theoretical calculations [2, 13-151. The potential which we use to evaluate
recent theoretical calculations El-31 of V’*(R) disthe He(2%)/H system [1,2,4] and we shall theret’ore use our results - in conjunction with reIations (1) and (2) - to obtain information OR these potentials. The most direct information is obtained from relation (l), namely the turning point Rd at V*(R). These experimental v&es RE, and REr for singlet and triplet potentials are given in tabIe 1 and compared with the values predicted by theory. Tfie agreement with the values of MiLler and Schaefer III [2] is excellent, showing that the repuIsive part (R = Rcl) of the potentials V*(R) is c&&ted accurately. The deviation from the other caIcuIated vdues [I, 31 is much larger than the pos.siXe error of the experimental value. Information on the depth of V*(R), E* = V*(W) - V*(R,), can be derived from relation (2). In the case of the singlet potential Rk (R& > R;) is large enough so that V*(m) - Vf(Rg) = 0, within the error of ek. Therefore RS = RX and es = e: to a very good approximation. Cmparison of %i s value e: with the theoretical values in tabIe I shows again agreement with the value of Milk et al. [Z] , whiIe the other theoretical potential [I, 4] shows no attraction at all. In the case of the triplet potential the determination 49s -.
Volume 10, number 5
CHEMICALPHYSICS~LBTTBRS
ofer.from the‘measured quantity EL is not quite so straightforward as in the singlet case, since here the turn&g point Ri lies’at a much smaller separation arrd .the corit+ution of the potentiai V+(Rj in-relation (2) cannot be neglected. Therefore we compare in tabIe 1 the experimental EL directly with the corresponding values taken from the theoretical potentials. A’good estimate on’e,* c-an be obtained in the foliowing way: Inspection of known potentials of a similar type as V*(lZ) for He(23S)/H, namely those for Li/HilZ) and Li/aikah(lZ), shows that tht equilibrium distance R, Ii& at approximately R, % 1.5 K, where R, is the zero of the potential. Since R, T Rcl we expect for the He(23S)/H(2Z) potential R, 53 1.5 RL. At this separation v*(R) is still slowly varying so that the minimum of Y+(R)- P+(R) is R& * Ri. In this way, replacing R, in relation (2) by RE m 1.5 R& we obtain
1 Septembir 1971
-.
ter of V*(R) has been neglected. The simplified model for Penning ionkation, proposed by Miller and Schaefer [2] ‘f in which the’transiticn probability I’(R)/h for transitions V*(R) + V+(R) is approximated by.a S-function of R at the classical turning points of the,respective trajectories, is not able to predict the actual electron distribution. This is shown’by the.dotted lines in fig. 1, which inark width and position of the‘distribution obtained by the model?. Au electrons arising from transitions close to the minimum of V*(R) are missing in this distribution. The cross.section ratio cs/ut for ionization of H by I-ie(2lS) and He(23S) can be obtained from the measured step heights of the integral electron stopping curves when H and Ar atoms are ionized using the same metastable beam. A preliminary evaluation leads to a value of c&Jt = 1.5~50%.
This value is compared in table 1 with the theoretical binding energies. All experimental values shown in table 1 definitely favor the calculations of Miller and Schaefer [2], especially so in the case of the He(2%)/H potentia!, where,Nakamura et al. [I,, 41 predict a repulsive inter.action. But also the position (Rk = RL), and the depth (et*) of the triplet potential, as given in refs. [.I, 33, are obviously not correct, In the quantum mechanical formulation given by Miller [I l] the width of the low energy “edge” of the distributions is closely connected to the curvature of the potential difference V*(R) V+(R) at R a R,$ , and can be evaluated to give the curvature df Z’*(R) at R =R,. A preliminary evaluation gives approximate agreement with the potentials calculated by Miller and Schaefer [2] . An additional test of the approximate consistency of our results,with the potentials calculated by Miller and Schaefer [2] can be achieved by computing the electron distributions from these potentials using the method described by us (H. Hotop and A. Niehaus),,in ,a recent publication [6]. IF. this wzy information on r(R) is ako’obtained. 4 detaiIed discussion will be given in a forthcoming paper C.omparison of computed and measured distributions, ‘aswell as the vaiues of table 1 seem-to indicate to& the interaction as calculated in ref. [2], both _m the singlet ,and,in the triplet case,. is not strong en+&. Thiamay be due to,the fact that the resonance charac.’
Tire deviation of the value of Miller and Schaefer [2], %l% = 3, from our result is to be expected because
the ionization probability per close collision should be smaUer in the singlet case than in the triplet case due io a larger value of Rz, instead of being equal (= l), as was assumed in the simple model. Assuming that the long range part of the potentials V*(R) has been calculated correctly by Miller and Schaefer [2], comparison of their close collision cross section with the experimental value of ut of Shaw et al. [S] leads in the triplet case to an ionization efficiency per close collision (averaged) of ‘I, m 0.50 (at E,, = 27 .meV) ; comparison of the cross-section ratio derived from the resuits in xef. [2] , with our experimental value then leads, for the singlet case, to the corresponding approximate ionization efficiency of 7/s * 0.25 f 50%. We would like to thank W. Frobin, E. Hierholzer, and C. Schmidt for helpful discussions concerning the rf cIis&rge used for production’of H atoms. t Hsre g discrete relativb collision energy of 60 meV was u&d. If in&&a maxwslliar’distibution were’as&ed, t5e ac-
tuaKy me&u& .&ctru?n would kill be very differ&if from ,.thecala$atedgne~~ . ..
.-.:. ,, . . ‘..
., ;
Volume10. number 5
CHEMICAL PHYSICS LEmRS
References [l] H.Fujii, H.Nakamun and M.Mori, J. Phys. Sot. Japan 29 (1970) 1030. [2] W.H.Milier and H.F.Schaefer III, J. Chem. Phys. 53 (1970) 1421. [3] K.L.Beil, J. Phys. B3 (1970) 1308. [4] H.Nakamura, J. Phys. Sot. Japan 31 (1971). to be published_ [S] M.J.Shaw, R.C.Boiden, R.S.Hemsworth and N.D.Twiddy, Chem. Phys. Letters 8 (1971) 148. [S] H.Hotop and A.Niehaus, 2. Phyjik 238 (1970) 452. [7] H.Hotop and A.Niehaus, 2. Physik 228 (1969) 68.
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September 1971
[B] H.Hotop and A.Niehaus, I. h&s Spectry. Ion Phys 5 (1970) 415. [9] H.Hotop and A.Niehaus, Chem. Phys. Letters 3 (1969) 687; H.Hotop, A.Niehaus and A.L.SchmeItekopf, Z. Physik 229 (1969) 1. [lo] E.S.Fry &d W.L.Wiiams, Rev. Sci. Instr. 40 (1969) 1141. 1111 W.H.MilIer. J. Chem. Phys. 52 EL97Gj 3563. [12] H.P.Weise, A.V.Mittmarm, A.Dingand A.Henglein, Z. Nahuforsch., to tre published. [ 131 L.Wolniewicz, J. Chem. Phys 43 (1965) 1087. 1141 H.H.Michels, J. Chem. Phys 44 (1966) 3834. [IS] SPeyerimhoff, J. Chem. Phys. 43 (1965) 998.