Experiments with Merging Beams

EXPERIMENTS WITH MERGING BEAMS RO Y H . N E YNABER Space Science Laboratory, General DynamicslConuair San Diego, California I. Introduction.. ................................................... 11. General Principles ................................................

111. Ion-Neutral Reactions ............................................ A. Symmetric-Resonance Charge Transfer .......................... B. Charge Rearrangement ........................................ IV. Ion-Ion Reactions ................................................ A. Symmetric-Resonance Charge Transfer .......................... B. Mutual Neutralization ......................................... C. Radiative Recombination. ...................................... V. Neutral-Neutral Reactions ........................................ A. Charge Transfer and Ionization ................................. B. Rearrangement.. ............................................. VI. Electron-Ion Reactions. .......................................... A. Theory ...................................................... B. Dissociative Recombination ................................... VII. Current or Very Recent Studies ................................... VIII. Concluding Remarks. ............................................ References .....................................................

57 59 62 62 72 80 80 83 87 89 90

,100

.lo0

100 .lo1 .lo5 .lo6 .lo7

I. Introduction The merging beams (mb) technique was originally developed to study twobody collisions in the energy range from a few tenths to several electron volts (henceforth called the low energy region) because other experimental methods could not be used in this range. Typical problems with these other methods include low ion intensity because of space charge effects, poor energy resolution, and a low upper limit to the energy (i.e., about 0.3 eV) of neutrals generated from thermal sources. The mb technique consists of two beams traveling in the same direction along a common axis. Various other names that have been given to the method include superimposed beams, overtaking beams, and confluent beams. The laboratory energy of each beam is typically several kiloelectron volts with an energy spread of a few electron volts, whereas the relative energy of the beams in the c.m. system is in the low energy region. The energy spread 57

58

Roy H. Neynaber

at this relative energy is generally just a few percent. The use of high laboratory energies minimizes space charge difficulties. The method can also be used to study collisions at energies outside of the low energy region, e.g., at thermal energies and at several hundred electron volts. The mb technique is also of interest in the low energy region and above because it can be used as a method, with good energy resolution, for studying reactions between two, general labile species. In ion-neutral studies up to the present, crossed beams have been used where the neutral species is labile. This conventional method is advantageous when the neutral species can be obtained from a thermal source (e.g., 0 from an rf source or H from a high temperature oven) since beam fluxes from such a source are relatively large. However, a more comprehensive series of free radicals can be obtained by the more general technique of neutralizing the parent ion by charge transfer. For reactions involving many of these species, the mb technique may be the only method for measuring cross sections because larger signals (arising from the availability of more intense beams and longer interaction regions) can be obtained for a given interaction energy. Other merits of the mb technique include easy collection of products for total reaction cross section measurements, and relative ease in detecting all products of reaction. Davis and Barnes (1929a,b, 1931), Barnes (1930), and Webster (1930) merged beams of electrons and alpha particles many years ago. More recently, Cook and Ablow (1959, 1960) suggested the use of superimposed beams for the study of collisions between two heavy particles. The possibility of a very low interaction energy, coupled with a high energy resolution was first pointed out by Trujillo et al. (1963, 1965). The technique can be used to investigate ion-neutral, ion-ion, neutralneutral, and electron-ion reactions. Merging beams studies that have been conducted of such processes will be discussed. Since the method (employment of the concept of low relative energy coupled with high energy resolution is assumed) is in its infancy, the total number of such experiments is small. An earlier review of the subject has been written by the author (Neynaber, 1968). It will be noted, as the discussion proceeds, that an mb apparatus is relatively complicated. Its configuration is tied closely to the type of reaction for which it is to be applied, and this configuration is generally quite inflexible. Although some of the machines to be discussed have been used to study more than one type of process, it would be safe to say that none of them is a universal apparatus for the study of all the above types of reactions. The development of merging beams has ushered in the concept of the study of two-body collisions by the intersection of two beams at a small angle. This method is characterized by properties, as one might expect, that are in between those of crossed and merging beams. The method has been called inclined beams.

EXPERIMENTS WITH MERGING BEAMS

59

There will be no further discussion of inclined beams except to comment briefly on the contemplated work of two groups of scientists. M. F. Harrison and R. Rundel of the Atomic Energy Laboratory at Culham are constructing a machine in which two beams will intersect at 20”. They plan to study H + + H- + H + H at interaction energies of about 200 eV to 30 keV. An advantage of using inclined instead of merging beams for this experiment is that the parent ion of each product can be identified. However, for the same laboratory energy of the reactants, lower interaction energies could be achieved in an mb experiment. Harrison and Rundel also plan to study H + + H- + H(2S) + H and H C + H - + H + H + e using the inclined beams method, J. Schutten and colleagues of the FOM Institute for Atomic and Molecular Physics, Amsterdam, are also constructing an inclined beams machine in which the angle of intersection will be 10”. Included in their plans are experiments to measure cross sections for multiple ionization in neutralneutral, ion-neutral, and ion-ion collisions. The inclined beams method will also enable them to identify the parent ion of each product for all reactions studied. In addition, the mechanics of bringing about the interaction of two charged beams of the same polarity is easier for inclined than for mb systems.

+

11. General Principles

A low interaction energy (i.e., relative energy in c.m. coordinates) can be obtained with an mb system because the difference in beam velocities can be made small even though high energy beams are employed and because the difference of the laboratory energies of the beams is many times larger than the interaction energy. Analytical expressions are presented below. If we assume that all particles in the two beams move along parallel lines (ideal case), then the interaction energy W is

w = t p ( c , - u$,

(1)

where p is the reduced mass of the system, and u1 and u2 are the laboratory velocities of the particles in each beam. We may also express W a s follows:

where m, and m 2 are the masses, and El and E, are the laboratory energies of the particles in each beam. For simplicity, let m, = m, = m. The general conclusions reached for this case apply equally well when m, # m 2 .For equal masses, Eq. (2) becomes

60

Roy H. Neynaber

When the absolute value of the difference in beam energies, AE, is small compared to these energies and E is the average of the two beam energies, it can be shown that W w AE ' / 8 E .

(4)

Now define D = AE/ W. The term D is an energy deamplification factor. We have (again for small A E ) D = A E / W z 8 E / A E + 1.

(5)

Equation ( 5 ) indicates that the interaction energy is small compared to the difference of the laboratory energies of the particles for large laboratory energies. As an example, let El = 5000 eV and E, = 5100 eV. Then AE = 100 eV, and from Eq. (5), D w 400 and W w 0.25 eV. The concept of a deamplification factor can also be applied to the more realistic case of two beams each having an energy distribution rather than being monoenergetic. From Eqs. (4) and (5) it can be shown that a perturbation 6 E in AE gives approximately the following perturbation 6 Win W :

6 W/W x 2 6E/ W D =2 6E/AE.

(6)

Assuming a reasonable energy spread, i.e., full width at half-maximum, of

1.5 eV for each beam (6E = & 1.5 eV), we obtain an approximate spread in W of 6 W = 10.0075 eV, or an uncertainty in W of A 3 %. Therefore, because

of the deamplification factor for an mb experiment, good resolution for the interaction energy can be obtained. Similarly, small, random fluctuations in El or E, result in negligible perturbations in W. Equation (6)rigorously applies to rectangular energy distributions. If the distributions are Gaussian, the expression for 6 W/W should be divided by Therefore, for Gaussian distributions, Eq. (6) conservatively estimates the fractional perturbation in W . We have previously assumed that the particles in the two beams have parallel paths. In a realistic case, there is nonparallelism, and transverse velocities exist. This could result in an average energy of interaction Wfor the realistic case that is different from W , and could cause an uncertainty in the measured cross section. Thus it is necessary to take proper account of transverse velocity components, or to ensure that the largest of these is insignificant. The mathematical formalism for extracting a cross section from an mb measurement in which transverse velocities exist appears formidable (Cook and Ablow, 1959, 1960). To circumvent this task it seems desirable to eliminate particles with large transverse velocity components and to keep only those particles with sufficiently small transverse velocity components. The undesirable particles can be removed by passing the beams through

fi.

EXPERIMENTS WITH MERGING BEAMS

61

two collimating apertures. Small, residual transverse components exist after the passage of the beams through these apertures. For the case when the distance I between the collimating apertures is equal to the length of the interaction region (i.e., that region in which cross section measurements are made), when AE is small compared to the beam energies, and when m, = m2, we have derived the following expression for the upper bound of the fractional difference between Wand W : ( W - W ) /W c 0.54(Ed/AEl)2,

(7)

where W is the energy of interaction averaged over all possible angles of intersection of the beams and over all points in the interaction region, and d is the diameter of the collimating apertures. Applying Eq. (7) to the previous numerical example and choosing the values d = 0.25 cm and 1 = 25 cm, we obtain an upper bound on the percentage difference of approximately 13.5%. Similar studies have been made for the effect of the residual transverse components on the measured cross section. An energy dependence of the cross section must be assumed to make the computations. For a resonant charge transfer process at low energy the effect has been computed and, for the conditions above, the cross section for the realistic case is different from that of the ideal case by less than 6 % . As W increases, these percentage differences due to the residual transverse components become even smaller for a given E. An experiment might consist of determining the number of particles per second S which has been generated in the interaction region by the desired reaction. The expression relating the cross section Q in square centimeters per particle to S is (again assuming equal masses)

Q = (S/I)(EiEz/mV1", where

s,

(8)

I = J1J 2 d x d y d z , and the integral is performed over the volume of the beams in the interaction region; z is along the axis of the beams in the interaction region; J1 and J, are the beam flux densities in particles per square centimeter per second for the respective particle energies El and E2 in ergs. Since the integrand is nonzero only where the beams overlap, I is called the overlap integral. Also, W is in ergs, and rn in grams. The mb technique should be useful for measuring total reaction cross sections even when the collisions are accompanied by appreciable c.m. scattering since the maximum solid angle for reaction products is much smaller than that for conventional experiments. This is because the kinetic

62

Roy H . Neynaber

energy in the center of mass is much smaller than the laboratory energy of the reactants. For example, with a kinetic energy in the center of mass of several electron volts and initial reactant energies of several kiloelectron volts, the products are confined to a cone whose vertex angle is a few degrees. Finally, the reaction products are easily detected by secondary electron emission because they have large laboratory kinetic energies.

