Recent Measurements on Charge Transfer

RECENT MEASUREMENTS ON CHARGE TRANSFER J. B. HASTED Department of Physics, University College

London, England Introduction .................................................. 237 Total Cross Sections for the Symmetrical Resonance Process . . . . . . . ,237 Total Charge Transfer Cross Sections for Unlike Ions and Atoms ... ,242 Differential Scattering with Capture ............................. .243 Pseudocrossing of Potential ................246 Molecular Charge Transfer . . . . . . . . . . . . . .248 Experimental Techniques . ...................249 Role of Excited Species . . . . . . . . . . . . . . . . . ..254 A. Experiments with Excited and Ground State Ions ............... ,254 B. Processes Terminating in Excited Species ........... IX. Miscellaneous Topics ........................................... .259 A. Ionization with Capture ..................................... .259 B. Radiative Charge Transfer ................................... ,261 C. Two Electron Capture Processes ............................. .261 References ..................................................... .263

I. 11. 111. IV. V. VI. VII. VIII.

I. Introduction This article discusses recent experimental research carried out on charge exchange collisions at low and moderate impact energies. The intention is to concentrate on the features which are closest to the center of understanding in terms of quantum theory.

II. Total Cross Sections for the Symmetrical Resonance Process

At intermediate impact velocities, there exist valuable generalized treatments using semiempirical orbitals (Firsov, 1951; Rapp and Francis, 1962). The derived cross section 0 at impact velocity u has the general form where a and b are constants. Little relevant laboratory work has been done since the comparison with experimental data made by Rapp and Francis (1962). However, there are still discrepancies between different measurements, 237

J. B. Hasted

238

sufficientto make the comparison a complex matter. One important source of error arises in the McLeod pressure gauge which is almost always used as an absolute standard. Ishii and Nakayama (1961) have pointed out that the mercury vapor stream in the gauge acts as a diffusion pump, so that the measured pressure p m is low by an amount Ap given by dp/pm= 0.905rpH,(T/D)'/2

(2) where pHgis the vapor pressure (Torr) of mercury, r the inside radius of the tube connecting to the gauge, D the gas diffusion coefficient, and T the gas temperature. This formula has been verified experimentally within limits. Measurements can now be made with commercial refrigerated gauges with pHg so low that Ap is negligible. The early symmetrical resonance charge transfer measurements should be repeated. It may be noted that the errors are, in general, higher for the heavier gases.' As McLeod gauge tube diameters have tended to be larger in recent years, some old measurements may be the best available. It is possible to rearrange the Firsov and RappFrancis formulations in such a way that a direct comparison may be made between them (Lee, 1967). This arrangement leads to the graphical representation of cross-section functions shown in Fig. 1, in the form yp,(log,, v), where the cross section is a = +npI2

(3)

y = (Ei/13.6)'/2

(4)

with2

Ei being the ionization potential in electron volts. The symmetrical resonance cross section at a given impact velocity is inversely proportional to the ionization potential in the Rapp-Francis, but not in the Firsov formulation. This dependence appears in the logarithmic plot shown in a previous article (Hasted, 1962). In the Firsov formulation the cross sections of low ionization potential atoms are higher than in the RappFrancis formulation. A search for systematic deviation shows that cross-section functions for high ionization potential E j agree with theory within the experimental error; but as the ionization potential decreases the measured cross sections become progressively larger than predicted. The form of Eq. (1) is in agreement with experiment. The position with regard to the parameter b is uncertain. However, the experimental parameter a, for low ionization potential atoms, is undoubtedly larger than given by the Rapp-Francis or even the Firsov formulation. This judgment is based on a number of experiments (Kushnir et a[., An error of 50% is possible. Note that y (Rapp and Francis, 19621, which is used here, is equal to y-' (Firsov, 1951).

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239

16 -

14 -

12 -

I

-

10-

0

n

8-

6-

4-

FIG. 1 . The function ypl(log,, v ) , which leads directly [Eqs. (31, (4)] to symmetrical resonance charge transfer cross sections in both Firsov (thin line) and Rapp-Francis (thick line) formulations. In the Firsov formulation, the function is dependent on y , while in the RappFrancis formulation, it is not.

1959; Marino et al., 1962; Chkuaseli et al., 1963; Edmonds and Hasted, 1964; Palyukh, 1967). The conflict with theory is not obscured by the considerable discrepancies existing between the measurements. In electron capture by an atom from its negative ion, the electron moves in the relatively weak fields of two atoms. The effect of this is seen, in Fig. 3, to result in enhanced cross sections even for nonresonance collisions, since the small value of y not only raises the cross section by virtue of the relative invariance of y p I with y (bearing in mind that the cross section is trip,'), but also by virtue of the fact that in the Firsov formulation ypI is actually large for small values of y. Use of this formulation has enabled the electron affinities E, (eV) of alkali metals to be inferred from the charge transfer cross sections of their negative ions in their own vapor (Bydin, 1964). The inferred values are: Na, 0.41 eV; K, 0.22 eV; Rb, 0.16 eV; Cs, 0.13 eV. However, the possible errors are rather large. The affinities derived from collisional detachment measurements (Bydin, 1966) using the theory of Smirnov and Firsov (1964) should be more accurate.

J. B. Hasted

240

0

lo4 2

5

to5

2

5

lo6 2

5

10'

2

5

lo8

V Icrn/sec)

FIG.2. Symmetricalresonance charge transfer and mobility data displayed as o'/*(logl0 v). Broken lines represent calculations from Rapp-Francis (1962) formulation and from Eq. (5). Experimental data are represented as full lines and points. (1 967) A M Mahadevan G H Gilbody and Hasted (1956) (1957) (1954, 1956) F Fedorenko et al. BC Biondi and Chanin (1966) FS Flaks and Solov'ev (1958) P Patterson (1955) (1953) D Dillon et al. Ziegler 0 Z G Ghosh and Sheridan (1 957) Nichols and Witteborn (1966) 0N (1959) (1964) KLS,S Kushnir et al. E Edmonds and Hasted

An interesting problem arises in symmetrical resonance charge transfer at very low impact energies where the approximation of rectilinear motion is unsatisfactory (Edmonds and Hasted, 1964). As the impact parameter decreases, at a fixed impact velocity u, the polar scattering angle increases until a critical impact parameter p c is reached, when the system passes into stable orbiting. Within this impact parameter, inward spiraling orbits occur. Rapp and Francis (1962) have proposed that for sufficiently small impact velocities p c > p1 [of Eq. (3)], so that for p < p c the system will spiral inwards

24 1

RECENT MEASUREMENTS ON CHARGE TRANSFER

until p < p l , when the probability of charge transfer becomes one-half. The cross section is thus

a = +zp, =

-(-)

ne a U

'I2

(5)

P

This may be written a=

4.6 x lo-''

(;)'I2

cm2

U

where the velocity vis in centimeters per second, the polarizability a is in atomic units, and the reduced mass p is on the chemical scale. At impact velocities such that p1 > p c , the cross section remains approximately +npI2.The extent to which the experimental data justify these proposals is shown in Fig. 2. The charge transfer cross section is displayed in the form a'12(v), so that a linear fall is expected on the basis of Eq. (1). Reduced mobility measurements (Biondi and Chanin, 1954; Patterson, 1966) at low field strength to pressure ratio, but variable gas temperature, are converted to average diffusion cross section and thence to charge transfer cross section (Dalgarno et al., 1958). Beam measurements have, in general, been selected only from among the most recent. However, those due to Gilbody and Hasted (1956) have been included because the McLeod gauge employed is known and the laboratory temperature can be estimated so that fractional pressure corrections may be made.