III. Ion-Neutral Reactions A. SYMMETRIC-RESONANCE CHARGE TRANSFER 1. Double Source Experiment Symmetric-resonance charge transfer experiments in Ar have been conducted with a double source apparatus (Neynaber et al., 1967a,b). Relative cross-section measurements were made in a range of W from 0.1 to 20 eV. In addition, absolute cross section measurements were made for W = 0.3 and 100 eV. In Section III,A,2, similar experiments in H and D will be discussed in which only a single source was used. a. Description of Apparatus. The double source apparatus (Trujillo et al., 1966) was designed to study the Ar reaction by observing product ions. The process is Arc(El) Ar(Ez)--+Ar(EA +Art(.&) (9) where the E's represent the laboratory energies of the particles in a given interaction region. Outside of the interaction region, the laboratory energy of the particles in each primary beam was Eo = E, = 3000 eV. For E, > E l , as was the case, El = (3000 - A E ) eV, where AE was defined in Section 11. A schematic diagram of the apparatus is shown in Fig. 1. The sources were of a low-pressure, oscillating-electron-bombardment type (Carlston and Magnuson, 1962) which produced beams with a spread of about 1.5 eV. An Ar' (3000 eV) beam from source 1 was merged with a mechanically chopped Ar (3000 eV) beam. The Ar beam was obtained by passing Ar' from source 2 through a charge-transfer cell containing H, . It was assumed that negligible energy was lost in the near-resonant charge transfer process and that the energy and energy spread of the Ar beam emerging from the cell were the same as that of the Ar' beam entering the cell. An electric field between the condenser plates that follow the cell was used to remove Ar ' which did not undergo charge transfer. The superimposed beams were then collimated to eliminate large transverse velocities and were passed into a decelerating-accelerating system containing the interaction region. The energy difference between Ar and Ar' that was necessary to

+

MOVABLE DETECTOR APERTURE

FIG.1. Schematic diagram of douole source, mb apparatus for studying Ar+

+ Ar -+ Ar + Ar+. Apertures are not to the scale shown.

64

Roy H . Neynaber

obtain the desired interaction energy W was established by raising the potential of the interaction region by an appropriate amount AE/e, where e is the magnitude of the electronic charge. The primary ion beam was thereby decelerated to (3000 - A E ) eV at the entrance to the interaction region and accelerated to 3000 eV at its exit. A schematic diagram of the apparatus for achieving this is shown in Fig. 2. Argon ions produced by the desired process GRID ,4

LFIRST COLLIMATING APERTURE

FIG.2. Schematic diagram of deceleration-acceleration apparatus for double source, mb system. For details of the geometry see Neynaber et al. (1967a). The grid structure and spacing between grids were chosen to achieve a compromise between maximum transmission, minimum electric field penetration, and uniformity of electric fields. Grids 2 and 3 are electrically connected together. Grids 3 and 4 and the electrostatic screen are attached to the movable detector assembly (see Fig. 1 ) and could be translated in all directions.

in the interaction region were accelerated at its exit to an energy equal to (3000 + AE) eV. After the merged beams left the interaction region, they entered the demerging magnet. The function of the magnet was to separate fast neutrals from primary and product ions. The magnet was not designed with a resolution that could separate the primary from the product ions. Other undesired particles were prevented from reaching the detector, a Bendix electron multiplier, by employing several components of a detector assembly (shown in Fig. 1 within the dotted box). One of these components was a retarding grid which was at a potential that would allow product ions to pass through but which would retard both the primary ions and ions formed by other processes. Another component was a low-resolution, hemispherical, electrostatic energy analyzer. Its purpose was reduction of ion noise, which is defined later. The sweep plates following the hemispherical analyzer were not incorporated in this experiment. Finally the output of the multiplier was fed into a lock-in amplifier. The detector assembly was supported on a carriage which could be moved along a set of rails parallel to the axis of the interaction

EXPERIMENTS WITH MERGING BEAMS

65

region and in directions perpendicular to this axis. The purpose of the movable assembly was to permit profiles of each primary beam to be taken along the interaction region to obtain information for calculating Zof Eq. (8). b. Absolute Cross Section Determinations. To obtain an absolute value of the neutral current for determining absolute cross sections, the secondary electron emission coefficient y of the “dirty” A1 plate (part of the neutral beam monitor shown in Fig. 1) for neutrals must be known. It was assumed that y was the same for ions and neutrals of the same energy. Utterback and Miller (1961) have obtained experimental evidence that the y’s are equal to within 20 % at energies above several hundred electron volts for N, on gold surfaces that were not clean. Haugsjaa et al. (1968) have found similar evidence for Ar above 140 eV on a “dirty” gold surface. Other investigators have also reported equal coefficients for energies above 100 eV (Berry, 1948; Rostagni, 1934). With this assumption, an absolute measurement of the neutral current was obtained. The y for ions was measured using ions from source 2, but without gas in the cell, with grounded condenser plates at the exit of the cell, and with the merging and demerging magnets turned off. The ratio of ion currents at the A1 plate with extraction and with suppression of secondary electrons was equal to y + 1. For absolute cross section measurements, J1 and J2 were measured at a number of points in space to permit I to be evaluated numerically. The flux densities were determined by measuring the current under investigation after passing it through an aperture of known diameter. c. Noise. A typical signal arising in the interaction region was about A (the primary beams were each several hundred nanoamperes). Two sources of noise were important. One of these depended only on the presence of the primary ion beam while the other depended only on the presence of the primary neutral beam. These are designated as ion noise and neutral noise, respectively. The ion noise was partially dependent, whereas the neutral noise was totally dependent, on background pressure. Since only the primary neutral beam was chopped, the output from the lock-in amplifier for neutral noise was coherent while that for ion noise was random. It was not surprising that these sources of noise existed since the ratio of desired signal to primary beam current was The effect of ion noise was reduced by using suitable integrating times. The coherent, or neutral, noise was probably due to stripped neutrals from the primary beam. The least energy the primary particles could lose in stripping reactions was their ionization energy. The voltage of the retarding grid could thus be set to minimize the neutral noise without reducing the desired signal. The voltage was (2985 + AE/e) V. The existence of excited neutrals in the beam would probably result in more neutral noise than for a ground state primary beam since excited particles would have larger stripping

66

Roy H . Neynaber Neynaber

cross sections. Since the neutral noise could be obtained separately, it could be subtracted from the signal which appeared with both beams present. There was evidence that excited species existed in the Ar beam when the gas in the charge transfer cell was Ar, since for a given neutral intensity and grid potential the neutral noise was larger than when the gas in the cell was H, . Accordingly, H, was used. d. Results and Discussion. The potential of the interaction region was raised to that AE/e appropriate for the desired W . From the total output of the lock-in amplifier, neutral noise and an anomalous output that was dependent on the presence of both beams when AE/e was zero were subtracted. The net result S was proportional to a relative Q. Each cross-section measurement at W was accompanied by a measurement at 1 eV. From these measurements and Eq. (8), the square root of the ratio of the cross section at W , Qw, to the cross section at 1 eV, Q , , was computed. These ratios, (Qw/Q1)''2, are shown 1.3

I

: *z+s-d: ;-

I

I

r

I

I 1 1 1 1

I

I

0.7

'

1

l

l

l

l

I

>

-

FIRSOV ;RAPP AND FRANCIS PRESENT EXPERIMENT

OI 0.9o.8-

l

a..

-_

POPESCU IOVITSU AND IONESCU -PALLAS 1

1

I

I

1

I l l

1

I

I

I

1

1 1 1

-2

1 I

FIG.3. (a) (QW/QI)'12vs W for symmetric-resonance charge transfer in Ar. Each dot represents a value obtained for a single measurement; a dot accompanied by a number 2 means that two measurements resulted in the same quantity. Crosses indicate arithmetic averages of dots. The standard deviation of the slope of the experimental line confines the extremities of that line to the space between the arrows. (b) Square root of the absolute cross section for symmetric-resonance charge transfer in Ar.

67

EXPERIMENTS WITH MERGING BEAMS

in Fig. 3(a). The theoretical results of Firsov (F) (1951), Popescu-Iovitsu and Ionescu-Pallas (PI) (1960), and Rapp and Francis (RF) (1962) are included in the figure. The slopes of the F and R F lines are almost equal. The error bar is about f6 % and represents the standard deviation for measurements at 10 eV. Uncertainty in (Qw/Q1)1/2at W = 0.1 eV due to the anomalous signal, end effects of the decelerating-accelerating system, and residual transverse velocity components of the beams in the interaction region is less than 8 % . At higher W the uncertainty is even smaller. The experimental line is made to pass through ( Qw/Q,)”* = 1 at 1 eV. Its slope was obtained from the crosses (properly weighted) by the method of least squares. From Fig. 3a it is noted that a straight line appears to fit the crosses. The extremities of the F and RF lines fall well within the limits of the extremities of the experimental line. The end points of the PI line fall outside these limits. Absolute Q measurements at 0.3 eV were made using the technique described above and also a slightly different one (Trujillo et al., 1966). (This latter method was also used to measure an absolute Q at 100 eV.) The results were compatible and gave an average Q at 0.3 eV of 47.1 A’ with an estimated total error of + 25 and - 21 % . The error excludesthe possibility of metastable reactants, about which little can be said. This value of Q together with the experimental line in Fig. 3a were used to obtain the experimental line in Fig. 3b. The R F line is in agreement with the experimental results, the F and PI lines are not. The average value of the cross-section measurements at 100 eV is 18.1 A2 with a total error (again excluding the possibility of metastable reactants) of + 18 and - 13% . It can be shown that this cross section is compatible with the results in Fig. 3b. Table I is a compilation of some representative theoretical and experimental cross sections for the resonant charge transfer of Ar at W = 100eV. The TABLE I CROSSSECTIONSAT W = 100 eV FOR RESONANT CHARGE TRANSFER OF Ar Experimental or theoretical

Result

Reference Potter (1954) Ghosh and Sheridan (1957) Popescu-Iovitsu and Ionescu-Pallas (1960) Cramer (1 959) Rapp and Francis (1962) Hasted (1951) Kushnir ef al. (1959)

E E T E T E E

19.9 20.9 23.0 23.2 24.0 27.0 30.8

(A2)

68

Roy H. Neynaber

values for the mb experiment agree with Potter’s and Ghosh and Sheridan’s within the mutual errors of the experiments. The experimental cross sections listed in Table I were obtained using beam-gas techniques. Their accuracy depends linearly upon absolute pressure measurements performed with a McLeod gage. These measurements were made prior to the discovery of a systematic error in the normal use of McLeod gages, i.e., the Ishii-Nakayama effect (Ishii and Nakayama, 1962; Rothe, 1964). This error would result in measured cross sections that are too large by, perhaps, 10-30 % . Systematic errors in absolute Q determinations for the mb experiment could be due to excited species in either primary beam (the magnitude of this error is difficult to estimate), the determination of y for neutrals (-5 to + lo%), and the determination of the overlap integral I (+ 10 %). An estimate of the composite systematic error (excluding errors due to excited states) is then - 5 to + 14 ”/,. Excited species could be more easily controlled through the use of electron-bombardment ion sources which operate at lower pressure and in which only single collisions between electrons and atoms occur (Stebbings e t a / . , 1966). The determination of y for neutrals could be made by the alternate method of measuring the heat input to a thermopile from the neutral beam; then the assumption that the y for ions and neutrals is the same would not be necessary. Finally, the overlap integral could be more accurately and readily determined by incorporating automatic or semiautomatic equipment to permit J , and J , to be measured at many more points in the interaction region.

2. Single Source Experiment Belyaev er a/. (1966, 1967a,b) have conducted mb studies of the symmetricresonance charge transfer processes H f + H -+ H + H + and D + D -+ D + D + in a range of W from 5 to 100 eV using a single source apparatus. A mixed atom-ion beam was obtained through partial charge transfer of a single ion beam from the source. In the interaction region the ion beam passed completely inside the atomic beam. a. Description ofApparatus. Figure 4 is a schematic diagram of the apparatus. The anode of the ion source (which is described as an oscillating type operating in a longitudinal magnetic field) was maintained at a potential E/e = + 1 kV with respect to the system. Protons (deuterons) were extracted from this source and focused by lens 2 into a 90“, second-order spatial focusing, monochromator magnet 3. About 10 % ofthese ions were neutralized when the beam passed through the charge transfer cell 5, which contained COz . Some of the resultant atoms were left in the metastable 2 s state. After collimation of the mixed atom-ion beam, the metastable atoms were con-

+

EXPERIMENTS WITH MERGING BEAMS

69

FIG.4. Schematic diagram of single source, mb apparatus. (1) ion source; (2) extracting lens; (3) monochromator magnet; (4) quadrupole lenses; (5) charge transfer cell; (6, 9-13, 15) circular apertures; (7) condenser array; (8) region of high vacuum; (14) collision chamber; (16, 23) electron suppressors; (17) Faraday cylinder; (18) electrometer; (19) analyzing sector magnet; (20,22) adjustable holes; (21 ) cylindrical condenser; (24) calibrating Faraday cylinder; (25) galvanometer; (26) detector; (27-30) diffusion pumps; (31) titanium pump; (Sl, S,) switches.

verted to the ground state during their passage through a n electrostatic field produced by the condenser array 7. The electrodes of this array were divided into three sections, the field in the center section being opposite to that in the end sections ( S , in position a). The ratio of the fields in the sections was chosen so that the ion beam, after passing through the electrodes, returned to the extension of its previous trajectory. The angular divergence of the beam entering the collision chamber (interaction region) 14 was determined by the circular apertures 6 and 9 and was 1'20'. Aperture 9 was placed at the focus of magnet 3. In the collision chamber the energy spread of the ion beam was about 4 eV, and the ion current was approximately A. Because of the discharge voltage of the source, the energy spread of the ion beam at the exit of the source was considerably larger than it was in the interaction region. The laboratory energy and energy spread of the atom beam just outside the collision chamber were presumably about the same as for the ion beam since near-resonance charge transfer took place in cell 5. The collision chamber was cylindrical. At the ends were circular apertures I 1 and 12. The curved surface consisted of fine wires parallel to the axis of the cylinder. The chamber was maintained at an appropriate potential, AE/e, and was used in much the same way as the decelerating-accelerating system previously described for the double source experiment.

70

Roy H. Neynaber

The weakly focusing electrostatic lens formed by apertures 9-11 at the entrance to the collision chamber guaranteed passage of the ions inside the atomic beam along the entire length of interaction. Ions formed in the collision chamber (including stripped primary neutrals) passed through an energy analyzer consisting of a sector magnet 19 and a cylindrical condenser 21, which were tuned for ions of energy E + AE. Primary particles were rejected, but the resolution of the analyzer was not sufficiently good to eliminate neutral noise. The ions that passed through the analyzer were measured at the detector by counting scintillations induced by secondary electrons. These electrons were ejected from a metal plate by the impinging ions and accelerated to 15 keV. To minimize neutral noise, the Torr. pressure in the collision chamber was maintained at about 2 x 6 . Measurements. Cross sections were determined by applying Eq. (8); S was equal to the ion counts per second when the primary ion beam was not deflected away from the collision chamber by the condenser array 7 ( S , in position a ) minus the counts per second when the beam was deflected ( S , in position 6). Neutral noise was eliminated by taking this difference. The ion current corresponding to this difference was in the range lo-’’ to A. In determining the overlap integral, it was assumed that the flux density of the neutral component of the mixed beam was uniform everywhere in the interaction volume, i.e., that volume of space swept out by the narrower ion component of the beam. Under this assumption, the integral was equal to the product of the currents of both components in the interaction region, the length of the region, and the inverse of the cross sectional area of the neutral beam in the region. The ion current through the collision chamber was measured at the Faraday cup 17 ( S , in position a). The bottom of this cup was removable. The neutral current was determined by (1) measuring the current of secondary electrons from the bottom of the cup ( S , in position b) produced by the ion current and that produced by the neutral current and (2) measuring, in a separate experiment, the ratio of the secondary electron emission coefficients of the same metal as the bottom of the cup for ions and atoms at an energy of 1 keV. The ratio was approximately unity for protons and hydrogen atoms and for deuterons and deuterium atoms. An average cross sectional area of the atomic beam was determined from geometrical considerations. The length of the interaction region was obtained from the potential distribution along the axis of the collision chamber. This distribution was measured using an electrolytic bath. c. Results and Discussion. Cross sections as a function of Ware shown in Fig. 5. Included are the results of the single source mb experiments, of other experiments (Fite et al., 1960; Fite et al., 1962; McClure, 1966), and of theoretical studies (Smirnov, 1964; Dalgarno and Yadav, 1953). Belyaev

71

EXPERIMENTS WITH MERGING BEAMS INTERACTION ENERGY, wd (eV)

10

10 6 n

5

N

ms

4

rl I

a

0

3

U

2

1

loo

101

lo2

10

lo4

INTERACTION ENERGY, Wp(eV)

FIG.5 . Cross sections for charge transfer of protons in hydrogen atoms (1, 3-7) and deuterons in deuterium atoms (2) as a function of interaction energy (W, for proton experiment and W, for deuteron experiment). ( I , 2) single source, mb results; (3) Fite et al. (1960); (4) Fite et al. (1962); ( 5 ) McClure (1966); (6) theoretical curve of Smirnov (1964); (7) theoretical curve of Dalgarno and Yadav (1953). The values of W, and W dassociated with any point on the graph correspond to the same relative velocities of particles in the H H and D D reactions.

+

+

et al. (1967a,b) indicate that the uncertainty in the mb cross sections was caused mainly by statistical error in the measurement of S of Eq. (8) and by the presence of energy and angular spread in the interacting beams. It is noted that for the same relative velocity, the mb cross sections for the H + + H and D + + D reactions are the same. This is expected on theoretical grounds. Using crossed beams to study the same reactions (where proton energies are in the range from about 200 to 1500 eV), Fite et al. (1958) do not achieve this result. Figure 5 shows quite good agreement between the various experimental results. Agreement of experiment with theory is best at the higher energies. Resolution in W could be improved in this experiment by using a source that emitted ions with a smaller energy spread. A source like those used in the double source experiment would probably suffice. The aperture arrangement at the entrance and exit of the collision chamber is not the most effective means of achieving uniform decelerating and accelerating fields and of minimizing field penetration into the chamber. Grids such

72

Roy H . Neynaber

as those used in the system shown in Fig. 2 would be better and would probably allow measurements to be made at considerably smaller W. A disadvantage of the single source experiment (in addition to the fact that the reactants must be of the same species) is the inability to use modulation techniques effectively. Much of the statistical error in the measurements probably arises from ion noise. This could be largely eliminated as a source of trouble if the neutral beam were modulated and phase and frequency-sensitive detection methods were used. The difficulty of modulating the neutral beam without modulating the ion beam is obvious. Finally, a better determination of the overlap integral could be obtained if profiles of the atom and ion components of the beam could be determined in the interaction region. The single source experiment is another good example of the potential of the mb technique. With the method, cross sections for the H + + H and D + + D reactions have been obtained at lower W than have been achieved previously.

B. CHARGE REARRANGEMENT

+ H,+H,+ + H study of H,+ + H, H 3 + + H has been made with merging beams

1. H2+

A + (Neynaber and Trujillo, 1968) and represents the first application of the technique to charge rearrangement (ion-molecule) reactions. a. Experimental. Except for one modification, the apparatus used for this study is identical to that employed in the investigation of symmetric-resonance charge transfer in Ar (see Fig. 1). An H2+beam from source 1 was merged with a mechanically chopped H, beam. The energy of the particles in each beam was 3000 eV. The H, beam was obtained by passing H2+ from source 2 through a charge-transfer cell The energy difference between H2+and H, that was necessary containing H2. to obtain the desired interaction energy W was established by raising or lowering the potential of the interaction region by an appropriate amount AE/e. The product ions H,+ were then separated from the reactants by the demerging magnet. Other undesired particles were prevented from reaching the detector by employing the retarding grid and the hemispherical electrostatic energy analyzer tuned for the passage of the H,'. Before the addition of a set of sweep plates after the electrostatic analyzer (these plates were not used in the apparatus employed for charge-transfer studies and represent the one modification of that apparatus), the multiplier output was fairly sensitive to small changes in the fields of the demerging magnet and electrostatic analyzer. Such changes could cause small movements