0

106

2

4

7

10'

Velocity

2

4

7

108

(crnlsec)

FIG. 3. Negative ion nonresonant total charge transfer data (Snow,1966). 0 , O - H;

0 ,H - 0 ; 0, C - H ; 8 , C - 0 .

242

J. B. Hasted

The interest of the displayed a”2(u) functions lies not so much in the agreement with theory, but in the demonstration that orbiting can usually only contribute significantly at low temperatures. Charge transfer experiments using molecular ions and their parent neutral molecules are not measurements of the pure symmetrical resonance process, because neither the vibrational state distributions of the ion nor of the molecule formed from it are specified. Detailed analysis will not be possible until vibrational state population diagnosis is achieved. In the meantime, it would be unwise to expect the general theoretical treatment to be precisely applicable to the experiments. Recent measurements include those for N2’N2 by Nichols and Witteborn (1966). Molecular charge transfer processes at very low energies will be considered in Section VI.

III. Total Charge Transfer Cross Sections for Unlike Ions and Atoms Considering only the initial and final states of a colliding ion and unlike atom, approximate but realistic calculations of the total charge transfer cross section can be made. In general, the adiabatic criterion (Massey, 1949) applies fairly well. According to this, the probability of charge transfer is small if the time of transition h/lAE I is much shorter than the time of collision a/v (where A E is the energy separation of the states A’B and B’A at infinite nuclear separation, v is the impact velocity, and a is the “adiabatic parameter”). When the two times are comparable, the probability can be large. A successful experimental test was made (Hasted, 1951) with the arbitrary assumption that the cross section function rises with increasing v to a maximum value when h/lAEl is equal to a/u. For a large number of typical single charge transfer processes, it was found that this assumption was consistent with an invariant adiabatic parameter equal to 7 A. The application of this “ adiabatic maximum rule” to other types of inelastic heavy particle collision, such as ionization, is reasonably successful, although for different reasons (Hasted and Lee, 1962; Hasted, 1964). Since the energy separation of the initial and final potential curves does not remain constant during the collision, the replacement of AEm calculated at finite internuclear distance by a value suitably averaged over the collision region, results in improved correspondence with the data (Lee and Hasted, 1965). The effect may be very striking. Thus the cross section for

=

He2+

+ H+He+(2s, 2p) + H + ,

(7) which is in exact energy resonance, passes through a maximum at about 30 keV (Fite et al., 1962).

RECENT MEASUREMENTS ON CHARGE TRANSFER

243

The general intermediate impact velocity features of the unlike ion-atom charge transfer function are reasonably consistent with the results of a set of approximate, but generally applicable, calculations due to Rapp and Francis (1962). Tables of functions from which any cross section can readily be derived are available (Lee and Hasted, 1965). The predicted cross section functions are v4 dependent at very low energies, and rise to maxima when the collisions cease to be adiabatic. A relation yielding v,,, , the impact velocity for maximum cross section, similar to the adiabatic maximum rule, but containing no empirical adiabatic parameter, can be deduced (Lee and Hasted, 1965) from the RappFrancis equations, as follows : -

uiaX==2.25 x

lOI4

Y

2.5

+ 2 log,,

)

Ei (cm/sec>Z IAEI

(8)

The dependence of u,,, on y might possibly be inferred from recent negative ion data (Snow, 1966), some of which are displayed in Fig. 3. Here the apparent adiabatic parameter a is about I8 A. Further deductions concerning the dependence of v,,, on AE have recently been presented by Drukarev (1967). In interpreting intermediate velocity charge transfer collisions, the two atomic systems should be considered in terms of the states of the quasimolecule they compose. The comparison of O'H, H'H data (Stebbings et al., 1964) is consistent with this approach, and so are rare gas data taken at high energies (Lee and Gilbody, 1964; Gilbody et al., 1963). It is even possible to make inferences concerning the type of angular momentum coupling applicable to the quasimolecule (Edmonds and Hasted, 1964).

IV. Differential Scattering with Capture On the two-state impact parameter approximation, the probability Po of symmetrical resonance charge transfer considered as a function either of p or of v, oscillates between zero and unity (cf. Bates and McCarroll, 1962). The oscillation is thus observable both in collisions at fixed polar scattering angle and varying impact velocity, and in collisions at fixed impact velocity and varying polar scattering angle. Such experiments were first carried out by Everhart and his colleagues (Ziemba et al., 1960; Everhart et al., 1964). Some important data are illustrated in Figs. 4a and 4b. For collisions between unlike ions and atoms, the maxima of the oscillations are not constant at unity, but decrease with increasing p (Fig. 4b). Even for symmetrical resonance collisions, the probabilities do not reach zero or unity. This is because of wave effects (Massey and Smith, 1933; Smith, 1964) and because of coupling to other states (Bates and Williams, 1964).

N P P

FIG.4. Data for differential scattering with capture. (a) Symmetrical resonance capture probability for H+ on H at 0=3", as a function of 0-l. (b) Some resonance and nonresonance capture probabilities. (c) Total charge transfer cross section functions for cesium and rubidium (Perel et ul., 1965). 0 , Rb+ C S ; 0, Cs+ Rb; x, Rb+ Rb; 0, Cs+ Cs. 1

0

1

1

1

1

1

100 Reclprocol veloclly.

FIG.4a.

1

1

200

IdB sec/rneler

I

I

I

I

300

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C

-

245

246

J. B. Hasted

Under certain circumstances, oscillating behavior is found in total charge transfer collision functions, both symmetric and asymmetric (Perel et al., 1965; Smith, 1966). Typical data are shown in Fig. 4c. Everhart's experiments on differential scattering with capture involve a measurement, at the same polar scattering angle, of both charged and neutral components. However, it is possible to obtain information about charge transfer (except in the adiabatic region) from measurements only of the differential scattering of the charged particles (Lorents and Aberth, 1965; Marchi and Smith, 1965). The structure in the scattering functions arises from rainbow effects, from nuclear interchange, and from interference between waves scattered from the symmetric and antisymmetric potentials of the quasimolecular ion.

V. Pseudocrossing of Potential Energy Curves When the initial and final interaction energy functions approach each other and pseudocross, at nuclear separation R, , then anomalous large total cross sections at low impact velocities are to be expected. Such a situation is found in exothermic single electron capture by a multiply charged ion: An+ + B+A(n-I)+ + B +

(9) for which the Coulomb repulsion between the products greatly exceeds the polarization attraction between the collidants. Even in such processes as H+

+ Xe +H(ls) + Xe+

(10) pseudocrossing is found. It is possible that antibonding interaction curves might take part in pseudocrossing and produce large cross sections at low impact energies. The earliest approximation by which pseudocrossing was treated is that due to Landau (1932) and Zener (1932). Using this approximation and simple wave functions, calculations have been carried out on some processes which have been studied in the laboratory (Hasted et al., 1964; Flaks and Ogurtsov, 1963). The comparison of pseudocrossing energy separations A U deduced from experiment, with those calculated from the wavefunctions, is not entirely satisfactory, as can be seen from Table I. This may be associated with the fact that in very few of these processes does the active electron start and finish in an s orbital (cf. Bates, 1960). For some years it has been recognized that the Landau-Zener approximation has certain defects (Bates, 1960; Mordvinov and Firsov, 1960). Another approach (Bates et al., 1964) is to solve numerically the equations of the twostate approximation. It is found that the probability of transition P oscillates with varying p and hence varying scattering angle 6 (Fig. 5). Calculations of

247

RECENT MEASUREMENTS ON CHARGE TRANSFER

TABLE I COMPARISON OF EXPERIMENTAL AND CALCULATED ENERGY DIFFERENCES AT PSEUDOCROSSING Collision

R, (a.u.)

AUcalc (eV)

AU exptl (eV)

Ar2+Ar Kr2+Kr Xe2+Xe Kr2+Ne ArZ He N2+He Kr3+He Kr3 Ne Xe3+Ne Xe4 Ne

3.35 3.80 4.37 9.1 8.90 5.40 4.70 3.80 5.35 3.80

1,75 1.60 0.93 0.03 0.0032 0.27 1.7 0.76 0.86 1.17

1.4 1.1 0.94 0.35 0.41 0.75 1.17 1.6 1.6 5.4

+

+

+

080

200175 150 ( 2 5 I

r

I

I

-

0 50

075

100 1

0 25 I

Angle in degrees

-

O*'+Ne-tO'+Ne*

-

E = 2600 eV

050-

-

030-

-

o 15

16

10 20 30 40 50 60 700, P17

18

19

20

21

22a,

I

I

23

24

25

FIG. 5. Probability of capture as a function of impact parameter, P(p) deduced from differential scattering measurements OZ+Ne,at impact energy 2600 eV (Alam ef al., 1967). Vertical arrow indicates crossover at 2 . 0 2 ~inset, ~ ; P(p) calculated by Bates et al. (1964) for BeZ+Hat 102.75eV energy.

J. B. Hasted this type lead to cross sections of the same form as those derived from Landau-Zener approximation, but larger. However, they may yield a second maximum in the cross section at higher energies than the Landau-Zener maximum. In general terms, this is in harmony with multiply charged ion experiments [such as Kr3+Ne(Hasted,1962)] in which a high energy maximum is observed, similar in form to those in noncrossing unlike ion-atom collisions. Figure 5 shows P ( p ) functions for 0 ” N e single electron capture at two different impact energies. With the resolution of this experiment, it is not certain that the minima are not close to zero, as would be implied in calculations of Bates et al. (1964). The 0’’ ion beam contains a proportion of ‘D excited states, which will contribute with pseudocrossing at R, = 1.7a0, thus causing a second feature in the P ( p ) functions superposed on the principal feature at R, = 2.02a0.

VI. Molecular Charge Transfer Processes at Low Energies The interpretation of molecular charge transfer processes by theory is not possible unless the vibrational as well as the electronic states of the reactants and products are known. This information is rarely available. Exothermic molecular charge transfer processes have large cross sections over a wide impact energy range, because it is usually possible for the excess internal energy to be converted into vibrational and rotational energy. Thus near-resonance behavior can often be assumed. Similar reasoning can be applied to the dissociative charge transfer process A

+ BC -+ A + B+ + c.

(1 1) Instructive examples of such processes are the collisions (Stebbings et a]., 1963) of helium ions with oxygen and nitrogen, producing, even at impact energies as high as a few kilovolts, a great preponderence of atomic over molecular ions. The apparent accidental resonances are attributed to the processes He+ + N,+He + N,+ (C2C,+, u = 3) + 0.28 eV (12) He+ + 0,+ He + 0, (c4Zu-) -t0.02 eV. (13) These are followed by predissociation. Slow collisions between molecular ions and atoms and molecules can result in chemical interchange processes of the type +

+

A++BC-,AB++C. (14) These processes are also difficult to treat theoretically. Ion-atom interchange processes are not the subject of this article, but not only are the experimental methods for their study very similar to those used for charge transfer, but also the distinction between the two types of process is not always well defined.

RECENT MEASUREMENTS O N CHARGE TRANSFER

249

VII. Experimental Techniques The reaction products in ion-molecule collisions may have appreciable kinetic energy. Where product mass analysis is not required, the collection of the slowest charged products is relatively simple, but to focus these upon a small mass-spectrometer entrance slit is more difficult. I n older experiments of this type, an ion beam was directed through a gas in the presence of a uniform electric field transverse to the beam. The mass-spectrometer slit was located downfield from the beam, and two conditions were deemed necessary for a completely efficient collection at the slit to have been achieved: (1) independence of mass-analyzed ion current from variation of electric field (" saturation conditions ") ; (2) independence of mass-analyzed ion current from variation of entrance and exit slit widths (" flat-topped peaks"). At high impact energies, these conditions may quite readily be satisfied. But the problem becomes more difficult as the difference between energies of fast primary beam and slow charged product decreases. There is a case for setting up a ray-tracing computer program, and also for combining total crosssection measurements with measurements of product angular distributions In ion-molecule reactions the distinction between fast and slow collision products may be obscured. Successful use has been made of the strong focusing electrostatic quadrupole lens (Giese and Maier, 1963). The " flat-topped peak" condition must be satisfied both for the entrance and the exit slits of a sector magnetic mass spectrometer. The former tests the collision chamber optics and the latter the mass-spectrometer optics. A relevant difficulty is that the sensitivity of certain particle multipliers varies form point to point of particle impact on the first dynode. When a mass-spectrometer slit is widened for these tests, the resolution may inadvertently be lowered to the point where ionic products of different mass number are colcleted, thus compromising the flat-topped peak condition. It is necessary to search at high resolution, and then to conduct the experiment under flattopped peak conditions. A mass spectrometer for which this can be achieved without mechanical adjustment is the quadrupole mass filter. The most promising technique applicable to high and medium impact energies is the spectrometer utilizing crossed electric and magnetic field. This has proved successful for the analogous electron impact problem (Schram et al., 1966). The magnetic field is parallel to the impacting beam, and slow collision products emerging at any azimuthal angle will be focused onto a collector placed parallel to the beam, provided that the mass number bears the correct relation to the field intensities.

250

J. B. Hasted

At impact energies of a few electron volts these techniques cannot be operated satisfactorily, and recourse is often made to electronic pulse techniques for total cross-section measurements (retaining steady beams only for differential measurements). A pulsed extraction field will not interfere with the path of a pulsed ion beam provided that the timing and length of the pulses are suitable. For complex molecules at low energies such techniques would be essential, and reference may be made in particular to nanosecond techniques (Matus et al., 1967) for ion-molecule reactions. The original studies of ion-molecule reactions (Stevenson and Schissler, 1955; Talrose and Lyubimova, 1952) were made by passing a magnetically confined electron beam through a gas in the presence of a transverse electric field produced by the " repeller " in a conventional electron-impact massspectrometer source. The ions, mostly produced with only thermal energy, are continuously accelerated throughout the collision region. In general, the true cross-section function is not obtained, even though the repeller potential is varied. A significant advance was made (Talrose and Frankevich, 1960) by pulsing the electron beam, removing the steady transverse electric field, and applying a delayed pulse to the repeller; thus the ions diffuse thermally until the reaction products are extracted. Over a limited range the reaction product flux is directly proportional to the delay time, and a true thermal energy reaction rate can be deduced. Attempts have been made to combine the advantages of the pulse technique with the facility of varying the ion velocity, using a steady repeller potential, but it is clear that this compromise retains the disadvantages of the original steady potential technique. However, with sufficient detection sensitivity and time resolution, this difficulty can be surmounted (Matus et al., 1967) by applying a pulsed repeller potential for accelerating the ions. This pulse is applied directly after the electron beam pulse, and after its completion the ions move in Newtonian fashion in a field-free region. Their energy distribution is therefore relatively narrow, and many of the inherent defects of the previous " mass-spectrometer source " techniques are removed. Analysis of the dependence of the product ion current on the time delay of the third pulse (applied to an electrode outside the chamber) allows information to be obtained about the momentum transfer in the collision. But at present the width of the electron beam, and the relatively undeveloped state of the apparatus, limit the energy range of the technique. However, pulsed techniques have not been widely used for charge transfer studies, for which the tradition stems from the passage of a mass-separated ion beam through a collision chamber. Confinement of the collision region to a short parallelepiped rather than a long track is often an aid to the ion optics of the system, and may be achieved with the aid of crossed-beam techniques (Stebbings, 1968). Collisions of the ion beam with background gas can be minimized if mechanical interruption of the molecular beam is associated with