EXPERIMENTS WITH MERGING BEAMS

73

of the H3+ beam over the multiplier face, and assuming gain irregularities over the face, could result in output variations. The plates were designed to sweep the H,' beam over an area on the multiplier face and so smooth output variations caused by gain irregularities. The use of these plates did solve the above problem. A retarding potential curve for the product ions could be obtained for each W. From the plateaus of these curves relative cross sections could be derived. For positive and negative AE/e's associated with the same W, ion currents at plateaus had the same value, within experimental error. The energy resolutions of the demerging magnet and electrostatic analyzer were such that, for a given AE/e, and therefore, W , H3+ of all possible energies would be passed for fixed settings of these detector components. Because of transverse velocities, H3+ was formed along path lengths of the merged beams where the reactants had the same energy. Therefore, from this mechanism, H 3 + was continually being generated outside the interaction region and, when AE/e = 0, inside as well. If the potential of the retarding grid in the detector were sufficiently low, these ions would be detected. When AE/e # 0, the detector signal was due to H3+ formed inside the interaction region at energy W, and, if the retarding grid were at a sufficiently low potential, to H3+ formed outside. The contribution from H3+ outside could be measured independently by applying any AE/e that would result in no measurable signal from inside the interaction region. For this purpose it was determined that the AE/e associated with W = 10 eV, which will be labeled AE'/e (AE'/e = +470 or -510 V), was satisfactory. The contribution associated with W due to H 3 + formed inside the interaction region was the difference between signals measured with the potential of this region at AE/e and at AE'/e. The retarding potential curve for a given W could be derived from this difference. Each cross-section measurement at W was accompanied by a measurement at 1 eV so that ratios of cross sections, Q,/Q,, were obtained. It was not necessary to take measurements for complete retarding potential curves (i.e., curves for a succession of retarding potentials beginning with potentials sufficiently large to result in no measurable signal to potentials well into the region of the plateau) to derive a given ratio. Only a single measurement on each plateau was required, and, in general, this was the technique followed. Data for a given cross-section ratio could be obtained in a few minutes. Absolute cross-section measurements could be made by the technique discussed for the Ar experiment. b. Results and Discussion. The mb results for Qw/Ql are shown in Fig. 6. Included are data for positive and negative AE/e's associated with the same W. To give an idea of the accuracy of ratios designated by crosses, the error for the ratio at 0.1 eV is estimated to be - 11 to + 6 % , At 3 eV the standard

74

Roy H . Neynaber

-

0.1 1

INTERACTION ENERGY W (aV) 0.25 0.5 I 1

--

1

1

2 3 4 7 I

1 ,

v

PRESENT EXPERIMENT

w-l/z

( e v I-'''

-

-

+

+Hz+ H 3 + H. Each dot represents a FIG.6. Qw/Ql vs W-'/' and W for H2+ value obtained for a single measurement; a dot accompanied by a digit means that number of measurements resulted in the same quantity. Crosses indicate arithmetic averages of dots.

deviation is about 18%. Also shown in Fig. 6 is a W - ' / 2 straight-line fit to the data for 0.1 eV < W < 1 eV. This line has the energy dependence predicted by Gioumousis and Stevenson (GS) (1958). For W 2 1.5 eV the ratios fall below the line. Perhaps a spectator-stripping model (Henglein, 1966) could be used to explain this fall-off. The values of the crosses in Fig. 6 are given in Table 11. Also included are the ratios Qw/Ql for a tandem mass spectrometer experiment by Giese and Maier (GM) (1963), and for a single-stage mass spectrometer experiment by

75

EXPERIMENTS WITH MERGING BEAMS

TABLE I1 RATIOOF CROSS SECTION AT

W (ev) 0.1 0.2 0.3 0.4 0.6 1.o 1.5 2.0 2.5 3.0 4.0 5.0 7.0 10.0 12.0 13.5

mb experiment QwlQi

3.22 2.45 2.04 1.45 1.oo 0.69 0.53 0.33 0.20 0.15 0.07 0 0

w,Qw, TO CROSS SECTION AT 1 ev, Ql Giese and Maier (1963) (QwlQih

1.63 1.39 1.oo 0.65

0.44 0.29 0.19 0.08 0.04

-

Reuben and Friedman (1962) (QwlQih~

’

1.35 1.oo 0.78 0.63 0.52 0.45 0.35 0.29 0.28 0.27 0.18 0

Ratios taken from curve labeled Q = 0 of Giese and Maicr

(1963).

Ratios are the result of an analysis of the Reuben and Friedman

(1962) data as outlined by Giournousis (1966).

Reuben and Friedman (RF)(1962). The mb results are in better agreement with the GM ratios than with the RF values. An absolute measurement was made at 1 eV with the result that Q , = 12 A2 with an estimated error of -26 to + 37 %. Considerably more reliability should be placed on the ratios Q,/Q, than on the absolute value of Q , as evidenced by the estimated errors indicated above. This is primarily because the absolute value of Q , depended upon measurements of the transmissions of the grids in the decelerating-acceleratingsystem, the secondary electron coefficient of the ion collecting plate in the neutral beam monitor, the primary ion and neutral beam shapes, the relative positions of the primary beams, and the gain of the detector assembly (Trujillo et al. 1966). These quantities were subject to rather large errors. The determinations of ratios did not depend on these quantities. The value of Q,, subject to its rather large uncertainty, overlaps the value of 15AZpredicted bytheGS theory. The experimental errors associated with Q,/Q, became larger as W increased because the Q , became smaller and were more difficult to measure.

Roy H. Neynaber

76

Experience with crossed beams, on the other hand, has indicated that the cross section errors become larger as beam energies decrease. This is attributed to beam intensities (which largely dominate such errors) becoming smaller with decreasing energy. From Fig. 6 it appears that the best fit to the data between 0.1 and 1 eV is a smooth curve that is concave downward. The possibility that this curve represents an actual departure of the cross-section ratio from a linear dependence on W-'12 should not be discounted. There is concrete evidence from signals at an extremely low energy (i.e., W 6 0.03 eV) that the quantity (QW/Ql)W'I2 is from 15 to 30% less than the corresponding value given by the slope of the W -'I2 fit in Fig. 6 . In other words, the W fit shown does not apply at this low energy. These signals arise when AE/e = 0. Transverse velocities account for the interaction energy. An upper bound to the energy has been calculated as 0.03 eV. Uncertainty in the energy prevents a determination of the cross-section ratio. Wolf (1968) has used a modified phase-space theory to calculate cross sections for the process under discussion. He predicts a curve of cross-section ratio versus W that has the same general shape as a smooth curve that fits the mb data. It should be noted that the states of the mb reactants are unknown. If excited states did exist, cross sections for ground state reactants could be obtained, in principle, by applying corrections to the quoted values. The percentage correction to the value of Ql would probably be considerably larger than the percentage correction to the cross-section ratios. Chupka et al. (1968) find that for W less than a few electron volts the reaction cross section decreases with increasing vibrational excitation of H,' ; whereas at higher W a mechanism for which the cross section increases with increasing vibrational energy of the ion becomes more prominent. The existence of such excitation in the mb experiment would therefore result in a smaller Q, than would be obtained from just ground state H,'. If the GS theory applies at 1 eV, electronically excited H, primaries would be expected to result in a Q, larger than would be extracted from measurements with a pure, ground state neutral beam. This follows from the larger polarizability of an excited neutral.

-'',

2. Na

+ 02++ NaO' + 0

The existence of NaO' has been established (Rol and Entemann, 1968) through the use of merging beams of Na and 0,'. The failure to observe NaO' in a flowing afterglow experiment is mentioned by Fite (1968) in a paper in which he discusses the merits of the mb technique. In the mb experiment, a Na beam of 2810 eV and an 02' beam with an

EXPERIMENTS WITH MERGING BEAMS

77

energy ranging from 3953 to 4354 eV were merged, resulting in W's ranging from 0.05 to 5 eV, respectively. The NaO' ions were formed with nearly the same velocity in the laboratory system as the reactant particles, corresponding to a laboratory energy near 4765 eV, which was much higher than the energy of any primary beam particles. The cross section Q for the reaction Na 02+--t NaO+ + 0 was determined through the use of Eq. (8). This Q as a function of Wand W-l" is shown in Figs. 7 and 8, respectively. For each W the maximum of the NaO' distribution corresponded to a considerably higher relative c.m. energy W of the products than calculated from the spectator-stripping model. According to this model, W' =kW, where k is a constant. For this system, k = 0.3. The apparatus used for these measurements was similar to that shown in Fig. 1. However, the energy distribution of product ions was measured directly with an electrostatic hemispherical condenser instead of indirectly with a retarding grid. Good resolution was obtained by passing the ions through a decelerating lens system before they entered the hemispherical analyzer. Figure 9 is a schematic diagram of the apparatus. The Na beam was produced by symmetric charge transfer of Na' in a vapor cell. The Na' was formed from source 1 by emission from a heated glass (prepared from a mixture of NaOH, SO,, and A120,) and was subsequently focused and collimated. The 0 ' was produced in an electron

+

INTERACTION ENERGY, W (eW

FIG.7. Q versus W for Na + O2

--f

NaOt + 0.

78

Roy H. Neynaber

w-1/2, (e") - 1 0

FIG.8. Q versus W-'/'for Na

+ 02+-+NaO+ + 0.

bombardment-type ion source 2 using approximately 40-eV electrons. Only single collisions between electrons and 02+ occurred in the source. A fraction (Turner et al., 1968a) of the OZf ions was formed in a metastable electronic state (411,) which has a lifetime longer than the transit time through the apparatus. In order to determine whether the measured Q was for the reaction of Na with ground state or excited state 02+, the fraction of metascurrent) by lowering the energy of tables was lowered (as was the total 02+ bombarding electrons. The Q was negligibly affected, and therefore may be considered as characteristic of the reaction of Na with ground electronic state 02+. The vibrational and rotational states of the Oz+ were unknown. The intensity of the 2810-eV Na beam was determined by measuring the secondary electron current in a Faraday cup and assuming that the secondary electron emission coefficient for neutral atoms is the same as that measured for ions at the same energy. The NaO+ signal was measured with a Bendix Model 306 electron multiplier. The current was calculated assuming that the where gain for NaO' was equal to the gain for Na" plus half the gain for OZt, the Na+ and Oz+gains were each measured at the NaO+ velocity (Kaminsky, 1965). A transverse component of relative velocity introduced a mean relative energy of about 0.03 eV when the beam velocities had the same magnitude. Thus the fractional uncertainty in the energy, A W/W , becomes rather large for small W.