RECENT MEASUERMENTS ON CHARGE TRANSFER

25 1

phase sensitive detection of the collision products. The complexities of calculating the impact velocity distribution from the velocity distributions of the two beams are only avoided when the ion beam velocity greatly exceeds that of the molecular beam. There is an effective lower limit, set by space charge, surface contact potential variation, etc., to the energy of an ion beam with which charge transfer experiments can be carried out. Although this limit is at present in the region 2-3 eV, it is possible to perform simple symmetrical resonance total cross section measurements in a magnetic field using atomic ions and targets at energies as small as 0.1 eV (Bullis, 1965); in this case the surfaces of the entire electrode system are coated (by deposition or electrolysis) after assembly, in order to avoid variations of contact potential. But it will not be easy to extend these techniques to experiments involving mass analysis of collision products. Even at 2-3 eV the available primary ion beam intensities (lo-’A) limit the experimental capability. There are still two rival approaches to the problem of production of low energy beams, retardation, and momentum analysis of unaccelerated ions emerging from a source. There has been no real breakthrough in either approach, so that routes must be found round this energy barrier. One such route lies in the nanosecond pulse techniques described above. Four other routes exist: (1) ion cyclotron resonance spectroscopy (Wobschall, 1965; Anders et al., 1966); (2) retardation of ion beam by means of an electrostatic mirror (Schlier, 1967); (3) the merged beam method (Trujillo et al., 1966); (4) the drift tube method (Kaneko et al., 1966). We shall only discuss the last. It has developed from the theoretical and experimental work done on the analysis of ions drifting in gases under the action of uniform electric fields (Wannier, 1951 ; Allis, 1956; Dalgarno el al., 1958). Under “constant mean free path” conditions the mean energy of these ions is simply related to their drift velocity ud:

E

= - f m+ ud2

+ 3m,vdz + 3kT,

(15)

where the ion and gas molecule random velocities are respectively u+ and ug . The drift velocity can be measured by well-established electric shutter techniques, and is a function only of X / p , the ratio of field strength to p r e ~ s u r e . ~ In order to set up the collision events, this parameter is maintained constant, although buffer gas pressure may be varied. Buffer gas pressures of the order More strictly, to the number density n. The quantity X/n is sometimes described in terms of units known as Townsends, equal to lo-’’ volt cm2 molecule-’.

252

J. B. Hasted

of 1 Torr are maintained in the collision chamber, in order to minimize the radial and axial diffusion of the ions. The latter produces negligible effects, and the former introduces a correction factor which is treated in the original paper (Kaneko et al., 1966). An ion beam is injected into the collision chamber, which contains a buffer gas chosen for its inactivity to low energy inelastic processes of ground state ions. Helium has several advantages. Excited ions can be “filtered ” in the buffer gas in the manner described in Section VII1,A. Along the axis of the chamber a uniform electric field is maintained, and at the exit there is a sampling orifice, followed by mass spectrometer and detector. Measured traces of reactant gas are introduced and normally these will not affect the drift process appreciably. The cross section for conversion of ion A’ to B + is related to the sample currents ZA and I,:

where ud and v, are, respectively, drift and random velocities of A’, whilst 1is the length of the drift space, and no the density of reactant gas. Tests are normally made to ensure that the beam injected thermalizes to its normal drift conditions before the first drift velocity measurement grid is reached. For very small cross sections, it is possible to use the reactant gas as its own buffer. Cross sections as small as cm2 can be studied. At thermal energies it is possible to measure rate coefficients for charge transfer in the afterglows of electric discharges. The first experiment of this type was carried out by Dickinson and Sayers (1960), who sampled the time dependence of atomic ion densities in the afterglow of a pulsed radio frequency discharge. Since atomic ions cannot recombine with electrons in weak discharges except radiatively, the only serious competitive decay process for these ions is diffusion (ambipolar constant D,, diffusion length A). The decay is governed by the equations I, = I, exp(-t/z) 7-l

= (D,/A2)

+ n, noaij

where the cross section CJ is appropriate to a mean velocity of impact 6, and the symbols n represent number densities, The diffusion is minimized by conducting the experiment in a relatively high pressure of gas C which is chosen to be unreactive with the atomic ion A’. The diffusion coefficient can usually be related to the known ionic mobility of A + in C, and the rate constant separated by variation of the partial pressure of B. The exponential variation of A + density with time is observed over perhaps two orders of magnitude. The ion density is taken to be proportional to the flux of ions emerging from a metal

RECENT MEASUREMENTS ON CHARGE TRANSFER

253

orifice at wall potential exposed to the afterglow plasma, and backed by a mass spectrometer and detector. More complicated kinetic situations are treated (Fite el al., 1962) by monitoring not only of the time decay of A', but the time growth of the ionic species formed in the reaction. The principal disadvantage of the time-dependent afterglow is that during the excitation period the gas molecule can receive internal energy in a form which lasts as long as the positive ions. Thus the specification of reactants is not so exact as is desirable. A degree of refinement is added by converting the afterglow into a flowing system, after the manner used in chemical kinetics (Fehsenfeld et al., 1966). A mechanical pump is used to pump large volumes of gas along a wide tube; the speed may be as high as 500-1000 sec-' at 1 Torr, and care is taken to preserve laminar flow. A buffer gas maintains the flow, so that the different reactants can be introduced at different points in the flow, without interference. Ions can either be produced by means of an electric discharge, or by another arrangement discussed below; or they can be produced in the afterglow tube itself by Penning ionization from metastable atoms, produced at an earlier point in the afterglow tube:

+

He" 2 3S Ar+He Is

+ Ar+ + e.

(19)

In the flowing system the excitation energy applied to gas flowing through one introduction tube can be made to have little effect in exciting a reactant gas introduced to the main flow through a different tube. In the flowing afterglow system the sampling device, such as an orifice with pumped mass-spectrometer and particle detector, may be capable of being traversed along the tube axis, so that if the flow velocity is known, the time dependence of a species density may be calculated from its variation along the tube axis. The mass flow velocity is measured by measuring change of pressure in a gas reservoir, and is monitored by a pressure transducer. In principle, it is not necessary to traverse the detector, provided that the rate of introduction of the reactant gas can be varied and measured. Since the problems of raising gas temperature in a flowing afterglow system are formidable, this type of measurement is effective essentially only at room temperature. The great advantage of the flowing technique lies in the ability to apply electric discharge (or other) ionizing power to the important component A without exciting or ionizing the species B and C . But in view of the existence of laminar flow and the slow thermalization of electrons, it is advisable to pulse the electrodischarge even in a flowing system. Detailed description of the flowing afterglow technique has been given by Stebbings (1968). Some discussion of the relative advantages of different techniques of producing ionization in a gas is necessary. An ideal source of ionization would produce entirely " parent" ions from a molecular gas, whilst leaving the

254

J . B. Hasted

neutral molecules completely unexcited. The undesirable vibrational excitation of molecules is supposed (Schulz, 1959, 1962; Haas, 1957) to take placevia virtual negative ion states, and since these are present in a large number of molecules at energies of a few electron volts (Boness and Hasted, 1966), it follows that continued heating of the electrons in a discharge is to be avoided. Thus radio-frequency and microwave discharges are undesirable, even (although less so) in the pulsed form. Less undesirable are breakdown pulses applied to metal electrodes, and in particular the brush cathode investigated by Persson (1965) has been found to eliminate all components from the electron energy distribution except the thermal component and a group of electrons possessing energies given approximately by the cathode-anode voltage. Superior even to the pulsed brush cathode discharge are fluxes of very high energy electrons and of ultraviolet photons. Electrons of perhaps 50 keV energy can readily be directed through very thin metal windows dividing the gas inlet from a high vacuum. They discriminate in favor of those excited states whose oscillator strengths for transition from the ground state are largest (resonance states). Thus even if there are unwanted species present, their proportions can be estimated. Ultraviolet photons are still more refined, but difficult to make available. There are a number of sources which provide ultraviolet continua capable of ionizing many molecules, but too energetic to allow many long-lived excited states of the neutral molecule to be produced. However, such sources cannot be separated from the gas inlet by any sort of solid window, so that very fast pumping, and possibly a flowing gas window, must be used. Usually only pulsed operation is possible, otherwise the intensity will be insufficient. Screening of detectors from the active ultraviolet photons is important.

VIII. Role of Excited Species A. EXPERIMENTS WITH EXCITED AND GROUND STATE IONS

Several experimental investigations have been carried out using atomic ions produced in ion sources capable of eliminating most of the long-lived excited ions in the beam (Hasted, 1954; Amme and Utterback, 1964). Most ion sources (conventional electron impact, oscillating electron, radio frequency discharge, etc.) are inferred to produce a proportion of electronically excited ions whose lifetimes are sufficiently long for the excitation to persist right up to the moment of collision. In general the larger the internal energy of the excited ion, the lower the proportion that is likely to be produced. However, it is not possible at this stage to make reliable deductions of this proportion from theoretical analysis of the source; certain indirect inferences may be

RECENT MEASUREMENTS ON CHARGE TRANSFER

255

made from the experimentally determined charge transfer cross-section functions, provided that comparison can be made between conventional ion source data and “ground state ion source” data. Ion beams can be produced with ions all in the ground state by means of: (1) surface ionization; (2) monochromated ultraviolet radiation ; (3) controlled energy electron fluxes. Surface ionization is, of course, limited to atoms of very low ionization potential, that is, to the alkali atoms. The first experimental comparison of inelastic cross sections obtained with ground state positive ions and with conventional ion sources was made (Fogel et al., 1959) using Li’ produced by surface ionization. The production of monochromated photon fluxes of sufficiently high energy to ionize gases requires the use of vacuum ultraviolet techniques and grazing incidence monochromation. For this reason these ion sources are unlikely to be as widely accessible as those using electrons of controlled energy. Ionization functions by electrons are zero at threshold, whereas those for ionization by photons are finite at threshold. When ionization yielding a number of excited levels of the ion is possible, one might expect a piecewise linear function for electron impact, and a step function for photons. Thus electrons are inferior but convenient tools for the production of ground state ion fluxes. A compromise must be struck between the maximization of ion flux for the subsequent collision experiment and the optimization of the resolution of the electron energy selection. Where the lowest long lifetime electronic excited state of the ion lies several electron volts above the ground state, thermionic electron energy distributions are sufficiently narrow to allow of effective elimination of the excited states; a conventional or specially adapted electron impact ion source is adequate (Stebbings et al., 1966; Bohme et al., 1967), and will naturally produce a greater ion flux than a source using momentum-analyzed electrons. The latter (Scott and Hasted, 1964; Hussain and Kerwin, 1965) are necessary in experiments where the lowest long-lifetime state of the ion lies within about 1 eV of the ground state. The dependence of the charge transfer cross section O + N z upon the ion source electron energy is shown in another article in this volume (Stebbings, 1968). Momentum analyzed electrons are not used. The O’N, experiment yields a large cross section for the production of Nzf by excited 0’ ’0, while the cross section for the ground state ion is small. Elimination of excited ions from the beam can be achieved by passing it through nitrogen gas. The higher the ion beam energy, the less serious the effect of elastic scattering. The filtering technique is indispensable when the threshold ionization function is such that ground state ions cannot easily be produced without momentum-analyzed electrons. However, a Nier-Bleakney electron impact source

256

J . B. Hasted

with capillary gas feed (Edmonds and Hasted, 1964) is adequate (Bohme et al., 1967) for the production of ground state 0 ' beams. Figure 6 shows the dependence of 0 ' intensity upon electron energy for ion source gas CO; the curve follows closely recent mass-spectrometric investigations (Cuthbert et al., 1966), and allows the electron energy scale to be corrected to the sharp ' 2D appearance. The 0 ' 'D Ar charge transfer is 1.17 eV break at 0 exothermic, while the ground state process Of 4SAr is 2.15 eV endothermic; at 0.8 eV impact energy, the latter cannot take place. Figure 6 also shows the electron energy dependence of the Ar + intensity produced in 0.8-eV collisions. Under these circumstances it is possible to extract reliable ground state O f collision cross sections from data obtained several electron volts below 0 ' D appearance. The figure gives a good indication of the capabilities and limitations of this approach.

'

Laboratory electron energy lev)

I

I

20 I

25 I

35

30 1

0

I

9-

-VI

'E

a

7-

E

-a 3-

20

25

Electron energy ( e V ) normalized to ' 0

30

35

onset of 0'

FIG. 6. Ground state ion source data: appearance potential functions of O f ions from CO by electron impact (Bohme et al., 1967); 360 pA electron current: pressure < 1 x 10Tom. Open circles represent production of Art ions by inelastic O + *DAr collisions at 0.8 eV impact energy; the yields of ions below O + '0 threshold can be regarded as background.

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257

Investigations using ions produced by collisions with electron beams, which have been energy selected in analyzers, were applied (Scott and Hasted, 1964; Hussain and Kerwin, 1965) to the symmetrical resonance charge transfer collisions of singly-charged heavy rare gas ions. The lowest state of these ions can exist with inner quantum number J = +, 3, the J = 3 being, for example, 0.67 eV the higher in Kr. Thus the possibility arises of the ions at the commencement and termination fo the collision being:

At sufficiently low impact energies, the processes involving energy defects should be unlikely, whilst the symmetrical processes would be expected to have large cross sections (Section 11). But in the initial experiments at 250 eV impact energy (Scott and Hasted, 1964) the ratio of J = 3 to J = 4 cross sections were found to be 10.1. In subsequent experiments (Hussain and Kerwin, 1965) using a finer resolution of electron energy, the ratio was found to increase with increasing impact energy and pass through a maximum value 0.6 at 700 eV. No quantitative explanation of this interesting situation has been evolved.