SOURCE 1

SOURCE 2

FIRST COLLIMATING APERTURE

SECOND COLLIMATING APERTURE

DEFLECTION PLATES

\

\

NEUTRAL BEAM MONITOR ELECTROSTATIC DEMERGER

I

MOVABLE

I RETARDING

._ I

I

I I

I

I I I

I DECEL-ACCEL I

I LOCK-IN

-

MAGNET

PHOTOCELL LAMP

I PLATE

I

A

I

I 1

i

ELECTRON MULTIPLIER

I

WHEEL BEAM FLAG

10 cm

FIG.9. Schematic diagram of rnb apparatus for studying Na

/

FOCUSING LENS

/

HEMISPHERICAL ANALYZER

I

~ARADAY CUP

+ 02+ NaO+ + 0. Apertures are not to the scale shown. --f

Roy H . Neynaber

80

IV. Ion-Ion Reactions

A. SYMMETRIC-RESONANCE CHARGE TRANSFER Brouillard and Delfosse (1967, 1968) and Brouillard (1968) used an mb method in conjunction with delayed-coincidence techniques to make a preliminary cross section measurement for the symmetric-resonance charge transfer process He+ + HeZ+-+ He2+ + He+. Their measurements were made at W’s in the kiloelectron volt range and show the usefulness of merging beams for studying reactions at considerably higher energy than in experiments previously discussed. Figure 10 is a schematic diagram of the apparatus. The beam, a composite of He’ and HeZ+,was generated in the PIG source 1 with an energy spread of about 100 eV. It was accelerated at 2 by a voltage in the range 5 to 20 kV,

FIG.10. Schematic diagram of apparatus for studying He+ He2++ H e 2 + He+. ( I ) source; (2) accelerating and focusing region; (3) energy analyzer (electric deflector); (4-7) collimators; (8, 9) current probes and valves; (10-14) basic vacuum (diffusion pumps); (15, 16) high vacuum (sorption); (17) ultra high vacuum (ion pump); (18) ultra high vacuum (titanium sublimation); (19) collision chamber; (20) magnetic shielding; (21) magnetic analyzer; (22) Faraday cups for primary beam currents; (23) “cleaning ” deflectors; (24-25) magnetic quadrupole lenses; (26) phosphor; (27) 30-kV detector electrode.

+

+

EXPERIMENTS WITH MERGING BEAMS

81

focused at 2, and analyzed at 3 by a low-resolution electric deflector. After collimation, it entered the collision chamber 19. The diameter of the beam in this chamber was 1 mm and the current was about lo-' A (He'). The collision chamber was a 5-cm-long cylinder whose potential was negative with a magnitude equal to one-tenth of the accelerating voltage. The pressure in the chamber was lo-'' Torr. Collimators 6 and 7 were chosen so as to accept collisions with a deflection angle of less than about 5 x rad. After approximately 90" deflection in the magnetic analyzer 21, the primary ions were collected on Faraday cups 22. The exchanged ions left the magnetic analyzer through slits, passed through " cleaning" deflectors 23 and quadrupole lenses 24-25, and finally impinged on the negative 30-kV detector electrodes 27. The detectors were photomultipliers whose light input was obtained from scintillating phosphors 26. The phosphors, in turn, were excited by secondary electrons emanating from the detector electrodes. The " cleaning" deflectors swept out ions formed from primary ions whose energies had been slightly degraded by collisions with the residual gas in the region of acceleration after the source. Figure 11 shows ion trajectories in the magnetic analyzer. The source of the composite H e f , He2' beam is labeled S. The collision chamber, at negative potential V , , is shown by the dotted box. The primary beams followed trajectories 3 and 4 in the analyzer and were collected on Faraday cups P+ and P+ +. Ions created by the desired charge transfer process in the collision chamber at A , for example, followed trajectories 1 and 6 and were collected on detectors D and D . Ions created by charge transfer (at B ) or ionization (at C ) through interaction of the primary beam with residual gas followed paths 5 and 2, respectively, and did not reach the detectors. The potential on the collision chamber permitted discrimination between ions created by charge transfer within the chamber and those created outside. It also accurately defined the length of the interaction region. This region was maintained at very high vacuum to reduce noise, i.e., ion current produced from residual gas. Since noise was still larger than the desired signal, delayedcoincidence techniques were used. The desired He' ion triggered the $art input of a time-to-pulse-height converter; the He2+ triggered the stopfIn a subsequent pulse height analysis, the desired signal appeared in well-defined channels, whereas the noise was spread over all channels. The channel address yielded an unambiguous identification of the desired event. Bates and Boyd (1962) and Brouillard (1968) have calculated the cross section for

+

He+

++

+ He2++He2+ +He+

using the impact parameter version of the Coulomb-Born approximation. They neglected momentum transfer effects. Their results, which are naturally

82

Roy H . Neynaber

.'. '.

'\

I

D++ PULSE HEIGHT ANALYZER

t

TIME-TO-PULSEHEIGHT CONV. START A

P+

STOP

t

+

FIG.11. Ion trajectories in the magnetic analyzer of the apparatus for studying He+ HeZ++ H e Z + +He+. (S)source at positive potential V,; (dotted box) interaction region at negative potential V,; (+) primary He+ beam; (++) primary Hezf beam; (3, 4) trajectories of undisturbed primary beams; (1, 6) trajectories of HeZ+and He+, respectively, created at A by the desired charge transfer process; (2) typical trajectory of He2 created by ionization of primary He+ in residual gas at C ; ( 5 ) typical trajectory of He+ formed by charge transfer of primary HezC in residual gas; (P++,P+) Faraday cups to collect primary beams; ( D + + , D + ) product ion detectors. The curved, dotted lines associate trajectories in the magnetic analyzer with the process responsible for ion production. +

FIG.12. Q versus 2 W.Circles (solid curve) are predicted values from a semiclassical treatment by Brouillard (1968). Crosses are values from a theory by Bates and Boyd (1962).

EXPERIMENTS WITH MERGING BEAMS

83

in accord, are shown in Fig. 12. Brouillard also calculated the differential cross section for the process. A preliminary, experimental determination of the cross section Q has been made at W = 1.65 keV with the result that Q = 1 x 10-16cm2 (-30%, +SO%). It is noted from Fig. 12 that the theoretical Q is about 5.6 x cm2. This value is outside the limits of error for the experimental Q . The quoted error includes estimates of the uncertainty in the cross sectional area of the primary beam (which is assumed to be uniform in the collision chamber), in the angular acceptance and transmission of the system for the desired species, and in the detector efficiencies. The errors associated with angular acceptance and transmission seem to be the most serious of those included in the estimate. There are plans to modify the apparatus in order to reduce these errors (Brouillard and Delfosse, 1968). Another error, which is not included in the above estimate, arises from the existence of H 2 + in the primary beam. It is not sufficiently resolved from the primary He2+ and would result in an underestimation of Q . This problem is being attacked by using He3 instead of He4 (Brouillard and Delfosse, 1968). Additional results with improved accuracy are expected in the near future from this experiment.

B. MUTUALNEUTRALIZATION The ion-ion mutual neutralization cross section, Q, was measured for N + + 0- + N + 0 by an mb technique (Aberth et a/., 1968). Preliminary studies of similar reactions have also been made by Aberth et al. (1967). The measurements were made over a range of W from 0.1 to 86 eV with an uncertainty in W of 0.1 eV due to transverse velocities. The results represent the first direct cross-section measurements for this type of reaction in which the energy and particle identity are specified. A schematic diagram of the complete apparatus is shown in Fig. 13. The duoplasmatron sources introduced an energy spread in the primary beams (whose laboratory energies were in the kiloelectron volt range) of about 3 eV (Aberth and Peterson, 1967). The beams were superimposed with a merging magnet and then entered the interaction chamber (see Fig. 14). After traveling 30 cm in superposition, the beams were separated by electrostatic deflection. The neutral particles formed by ion-ion neutralization, as well as those formed by electron stripping and capture reactions of the beam ions with the background gas, continued along the superimposed beam direction and were detected by secondary electron emission from a stainless steel surface. The ion-ion neutralization products were separated from those due to beambackground interaction by chopping the primary beams at different frequencies and using a lock-in amplifier to detect the difference frequency.

84

Roy H. Neynaber

FIG.13. Schematic diagram of mb apparatus for studying mutual neutralization.

FIG.14. Schematic diagram of interaction chamber of mb apparatus for studying mutual neutralization.

The secondary electron emission coefficient, y, for the products of the desired reaction had to be obtained for absolute cross section determinations. It was considered equal to the average measured values of the secondary electron emission coefficients of the N + and 0-primaries. The overlap integral in Eq. (8) was obtained by assuming that the flux

85

EXPERIMENTS WITH MERGING BEAMS

density of the broad 0 - beam was uniform everywhere in the interaction volume, i.e., that volume of space swept out by the narrow N + beam. This flux density was determined with the use of the variable irises shown in Fig. 14. Because the flux density was not uniform in the interaction volume, an error was introduced into the results. These results are shown in Fig. 15. Aberth et al. (1968) chose to represent 0.1

1

5

10

INTERACTION ENERGY, W (eV) 20 30 40

60

80

100

+

FIG.15. Mutual neutralization rate measurements vs u and W for N C 0-. The solid curve represents an approximate least-squares fit of the data points to an eleventh degree polynomial. Energies associated with points above 30 eV reflect slight corrections to those in the similar figure of Aberth et al. (1968).

their results by a least-squares fit of the data points to an eleventh degree polynomial. This fit (except for some rapid oscillations, which were deemed insignificant and therefore smoothed out, between about 70 and 100% of the maximum speed at which measurements were made) is shown by the solid curve. The absolute accuracy of this curve is estimated to be & 50 % , except at energies below 0.5 eV where QU(u is the relative speed of the reactants) is rising rapidly with decreasing speed and the uncertainty in u becomes relatively large. Much of the error is attributed to uncertainty in y and the 0- flux density. Not only does the assumption of the uniformity of the flux density introduce an error, but uncertainty in the measurements of the density are introduced by hysteresis in the variable iris mechanism (Aberth and Peterson, 1968). Possible major sources of scatter in the data points are beam alignment and focusing problems. The state of excitation of Nf was not determined. On

86

Roy H . Neynaber

the basis of work done by Turner et al. (1968b), however, Aberth et al. are of the opinion that N + was in the ground state. An excited state of an atomic negative ion has never been observed. The general structure of the curve is similar to that calculated for H + H- neutralization by Bates and Lewis (1955) using a Landau-Zener approximation, and suggests that if this approximation is good then the neutralization cross section is relatively insensitive to the details of the atomic structure. Very recently (summer 1968) Aberth and Peterson (1968) measured the + 0,-in a mutual neutralization cross sections for N2+ + 02- and 0 2 + manner similar to that described above. The neutral species resulting from these reactions were not identified. The results are shown in Figs. 16 and 17. The state of excitation of the primary ions and the effect of excitation on the mutual neutralization rates are unknown. The standard deviations of the data from the plotted curves for N + 0-, N,+ + 02-,and 02+ + 02-are 1.56, 1.66, and 2.72 x lo-' cm3/sec, respectively. The general shape of the curve for N2+ + 02-is like that for N f + 0-. The rather sharp increase in Qo for these two curves is not observed for the curve of 02+ +O,-. This characteristic may be unobservable in the latter curve because of the large scatter of the data. There is also the possibility that vibrational and rotational excitation of the ions would obscure this rise. A

+

+

INTERACTION ENERGY, W (eV)

20

0.1

1

5

10

t 0

0 .o

0.5

1 .o

40

20

1

1.5

60

I

1

2 .o

RELATIVE SPEED, v(10

2.5 6

80

I

3.0

100

3.5

m/KC)

+

FIG. 16. Mutual neutralization rate measurements versus v and W for N2+ 02-. The solid curve represents an approximate least-squares fit of the data points to an eleventh degree polynomial.