B. PROCESSES TERMINATING IN EXCITED SPECIES Charge transfer processes terminating in excited states, whether of the ionized or neutral species or both, may be investigated experimentally by monitoring the radiation emitted from the collision region, provided that the states in question are not metastable. When they are, the experimental techniques are more difficult, but in cases such as H 2s it is possible to quench the state by an electric field, so that the Lyman-cr radiation from H 2p can be monitored. The experimental data for the processes H++H+H2s+H+

(21)

H C+ N e + H 2 s + N e f (22) are displayed in Figs. 7 and 8. The neon cross-section function exhibits two maxima, of which one falls at the same energy as that of the H'Ne total charge transfer cross section (Stedeford and Hasted, 1955) which is dominated by the H 1s product. Such processes are suitable for the investigation of coupling effects. The contribution of the path H'Ne+ H 1s Ne' + H 2s Ne' is significant. Rare gas studies made by Geballe and his collaborators (Jaecks et al., 1965) and by Ankudinov et al. (1965) serve to emphasize its significance.

258

J. B. Hasted

Following the work of Love11 and McElroy (1965), various workers have attempted atomic multi-state approximation calculations. Poluektev and Presnyakov (1967) take the overall probability P of transition from initial state (0) to final state (2), including the contribution of intermediate state (l), as (23) P = P,, $POlP,, .

+

The results of their calculations are displayed in Fig. 7. In passing, we note that the most recent experiments of Ankudinov et al. (1967) are conducted with the collision products exposed to electric fields sufficient to cause Stark separation of the substates of the H 3s level, which decay producing Ha and Lyman+ radiation, the observed relative proportions of which are dependent on the electric field.

FIG.7. Total cross sections for production of H 2s in proton collisions with Ne: full line, experimental data of curve 1, Jaecks et al. (1965) and curve 2, Ankudinov et at. (1965); broken line, calculations of Poluektev and Presnyakov (1967).

Calculations of cross sections for process (22) have been made by Wilets and Gallaher (1966, 1967) using Sturmian eigenfunctions. Comparison with experiment is made in Fig. 8. Recent experiments using optical techniques for the detection of excited species (Lipeles et al., 1965; Lorents et al., 1966) have shown that certain rare gas charge transfer processes terminating in excited states are not improbable even at impact energies as low as several electron volts. Pseudocrossing of potential energy curves may contribute to such collisions. It is reported that the total emission function is sometimes oscillatory with impact energy.

RECENT MEASUREMENTS ON CHARGE TRANSFER

259

E

0

20

I

I

40

I I

I

60

t--f---J100

00

Elab( k e V )

FIG.8. Total cross sections for production of H 2s in proton hydrogen atom collisions; points with error bars, experiments of Stebbings et al. (1965); broken line, calculations of Bates and Williams (1964); dotted line, calculations of Bell and Skinner (1962); full line with points, calculations of Wilets and Gallaher (1967).

The possibility must be considered that coupling to intermediate atomic states contributes frequently to total capture cross sections in the far adiabatic region. It often happens that such cross sections are larger than is expected on an atomic two-state approximation. The u4 dependence predicted by Rapp and Francis (1962) is not apparent from the data, although this may, in part, be due to the experimental difficulties inherent in measuring very small cross sections. An outstanding example is the exothermic collision (24) for which the cross section (Fig. 9) is as large as lo-’’ cm2 at 4-eV impact energy (Bohme et al., 1967). The neon ions used in these experiments were produced by controlled energy electron impact, so that they could include only the ground states (J = 4, 3). Differential scattering experiments show little indication of curve crossing. There remains the possibility of coupling to excited states, for example to Ne’(3s “P),which can undergo the accidentally resonant process Ne++Ar-+Ne+Ar+

+

+

Ne+(3s“P) Ar(3p6 IS)+ Ne(3s[l&]) Ar+(3d4D).

(25)

IX. Miscellaneous Topics A.

IONIZATION WITH CAPTURE

Ionization with capture is a collision process which may be represented typically as A + + B + A + B2++ e 10/02. (26)

J. B. Hasted

260

“I 2

L

10-l~

0.01

FIG.9. Total cross sections (Bohme er al., 1967) for Ne+Ar charge transfer. Full circles indicate experiments carried out with ion beams containing excited states; open circles indicate experiments carried out with ground state ions. Full line represents the difference, presumably dominated by process 25. Circles with centers represent earlier data of Stedeford and Hasted (1955).

Let us consider how far such collision cross sections differ from, and perhaps exceed, those for multiple ionization in which no capture takes place A+

+ B + A + + B3++ 2e

10/12.

(27)

It is of particular importance because the statistical theory of Russek and Thomas (1958) is reasonably satisfactory in interpreting multiple ionization collisions, but takes no account of any inclusion of capture. Processes (26) and (27) can only be distinguished if the charge state of the primary beam is determined simultaneously with that of the slow ionized product, possibly by detection with coincidence. This was pointed out nearly ten years ago (Hasted, 1960), but the first measurements directed at measuring the cross section have only been reported recently (Afrosimov, 1967). The coincidence technique has been developed at Leningrad for the study of the conversion of energy from kinetic to internal in the multiple ionization process, but here it is combined with extraction from the collision chamber using transverse electric field. Transferred momentum, which might seriously complicate this technique, is minimized in the first experiments by the use of the proton as projectile and rare gases as targets.

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26 1

It has been found that the cross sections for ionization with capture 10/02 and 10/03 are indeed much larger than the corresponding ionization cross sections 10/n2 and 10/n3, n = 1, 2, . . . . The cross-section functions also maximize at much lower energies, as would be expected on the basis of the adiabatic maximum rule. No detailed comparison with a wide variety of processes is possible at this stage, but it is of interest that the adiabatic parameter for 10/03 is smaller than that for 10/02. It has been proposed (Parilis, 1967) that the ionization with capture process is dominated by capture into autoionizing states and so may be treated by theory similar to that for pure capture processes.

B. RADIATIVE CHARGE TRANSFER The process

in which electromagnetic radiation carries away the excess energy, can, under some circumstances, be more likely than the similar process in which no radiation is produced. Radiative charge transfer can only arise if the quasimolecule of the collision is formed in a state which can radiate to another state, which in turn can dissociate in the required manner. Daly and Powell (1966) have recently made some studies in helium using the trapped-ion technique (Baker and Hasted, 1966). They observed the process

+

He2+ He + He+

+ He+

(+ hv)

(29)

at thermal energies. The nonradiative process would be exothermic by 5.2 eV. Even allowing for pseudocrossing and for the possibility of the collision products being in excited states, it is likely to have a much smaller cross section than that for the radiative process which has been calculated by Allison and Dalgarno (1965). Daly did not attempt to detect radiation.

C. Two ELECTRON CAPTURE PROCESSES Two electron capture 10/12 by singly charged ions has been observed for some years in beam experiments, principally those conducted by Fogel and his colleagues [references in Kozlov and Bondar (1966)l. It is not necessary that the negative ions be formed in their ground states in these processes. A proportion of fast positive ions passing through a gas will be converted into

J. B. Hasted

negative ions, and will be observed as such provided that their lifetimes are sufficiently long for them to live until collected, or at least momentumanalyzed. The lifetimes of the negative ion states involved in the elastic scattering of electrons by atoms (Burke and Schey, 1962; Schulz, 1964) are, in general, far too short for this condition to be satisfied. Some of the importance of two electron capture processes lies in their use in double electrostatic generators (Jorgensen, 1965);positive ions are accelerated, converted into negative ions, and further accelerated in the same electric field so that the energy achieved is twice that available in the conventional electrostatic generator. Typical cross-section functions (Kozlov and Bondar, 1966) for two electron capture processes are shown in Fig. 10. Over a range of one and a half orders of magnitude, the cross section is proportional to the exponential of -l/v (Hasted, 1959). However, the low energy rate of rise is less rapid. The capture of two electrons by a doubly charged ion has been observed by Islam et al. (1962).