87

EXPERIMENTS WITH MERGING BEAMS

20

0.1

--

20

10

5

1

I

0

L

40

I

0

OO

-

-

-

-

-

-

60

-

3

I

1

1

2

-3

comparison of the N + + 0-and N,' + 0,-curves indicates that the low energy rise is more suppressed for the molecular reaction. An improvement in this mb system, which has been recognized by Aberth and Peterson (1968), would be the adaptation of a collision chamber whose potential could be varied and used to create the desired energy difference between the primary beams. The mutual neutralization experiments are fine examples of the use of merging beams for obtaining measurements that could not be made by other techniques.

C. RADIATIVE RECOMBINATION Wiener and Berry (1 968) have constructed an mb system to be used principally for studying radiative recombination of two ions. The system consists of twin accelerating ion sources and a single analytical magnet (TAISSAM) with approximately 180" focusing for both beams. Initial experiments will be conducted with Li' emitted from a surface ionization source. The source of negative ions is similar to that used by Aberth and Peterson (1967). Figure 18 is a schematic diagram of the apparatus. There are two sets of accelerating

88

Roy H . Neynaber

I M

IwLrr, I

!

W

FIG. 18. Schematic diagram of mb apparatus for studying radiative recombination.

(S+, S - ) positive and negative ion sources; ( A + , A _ ) accelerating electrodes; ( E + ,E - )

focusing einzel lenses; ( C + ,C - ) collimating apertures; ( M ) magnet pole pieces; ( D ) detector (movable, shown in position to collect both beams); ( W )window above beam area; ( T + ,T - ) typical positive (Li+) and negative (0-) ion trajectories.

electrodes, focusing lenses, and collimating apertures (one set for each beam). The detector is movable for monitoring and determining characteristics of the ion beams. A large window is provided for optical monitoring, which will be done spectrographically in the initial stages of the experiments. Initial experiments are being conducted to test the utility of optical monitoring rather than to study radiative recombination. To this end, mutual neutralization of Li' and 0- will be studied at relative energies in the center of mass of 1 eV or less. Observations will be made of the emission of the lithium red resonance line at 6707 A which immediately follows the reaction Li+('S) + O - ( 2 P )+ Li(2P) + O(3P).Weiner and Berry (1968) estimate that the cross section for this reaction is reasonably large (at least cm2)on the basis of predictions for well-studied mutual neutralization processes. (The 6707 A line should be considerably stronger than emission from radiative recombination.) Since typical ion velocities are about lo7 cm/sec in the laboratory system, while the lifetime of Li(2P) is less than lo-' sec, most of the emission occurs in the immediate vicinity of the interaction region. The

EXPERIMENTS WITH MERGING BEAMS

89

Li+.O- system is advantageous for testing purposes because of a known, large oscillator strength and a sharp, concentrated, and easily identified spectrum. Li+ + H - has been selected as the first system for which radiative recombination will be studied (again at low relative energy in the center of mass). Since several potential curves of this system are now known, it is feasible to calculate the expected emission spectrum as a function of internuclear distance. Therefore, experimental spectra can be compared with theoretical, at least in the adiabatic approximation. Weiner and Berry (1968) explain that, in essence, the energy-selected pair of ions can recombine and emit radiation at any point along the collision trajectory. To a first approximation, emission from an ion pair at a given internuclear distance R, is restricted to the energy separating the right-hand turning point of the lower state at R, and the relative energy of the colliding pair. (This crude description neglects contributions from the left-hand turning points. These may also be important and account can be taken of them but to do so now merely complicates the present discussion.) In this approximation, each wavelength corresponds to a unique internuclear separation, so that the measured spectral intensities only need to be rescaled in order to give the oscillator strength or transition dipole amplitude as a function of internuclear distance. Thus, the continuous free-bound emission provides one probe for the study of electronic wave functions at large internuclear distances, which are in the range where the system is making its transition between behaving like separated particles and like a molecule. V. Neutral-NeutralReactions Neynaber et al. (1969) have used mb techniques to investigate some twobody collisions in each of which both reactants were neutrals. These reactions were Na + 0,+ N a + + 0,(charge transfer) (a) (ionization) Na + 0,+ Na+ + 0,+ e (b)

+ 0, Na+ + 0 + 0Na + 0, + NaO+ + 0Na + 0, NaO + 0 + e Na

+

(dissociative charge transfer)

(4

(4 (el For ground state reactants and products all of the above reactions are endothermic. The heat of the reaction, AH, is positive for an endothermic process. The values of AH for (a), (b), and (c) are 4.71, 5.14, and 8.78 eV, respectively, assuming the electron affinity of 0,is 0.43 eV (Pack and Phelps, 1966) and of 0 is 1.48 eV (Berry et al., 1965). The magnitude of A H is unknown for reactions (d) and (e). The discussion will be largely limited to the first three reactions with only a few words at the end devoted to the last two. +

+

(rearrangement) (rearrangement).

90

Roy H . Neynaber

A. CHARGE TRANSFER AND IONIZATION 1. Apparatus

To study reactions (a), (b), and (c) a retarding potential curve of product ions was obtained for each of several interaction energies, W. These curves yielded information on the laboratory energy distribution of the product ions and cross sections for the processes. To investigate (a) alone, attempts were made to detect 0,-. Although some measurements were made on 0,-, in general the signal-to-noise ratio was too small (for unknown reasons) to extract good data. Most of the information for (a) and all of it for (b) and (c) was obtained by observing Na', and further discussion will be confined to experiments involving detection of this ion. The apparatus used for these measurements was very much like that emH, --f H3' + H and described previously. ployed in the study of H,' Figure 19 is a schematic diagram of the apparatus. An Na' beam from source 1 was obtained by emission from a heated glass made from Na,O, S O , , and A1,0,, The energy spread of particles in the Na' beam was 1.5 eV or less. The Na' beam was then merged in the merging magnet with ,' at 4000eV from an 0,beam. The 0, beam was obtained by passing 0 source 2, which was a low pressure, oscillating electron bombardment source, through a charge transfer cell containing 0,. An electric field between the condenser plates that follow the cell was used to remove 0,' which did not undergo charge transfer. The energy spread of the 0, 'was I .5 eV or less. The energy of Na' was adjusted to give the desired W. After leaving the merging magnet, the superimposed beams passed through a collimating aperture and then a charge transfer cell containing Na vapor. The temperature of this cell was adjusted so that the vapor pressure of Na was optimum for neutralization of the Na' beam. Under these conditions the 0, beam suffered about 35 % attenuation. The Na vapor had negligible effect on the energy distribution of particles in the 0, beam. This conclusion was reached by measuring the energy distribution of 0,- particles in a beam formed by interaction of the 0, beam with background gas. The energy distribution of 0,-was the same for the Na cell at room temperature and at the optimum temperature for neutralization of Na'. The merged beams then passed through an electric field between a set of condenser plates. Charged particles were eliminated by this field. After passage through a second collimating hole, the resultant neutral beams entered the interaction region. This region was surrounded by a device used in previous ion-molecule experiments (Neynaber and Trujillo, 1968; Neynaber et al., 1967a,b) to establish the desired energy difference between the primary

+

FIG. 19. Schematic diagram of apparatus for studying Na-0, collisions. The collimating apertures are 2.5 mm in diameter.

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Roy H . Neynaber

beams and to accelerate product ions when they left the region. In the present experiment the device was used in conjunction with the retarding grid in the detector assembly to allow product ions formed inside the interaction region to reach the detector but to prevent those formed outside from doing so. This was accomplished by applying an appropriate potential, P, to the device in order to accelerate ions formed inside the region. The potential of the retarding grid R allowed transmission of these ions but prohibited the passage of slower product ions formed outside the region. Since deexcitation of excited states of Na to the ground state can occur by direct, optically allowed transitions or by cascading, it is assumed that the Na beam in the interaction region consisted of only particles in the ground state. The general conclusions of this experiment, however, are independent of this assumption. In this region the O2 beam presumably contained some excited particles. After leaving the interaction region, the reactants and products passed through a 0.874-cm-diameter hole in the aperture plate. Na’ was separated from the reactants by the demerging magnet. Other undesired particles were prevented from reaching the detector (a Bendix multiplier) by employing the retarding grid and a hemispherical electrostatic energy analyzer tuned for the passage of the Na’. The output of the multiplier was fed into a Cary 31 electrometer and then displayed on a strip chart recorder. The experiment was conducted using dc techniques. 2. Kinematics Kinematics for reaction (a) are shown by the Newton diagram of Fig. 20. In this case, the magnitude of the laboratory velocity of Na, Iv, 1, is less than that of 0 2 ,IvzI. General expressions for the magnitude of the c.m. velocity of Na before the collision, JV11, and that of Na’ after the collision, lV31, are given by Eqs. (10) and (11): IVII = ( 2 W ~ )”z/ml, IV3J= [2p( W - AU - A H ) ] 1 / 2 / m l

(10)

(1 1)

where p is the reduced mass before and after the collision, m, is the mass of sodium, and AU is the internal energy of the products minus that of the reactants. If W ’ is defined as the relative kinetic energy in the center of mass after the collision, then W ’ = W-AU-AH. (12) For the “ after collision ” case, three circles are shown for the loci of the tip of the c.m. velocity of Na’. Therefore, points on a given circle indicate

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EXPERIMENTS WITH MERGING BEAMS

BEFORE COLLISION

'AU
+

FIG. 20. Newton diagram for N a +Or + N a + 02-. Subscripts 1, 2, 3, and c refer to Na, O r , N a + , and the center of mass, respectively. (v) laboratory velocity; (V) velocity in c.m. system; ( A U ) internal energy of products minus that of reactants; ( v ~minimum ~) laboratory velocity of N a + for AU = 0. (Symbols with arrows in the figure are equivalent to boldface symbols in the text.)