FIG.10. Total cross section functions for two electron capture by protons. Open circles, Kozlov and Bondar (1966); closed circles and open squares, Fogel er af. (1959), see Kozlov and Bondar (1966). Vertical lines indicate thresholds. Energy in keV.

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REFERENCES Afrosimov, V. V. (1967). Abstracts. Proc. Intern. Conf. Phys. Electron. At. Collisions, 5th, 1967. Akad. Nauk, Leningrad. Alam, G. D., Bohme, D. K., Hasted, J. B., and Ong, P. P. (1967). Abstracts. Proc. Intern. Conf. Phys. Electron. At. Collisions, 5th, 1967. Akad. Nauk, Leningrad. Allis, W. P. (1956). In “Handbuch der Physik” (S. Fliigge, ed.). Springer, Berlin. Allison, D. C. S., and Dalgarno, A. (1965). Proc. Phys. SOC. (London) 85, 845. Amrne, R. C., and Utterback, N. G. (1964). Atomic collision processes. Proc. Intern. Conf. on Phys. Electron. At. Collisions, 3rd, 1964, p. 847. North-Holland Pub]., Amsterdam. Anders, L. R., Beauchamp, J. L., Dunbar, R. C., and Baldeschwieler, J. D. (1966). J. Chem. Phys. 45, 1062. Ankudinov, V. A., Bobashev, S. V., and Andreev, E. P. (1965). Zh. Eksperim. i Teor. Fiz. 48, I , 40. Ankudinov, V. A., Bobashev, S. V., and Andreev, E. P. (1967). Abstracts. Proc. Intern. Conf. Phys. Electron. At. Collisions, 5th, 1967. Akad. Nauk, Leningrad. Baker, F. A., and Hasted, J. B. (1966). Phil. Trans. Roy. SOC.(London) A261, 33. Bates, D. R. (1960). Proc. Roy. SOC.A257, 22. Bates, D. R., and McCarroll, R. (1962). Advan. Phys. 11, 39. Bates, D. R., and Williams, D. A. (1964). Proc. Phys. SOC. (London) 83, 425. Bates, D. R., Johnson, H. D., and Stewart, A. L. (1964). Proc. Phys. SOC.(London) 84, 517. Bell, R. J., and Skinner, B. G. (1962). Proc. Phys. SOC.(London) 80, 404. Biondi, M. A., and Chanin, L. M. (1954). Phys. Rev. 94,910. Biondi, M. A., and Chanin, L. M. (1956). Phys. Rev. 106,473. Bohme, D. K., Nakshbandi, M. M., Ong, P. P., and Hasted, J. B. (1967). Proc. Intern. Conf. Ionization Phenomena Gases, 7rh, Vienna,1967. North-Holland Publ., Amsterdam, Boness, M. J. W., and Hasted, J. B. (1966). Phys. Letters 21, 526. Bullis, R. H. (1965). Abstracts. Proc. Intern. Conf. Phys. Electron. At. Collisions, 4rh, Quebec, 1965, p. 263. Science Bookcrafters, New York. Burke, P. G., and Schey, H. M. (1962). Phys. Rev. 126,147. Bydin, Yu. F. (1964). Zh. Eksperim. i Teor. Fiz. 46,1612. Bydin, Yu. F. (1966). Zh. Eksperim. i Teor. Fiz. 50,35. Chkuaseli, D., Gouldamachvili, A. I., and Nikoleychvili, U. D. (1963). Proc. Intern. Conf. Ionization Phenomena Gases, 6th, 1963, p. 475. SERMA, Paris. Cuthbert, J., Farren, J., Prahallada Rao, B. S., and Preece, E. R. (1966). Proc. Phys. SOC. (London) 88,91. Dalgarno, A., McDowell, M. R. C., and Williams, A. (1958). Phil. Trans. Roy. SOC.(London) A250,411. Daly, N. R., and Powell, R. E. (1966). Proc. Phys. SOC.(London) 89, 281. Dickinson, P. H. G., and Sayers, J. (1960). Proc. Phys. SOC.(London) 76, 137. Dillon, J. A., Jr., Sheridan, W. F., Edwards, H. D., and Ghosh, S. N. (1955). J. Chem. Phys. 23, 776. Drukarev, G. F. (1967). Soviet Phys. JETP (English Transl.) 52,498. Edmonds, P. H., and Hasted, J. B. (1964). Proc. Phys. SOC.(London) 84, 99. Everhart, E., Helbig, H. F., and Lockwood, G. J. (1964).Proc. Intern. Conf.Phys. Electron. At. Collisions, 3rd, Univ. CON.,London, 1963. North-Holland Publ., Amsterdam.

264

J. B. Hasted

Fedorenko, N. V., Afrosimov, V. V., and Kaminker, D. M. (1957). Soviet Phys.-Tech. Phys. (English Transl.) 26, 1861. Fehsenfeld, F. C., Schmeltekopf, A. L., Goldan, P. D., Schiff, H. I., and Ferguson, E. E. (1966). J. Chem. Phys. 44,4087, 3022,4095; 45, 25, 404. Firsov, 0. B. (1951). Zh. Eksperim. i Teor. Fiz. 21, 1001. Fite, W. L., Rutherford, J. A., Snow, W. R., and van Lint, V. (1962). Discussions Furuday SOC. 33,264. Flaks, I . P., and Ogurtsov, G. N. (1963). Soviet Phys. JETP (EngIish Transl.) 33, 748. Flaks, I. P., and Solov’ev, E. S. (1958). Soviet Phys.-Tech. Phys. (English Transl.) 3, 564. Fogel, Ya. M., Kozlov, V. F., Kalymkov, A. A., and Muratov, V. I. (1959). Zh. Eksperim. i Teor. Fiz. 36, 929. Ghosh, S. N., and Sheridan, W. F. (1957). J. Chem. Phys. 26,480. Giese, C. F., and Maier, W. B. (1963). J. Chem. Phys. 39, 197. Gilbody, H. B., and Hasted, J. B. (1956). Proc. Roy. SOC.A238, 334. Gilbody, H. B., Hasted, J. B., Ireland, J. V., Lee, A. R., Thomas, E. W., and Whiteman, A. S. (1963). Proc. Roy. SOC.274,40. Haas, R. (1957). Z. Physik. 148, 177. Hasted, J. B. (1951). Proc. Roy. Sac. A205,421. Hasted, J. B. (1954). Proc. Roy. SOC.A222, 74. Hasted, J. B. (1959). J. Appl. Phys. 30, 25. Hasted, J. B. (1960). Nutl. Acud. Sci. Nutl. Res. Council. Rept. No. 29. Hasted, J. B. (1962). In “Atomic and Molecular Processes” (D. R. Bates, ed.), p. 696. Academic Press, New York. Hasted, J. B. (1964). “ Physics of Atomic Collisions.” Butterworths, London. Hasted, J. B., and Lee, A. R. (1962). Proc. Phys. SOC.(London) 79, 1049. Hasted, J. B., Lee, A. R., and Hussain, M. (1964). Proc. Intern. Conf. Phys. Electron. At. Collisions, 3rd, Univ. CON.,London, 1963. North-Holland Publ., Amsterdam. Hussain, M., and Kerwin, L. (1965). Abstracts. Proc. Intern. Conf Phys. Electron. At. Collisions, 4th, Quebec, 1965, Science Bookcrafters, New York. Ishii. H., and Nakayama, K. (1961). Trans. Natl. Vacuum Symp. 8, 518. Islam, M., Hasted, J. B., Gilbody, H. B., and Ireland, J. V. (1962).Proc. Phys. SOC.(London) 79, 1118. Jaecks, D., van Zyl, B., and Geballe, R. (1965). Phys. Rev. A137, 340. Jorgensen, T. (1965). Phys. Rev. 140, A1481. Kaneko, Y.,Megill, L. R., and Hasted, J. B. (1966).J. Chem. Phys. 45, 3741. Kozlov, V. F., and Bondar, S. A. (1966). Zh. Eksperim. i Teor. Fiz. 50, 297. Kushnir, R. M., Palyukh, B. M., and Sena, L. A. (1959). Bull. Acad. Sci. USSR Phys. Ser. (English Transl.) 23,995. Landau, L. (1932). Phys. Z. Sowjet union 2,46. Lee, A. R. (1962). Thesis, Univ. of London, London. Lee, A. R. (1967). Private communication. Lee, A. R., and Gilbody, H. B. (1964). Proc. Intern. Conf. Phys. Electron. At. Collisions, 3rd, Univ. Coil., London, 1963. North-Holland Publ., Amsterdam. Lee, A. R., and Hasted, J. B. (1965). Proc. Phys. SOC.(London) 85, 673. Lipeles, M., Novick, R., and Tolk, N. (1965). Phys. Rev. Letters 15, 815. Lorents, D. C., and Aberth, W. (1965). Abstracts. Proc. Intern. Conf. Phys. Electron. At. Collisions, 4th, Quebec, 1965, p . 296. Science Bookcrafters, New York. Lorents, D. C., Aberth, W., and Hesterman, V. W. (1966). Phys. Rev. Letters 17, 849. Lovell, S. E., and McElroy, M. B. (1965). Proc. Roy. SOC.A283, 100.

RECENT MEASUREMENTS ON CHARGE TRANSFER

265

Mahadevan, P. (1967). Abstracts. Proc. Intern. Conf.Phys. Electron. At. Collisions, 5th. 1967. Akad. Nauk, Leningrad. Marchi, R. P., and Smith, F. T. (1965). Abstracts. Proc. Intern. Conf. Phys. Electron. At, Collisions, 4th, Quebec, 1965, p. 296. Science Bookcrafters, New York. Marino, L. L., Smith, A. C. H., and Caplinger, E. (1962). Phys. Rev. 128,2243. Massey, H.S. W. (1949). Rept. Progr. Phys. 12,248. Massey, H. S. W., and Smith, R. A. (1933). Proc. Roy. SOC.A142, 142. Matus, L., Hyatt, D. J., and Henchman, M. J. (1967). J . Chem. Phys. 46,March 15. McCarroll, R. (1961). Proc. Roy. SOC.A264, 547. McClure, G. W. (1966). Phys. Rev. 148,47. McElroy, M. B. (1963). Proc. Roy. SOC.A272,542. Mordvinov, Yu. P., and Firsov, 0. B. (1960). Soviet Phys. JETP (English Transl.) 12,301. Nichols, B. J., and Witteborn, F. C. (1966). NASA Tech. Note T N D-3265. Palyukh, B. M. (1967). Abstracts. Proc. Intern. Conf. Phys. Electron. At. Collisions, Sth, 1967. Akad Nauk, Leningrad. Parilis, I. (1967). Abstracts. Proc. Intern. Conf.Phys. Electron. At. Collisions, 5th, 1967. Akad Nauk, Leningrad. Patterson, P. L. (1966). JILA Rept. No. 87. Univ. of Colorado, Boulder, Colorado. Perel, J., Vernon, R. H., and Daley, H. L. (1965). Phys. Rev. 138,A837, 336. Persson, K. B. (1965). J . Appl. Phys. 36,3086. Poluektev, I. A., and Presnyakov, L. P. (1967). Abstracts. Proc. Intern. Con$ Phys. Electron. At. Collisions, 5th, 1967. Akad Nauk, Leningrad. Rapp, D., and Francis, W. E. (1962). J. Chem. Phys. 37,2631. Russek, A., and Thomas, M. T. (1958). Phys. Rev. 109,2015. Schlier, C. (1967). Reported at Spring meeting of German Phys. SOC. Schram, B. L., Adamczyk, B., and Boerboom, A. J. (1966). J. Sci. Instr. 43, 638. Schulz, G. J. (1959). Phys. Rev. 116, 1141. Schulz, G. J. (1962). Phys. Rev. 125,229. Schulz, G.J. (1964). Proc. Intern. Conf. Phys. Electron. At. Collisions, 3rd, 1964. NorthHolland Publ., Amsterdam. Scott, J. T., and Hasted, J. B. (1964). Mass-Spectry. Symp., Paris, 1964. Inst. of Petroleum, ASTM, Philadelphia, Pennsylvania. Smirnov, B. M., and Firsov, 0. B. (1964). Zh. Eksperim. i Teor. Fiz. 47,232. Smith, F.J. (1964). Proc. Phys. SOC.(London) 84, 889. Smith, F. J. (1966). Phys. Letters 20,271. Snow, W. R. (1966). Thesis, Univ. of Washington, Seattle, Washington. Stebbings, R. F. (1968). This volume. Stebbings, R. F., Smith, A. C. H., and Ehrhardt, H. (1963). J. Chem. Phys. 39,968. Stebbings, R. F., Smith, A. C. H., and Ehrhardt, H. (1964). J. Geophys. Res. 69,2349. Stebbings, R. F., Young, R. A., Oxley, C. L., and Ehrhardt, H. (1965). Phys. Rev. 138, 1312. Stebbings, R. F., Turner, B. R., and Rutherford, J. A. (1966). J. Ceophys. Res. 71,771. Stedeford, J. B. H., and Hasted, J. B. (1955). Proc. Roy. SOC.A227,466. Stevenson, D.P., and Schissler, D. P. (1955). J. Chem. Phys. 23, 1353. Talrose, V. L., and Frankevich, E. L. (1960). Russ. J. Phys. Chem. (English Transl.) 34, 1275. Talrose, V. L., and Lyubimova, A. K. (1952). Dokl. Akad. Nauk SSSR 86,909. Trujillo, S. M., Neynaber, R. H., and Rothe, E. W. (1966). Rev. Sci. Instr. 37, 1655. Wannier, G.H. (1951). Phys. Rev. 83,281. Wilets, L.,and Gallaher, D. F. (1966). Phys. Rev. 147, 13.

266

J. B. Hasted

Wilets, L., and Gallaher, D. F. (1967). Abstracts. Proc. Intern. ConJ Phys. Electron. At. Collisions, Sth, 1967. Akad Nauk, Leningrad. Wobschall, D. (1965). Rev. Sci. Instr. 36,466. Zener, C.(1932). Proc. Roy. SOC.A137, 696. Ziegler, B. (1953). Z . Physik 136, 108. Ziemba, F. P., Lockwood, G. J., Morgan, G. H., and Everhart, E. (1960). Phys. Reo. 118, 1552.