different angular scattering of Na'. Each circle represents one of the three possible cases for the conversion of c.m. energy from internal to translational modes and vice versa. For AU > 0, translational energy of the reactants is converted into internal energy of 0,-. Sufficient energy to excite Na' was never available. When AU = 0, all of the internal energy of O2is converted into internal energy of 0,- or all of the reactants and products are in the ground state. When AU < 0, there is a conversion of internal energy of 0, into translational energy of the products. For the case of AU = 0, two directions are shown for the c.m. velocity of Na'. When the direction is the same as that of the c.m. velocity of Na before the collision, we define the c.m. scattering angle to be zero. Note that the minimum laboratory velocity of Na', vim, exists for this condition. The minimum laboratory velocity of Na' for AU = 0 is less than or greater than that for AU > 0 or
94

Roy H. Neynaber

been a source of noise in the study of the AU = O case (which was important because it included the case when all of the reactants and products were in the ground state), then JvlI had to be less than I v , ~ , where v3 is the laboratory velocity of Na'. Figure 20 and Eqs. (10)-(1 1) show that this was the case since IvlI c lv21 and JV31< IVII. Experiments for which IvlI > lvzl could not be conducted because of the noise introduced by stripped Na. Newton diagrams similar to Fig. 20 can be drawn for reactions (b) and (c). The diameter of a circle is proportional to W"". For a given AU the circle diameters are different for reactions (a), (b), and (c) because the AH'S are different. The diameter for reaction (a) is the largest. Kinematic considerations of reaction (b) show that Eq. (11) gives the magnitude of the c.m. velocity of Na' if the kinetic energy of the electron in the center of mass is considered as a contribution to the internal energy of the products of the reaction. With this interpretation, Eq. (12) gives the relative kinetic energy in the center of mass of the products Na' and 02. For reaction (c) and a given AU, Eq. (1 1) gives only the maximum IV, I, which occurs when the velocities (magnitude and direction) of 0 and 0-are the same. Equation (12) then gives the relative kinetic energy in the center of mass for Na' and the 0, 0-complex. 3. Method

As mentioned previously, the experiment primarily consisted of measuring retarding potential curves of Na'. It should be noted that the retarding grid only retards normal components of the Na' velocity. The desired Na' signal, or current I,, was the detector output with both primary beams on minus the sum of the outputs due to each beam separately. The output from a single beam was similar to ion noise, which has been described previously. Extraneous signals caused by one primary beam modulating (attenuating or enhancing) the noise associated with the other beam were investigated by making P = O . This had the effect of eliminating the real signal without altering the noise significantly. For this case, the detector output with both beams on minus the sum of the outputs for each beam by itself was negligible, indicating the absence of any significant modulation. An absolute cross section could be obtained by a technique discussed previously. This technique included measuring the profiles of each primary beam in the interaction region, the gain of the detector assembly, and determining the secondary electron emission coefficient of the neutral beam monitor for both Na and O2. Typical primary beam currents in the interaction region were 0.5 pA for both Na and 0 2 .

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EXPERIMENTS WITH MERGING BEAMS

4. Results and Discussion

Figure 21 shows Z3 as a function of R for W = 12 eV. (For this case, the laboratory energy of Na was E, = 2408 eV.) The solid curve (except the kink at 2995 V, which is assumed to exist and will be discussed later) is drawn on the basis of statistical evidence for the existence of inflections. These inflections suggest the existence of discrete energy distributions of Na'. The

3.0

-

v)

f 2.0 a

K >

2

cm

K

4

(CI

CI

1 .a

0 RETARDING POTENTIAL, R(W

FIG.21. Nat current (I3) vs R for Na-02 collisions at W = 12 eV (El = 2408 eV; P = 476 V). (E,) laboratory energy of Na; (P)potential of interaction region; (E.) minimum

+

+

) laboratory energy of Na+ from reaction Na O2+ Na+ 02- for AU = 0 ; ( E ~ minimum laboratory energy of Nat from reaction Na O2.+Na+ 0 2 e for AU = 0; (E,) minimum laboratory energy of Nat from reaction Na O2 Nat 0 0-for AU = 0. Each dot represents a value obtained for a single measurement; the dot accompanied by the number 2 means that two measurements resulted in the same quantity. The basis for drawing the solid curve is described in the text.

+

+

+ + --f

+ +

data are not sufficiently good to deduce fine details of these distributions. The inflections together with the data points and confidence limits (not shown) only give some indication of energy limits and integrals of the distributions. The solid curve of Fig. 21, which consists of straight lines, is used to represent this information. The curve is visually drawn consistent with the data and

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Roy H . Neynaber

with plateaus located in the regions of the inflections. The J3's of the plateaus represent the integrals of the distributions. It should be noted that the resolution of the retarding grid is such that a monochromatic beam will appear to have an energy spread of 4 or 5 eV and peak at about 4 eV less than its actual energy. The arrow labeled E, is at Re = 2942 eV (where e is the magnitude of the electronic charge), which is equal to the laboratory energy of Na' associated with v3"' for reaction (a). We will designate this energy as 8, , the minimum laboratory energy for the case AU = O . The arrows labeled &b and E, are analogous to E , , and they refer to reactions (b) and (c), respectively; &b is at Re = 2948 eV and E, at Re = 301 1 eV. The energy E, is calculated under the assumption that the velocities of 0 and 0 - are the same. It can be shown (Neynaber et al., 1969) that scattering of Na' in the center of mass after the collision was predominantly confined to angles less than 90" and that essentially all scattered Na' was detected. At R values less than 2995 V, there is evidence of two Na' distributions. One of these is between the two plateaus and includes the energy E , . This distribution is very narrow, i.e., a few electron volts or less. An analysis of these data (Neynaber et al., 1969) suggests that this energy distribution is associated solely with reaction (a). In addition, it seems likely that AU is very close to zero (Lee,AU < 0.6 eV), and therefore almost all the excess translational energy of the reactants (i.e., W - AH = 7.29 eV) is converted into translational energy of the products with very little going into internal energy. Finally, because of the very narrow energy distribution about E,, the products in the center of mass must be confined to a very small angle about the axis of the interaction region. In particular, Na' in the center of mass appears to be scattered almost completely in the 0" direction. Apparently the process proceeds via a direct, rather than a complex mechanism. The cross section for reaction (a) leading to the formation of Na' in this narrow energy distribution will be called Q, . Consider, now, the second distribution, which is between the plateau to the right of E, and the kink in the high energy tail. It will be assumed that this distribution is the result of reaction (b), that the scattering of Na' in the center of mass and in the vicinity of the peak of the distribution is at 0", and that AU 2 0. Under these assumptions, the lowest energy in this distribution would be equal to & b . Since measurements with the retarding grid shift an actual energy by an Re z 4 eV to the left in such a curve as Fig. 21, E~ would effectively come very close to or actually merge with the energy distribution associated with reaction (a). Figure 21 invalidates these assumptions since it indicates that the distribution is well removed from that of reaction (a) and that its lowest energy is effectively near 2960 eV. However, compatibility could be achieved within the rather flexible limitations imposed by the data

EXPERIMENTS WITH MERGING BEAMS

97

by departing from straight lines between about 2944 and 2963 eV and drawing an inflection between these energies. The introduction of another inflection point at Re 2 2963 eV would result in a well-defined peak at the point. From Eq. (1 1) as applied to reaction (b), the AU associated with this peak (if it were at Re = 2963 eV) would be about 1.3 eV. This means that at 12 eV, reaction (b) is most probable when 1.3 eV, or 19%, of the excess translational energy [i.e., W - AH = 6.86 eV) is converted into either kinetic energy of the free electron, internal energy of 0,, or both. The significance of such a partition of energy is not known. The high energy tail preceding the kink could be explained by the conversion of translational energy into kinetic energy of the electron and internal energy of 0, (the largest AU for the distribution would be about 3.5 eV) and/or by angular scattering of Na'. The cross section for reaction (b) leading to the formation of Na' in the energy distribution discussed above will be called Qb. There is no evidence for the kink at 2995 V in Fig. 21. Small signal-tonoise ratios in the vicinity of the kink make it extremely difficult to obtain such evidence. The straight lines meeting at the kink could be smoothed to form one continuous curve that would fit the data. This could be interpreted in two ways: (1) as simply a longer high energy tail associated with reaction (b) than that described above; and (2) for R > 2995 V, as adistributionresulting from reaction (c) with the peak of this distribution at about E,. The high energy side of this distribution could be explained by assuming a difference in the velocities of 0 and 0 - . The cross section for reaction (c) leading to the formation of Na' in this distribution will be called Q , . If the second interpretation is assumed, then from Fig. 21, Q, : Qb : Q, E 5 : 3 3 : 1. The retarding potential curves for W = 6 , 8, and 10 eV can be interpreted in a fashion similar to that used for W = 12 eV, and at these energies QJQb 1. At W = 10 eV, there were no observable signals for Re greater than or equal to the associated 8 , . If the high energy tail at W = 12 eV for R > 2995 V results from reaction (c), then at 10 eV the absence of signals for Re 2 E, could be due to very small Q , at such energies. At W = 6 and 8 eV there were no high energy tails analogous to those at 12 eV. At 6 and 8 eV there is insufficient energy for the onset of reaction (c). Therefore, for W = 6 , 8, and 10 eV, it will be assumed that Q, = 0. At W = 6 eV (El = 2540 eV and P = 234 V), the retarding potential curve was taken not only for Re > E, = 2877 eV but also for Re down to 2780 eV. Below E , there were two plateaus other than those associated with processes that have been discussed. These indicate the existence of two other processes. From Fig. 20 and Eq. (1 l), it is concluded that reaction (a) with AU < 0 is responsible for this part of the retarding curve. This means that some 0, is

98

Roy H . Neynaber

excited and that there is a conversion of some of this internal energy into translational energy of the products. For W = 4.71 eV (El = 2579 eV and P = 275 V), which is the threshold for reaction (a), E, = 3025 eV. If, indeed, this is the threshold for the process, then no Na' should be observed for Re 2 3025 eV. The largest R for which there was a nonnegligible Na' current was 2970 V. Two plateaus at smaller R were observed; these are further evidence for excited states of O2 and reactions for which AU < 0. Figure 22 shows I3 vs R for W = 6,8,10, and 12 eV. Only the data for those 1.0

I

I

. @

a

013% .5-

0

I

I

I

- 2.0

I

I

I

I

1

I

I

2

1

W = 1 2 eV

W = l O eV

2.0

I

I3 1.0-

1.00

2905

I

I

I

2915 R(V)

I

2925

2920

2930 R(V)

2940

FIG. 22. Na+ current ( I , ) versus R for W = 6, 8, 10, and 12 eV. Symbols have the same meaning as in Fig. 21. At W = 6, El = 2540 eVand P = 234V; at W = 8 eV, El = 2490 eV a n d P = 343 V; at W = lOeV, El = 2448 eV and P = 416V; at W = 12 eV, El = 2408 eV and P = 416 V.

Re values in the vicinity of E, and the plateau immediately to the left of E, are shown. No plateaus were observed for W = 15 and 25 eV. Figure 23 shows relative Po’sas a function of W where Q , is defined as Q, + Q,, Q,. These were obtained by measuring the 13’s of the appropriate plateaus (see Fig. 22) and normalizing the measurements to the same primary beam currents. The Z,s’ for each W were taken one after another as rapidly as possible. Source conditions (except E l ) for all measurements were kept the same. At W = lOeV, an absolute Q , was calculated as 0.1 A’ with an estimated error of - 50 to + 35 % . The primary beam currents used in this calculation were those measured at the neutral beam monitor.

+

99

EXPERIMENTS WITH MERGING BEAMS I

I

I

I

1

1

0 X

1.

I

I

a

If

0

a

4

-

v)

a

k

z 2 > a a

a

+

8

I 0..

-a a

d

0

”=:

t,

; Q d

1;

1 :

1’2

INTERACTION ENERGY, W (eV)

FIG.23. Relative Qoversus W. Qo is the cross section for the formation of Na+ in Na-02 collisions for AU 2 0. Each dot represents a value obtained for a single measurement. Crosses are arithmetic averages of dots. Qo was chosen as unity for the cross at W = 8 eV.

Relative Q, , Qb, and Q, versus W can be obtained from this figure and the known ratios (at given W’s) Q, : Qb : Q, . At 4.71 eV, Qo = Q, x 0.Since the ratios Q, : Qb : Q, are approximately 1 : 1 : 0 at W = 6, 8, and 10 eV, the relative Q, and Qb are the same as the measured relative Q, . The ratio of Q, at 10 eV to Q, at 12 eV is approximately 1.2. The corresponding ratios of Q,’s and Qb’s are about 1.1 and 1.6, respectively. Crossing of potential curves could contribute to the fall-off of Q, and Q b with increasing W above 8 eV. It is not known whether quantitative agreement with the data could be achieved through such a consideration. The threshold energy in Fig. 23 could not be obtained with less than 0.5 eV uncertainty since the signal-to-noise ratio was so small in the vicinity of

Roy H. Neynaber

100

threshold. As a result, the electron affinity for 0, could not be obtained accurately. As mentioned previously, Qo w 0.1 A’ at W = 10 eV. Therefore, at this same energy Q, w Qb w 0.05 A’. (These cross sections apply, of course, when the specific states of the reactants and their abundances are the same as exist in this experiment.) Since the states of the molecular reactant and product are unknown, the experimental results only shed light on the AU of a process. From the results it appeared that AU = 0 for the process with cross section Q, . This reaction is a charge transfer process, and presumably the FranckCondon principle applies. Since the equilibrium internuclear distance for the ground state of 0,and 0,-are nearly equal (Gilmore, 1965), the conversion of ground state 0,to ground state 0,-has a favorable Franck-Condon factor in addition to satisfying the condition that AU = 0. If it is reasonably assumed that ground state 0,to ground state 0,-was the only significant process occurring, then the cross section would be 0.05A2if all the O2 had been in the ground state. If only a fraction of the 0, had been in the ground state, the cross section would be proportionately larger.

B. REARRANGEMENT Reactions (d) and (e) were studied using the same method and procedures as for reactions (a), (b), and (c) except that the components of the detector assembly were tuned for the passage of NaO+ (by using a K + impurity beam from source 1). A signal attributable to NaO+ was obtained. This signal could have resulted from reaction (d) and/or (e). The first experimental evidence for the existence of NaO+ was recently reported by Rol and Entemann (1968). In the present experiment, the curve of the cross section for the formation of NaO+ as a function of Wrose from zero at about 5.5 eV, reached a maximum at 7eV, and became zero again at about 8.5eV. The cross section at W = l eV was estimated to be about 0.004AZ.

VI. Electron-Ion Reactions A. THEORY Because of the mass difference between an electron and an ion, the mb theory for electron-ion studies warrants special consideration. Subscript 1 will refer to the ion and 2 to the electron. From Eq. (2), it can be shown that for a reasonable percentage uncertainty in the ion laboratory energy (i-e., about 0.1 %) and a reasonable uncertainty in the electron laboratory energy (i.e., a few tenths of an electron volt), an approximate expression

EXPERIMENTS WITH MERGING BEAMS

101

for the fractional uncertainty in W, 6 W/ W,depends only upon the uncertainty in the electron energy and is 6 Wl W x 6E,/(E, W)'I2,

(13)

where 6E, is the uncertainty in E2. Of major importance in merging beams studies of electron-ion systems is the achievement of W considerably less than E, . Having done this, one can use a relatively large E, (and still have a small W) and obtain a concomitantly large electron intensity. Therefore, for these systems a deamplification factor, D,, might reasonably be defined as :

D, = E2/W.

(14)

From Eqs. (13) and (14), the following expression is derived :

6 W/W N D','' 6E,/E2.

(15)

In the following examples it will be assumed that the uncertainty in E, is due to the energy spread which we will choose as 0.3 eV, i.e., 6E2 = k0.15 eV. This relatively large spread is compatible with high beam currents of electrons. Such currents will be required for mb studies. Now, if E2=10eV and W = l eV, then GW/Wx k0.05 and 6 W x +0.05eV. If the ion is N 2 + , El w240keV. If W=O.1 eV, then 6 W/W x 50.15, 6 W x kO.015 eV, and El ~ 4 2 keV. 0 Finally, if E, = 1 eV and W=O.leV, then 6WIWwkO.5, 6 W x f 0 . 0 5 e V , and Elw24keV. Therefore, for best resolution, E2should be relatively large. The resolution is quite good for E2 = 10 eV and rather poor for E2 = 1 eV. An upper limit to to E, would be partially dictated by the high voltage requirements for the associated El. It should be noted that the laboratory velocities of the reactants would be relatively high in an electron-ion, mb experiment compared with those for studies involving two heavy particles. Equation (8) indicates that such high velocities would result in relatively small signals. There would be some mitigation from the rather large flux density that presumably could be achieved for the high velocity ions. B . DISSOCIATIVE RECOMBINATION

Hagen (1967, 1968) has measured cross sections for the dissociativerecombination process N 2 + + e + N* +N** (where the stars refer to either an excited or the ground state of N) in a range of W from 0.1 to several electron volts. The experiment consisted of superimposing a beam of N2+ at 1 keV with a beam of electrons whose energy was varied between about 0.1 eV and about 4 eV. Throughout most of the electron energy range, the

102

Roy H . Neynaber

electron velocity was considerably greater than that of N 2 + and, to a first approximation, N2+could be considered at rest with respect to the electron. Except for the fact that the laboratory velocity of N2+was sufficiently high to permit easy detection of the products, the principles of merging beams were not applied in this experiment. It is discussed because, with a slight modification of the apparatus, a true mb experiment could be conducted. In the experiment, N2+ was generated in a directly heated hot cathode bombardment source (see Fig. 24). The extracted ion current was about

SECTION1

j

SECTION

II

SECTION

IlI

NEUTRAL BEAM DETECTOR' SECTION I ION SOURCE

II lII

MASS F I L T E R INTERACTION REGION

PUMP 1500 I l s e c D P

1000 I I s c c 0 P TITANIUM SUBLIMATION PUMP

PRESSURE

2 a IO-'Torr 2 x 10-6Torr

2

x IO-~TOII

FIG.24. Schematic diagram of apparatus for dissociative recombination experiment.

100 PA. The ions were focused and then passed through an rf quadrupole mass filter. Charge transfer of N 2 + with residual gas resulted in a large fast neutral current which was collected in a titanium sublimation pump. The N2+ beam was bent 45" by an electrostatic analyzer and collimated before it entered the interaction region. Figure 25 is a schematic diagram of the interaction region. It consisted of a hollow, cylindrical permanent magnet. Typical magnetic field lines are shown in the figure. The field was uniform at the center of the region. The

103

EXPERIMENTS WITH MERGING BEAMS ELECTRON REPELLER COLLIMATING APERTURE

\

CUP PROBE

P

.ELECTRON .LECTOR

,EXIT APERl‘U RE

ION BEAM

/

OXIDE CATHODE

I

.- -- ,

POLE. P . lFrF

ALNICO V MAGNET

MAGNETIC FIE1.D IC I IUCS 8 . L

FIG.25. Schematic diagram of interaction region of apparatus for dissociative recombination experiment.

electron emitter was an indirectly heated oxide cathode in the shape of a ring and at a potential equal to the desired electron energy. The electrons followed the magnetic field lines and were collected at the other end of the region. The 1.5-mm-diameter electron beam was contained within the collinear ion beam, which was typically 5 mm in diameter. Beam profiles were measured with a small scanning probe. The electron current was about 1 pA per electron volt of energy with an energy independent spread for the electron beam of about 0.2 eV. The perturbation of the ion beam by the magnetic field was negligible. After leaving the interaction region, the N2+ beam was deflected into a collector. Fast neutrals were detected by an electron multiplier. To discriminate against fast neutrals generated by charge transfer of N2+ with the background gas, the electron beam was modulated. The electron energy was continually swept and data were obtained automatically. The electron energy scale was calibrated by measuring the appearance potential of N, . Figure 26 shows the experimentally measured recombination coefficient, u, as a function of Wand the rms deviations associated with random errors. For any W in the range from 0.1 to 0.6 eV the average u = 2 x cm3/sec within f0.5 x lo-’ cm3/sec. Kasner (196?) measured the same u in an afterglow experiment over a range of temperatures from 205 to 480°K. Over this range, u =(2.7 f 0.3) x lo-’ cm3/sec fits the data. The systematic error for the experiment is estimated by Hagen (1968) as + 10 to - 15% . Included in the systematic error are uncertainties arising from the assumption that the ion flux density in the interaction region was always uniform everywhere within the confines of the electron beam, from

104

Roy H . Neynaber

0

1

2

3

4

5

INTERACTION ENERGY, W (eV)

FIG.26. a. versus W for dissociative recombination of N2+-ecollisions. The solid curve is considered the best visual fit to data points obtained at 0.05-eV intervals over the entire range of the curve. Each data point represented an average of continuous measurements over a 0.025-eV interval. Vertical distances between the solid and dashed lines give rms deviations.

absolute determinations of the desired fast neutral current, and from spiraling of the electrons around the magnetic field lines. The spiraling resulted from components of the thermal contribution of the electron velocity and, to a smaller extent, from components of the electric field each being transverse to the magnetic field at the cathode. The primary result of this was an effective increase in the length of the interaction region and a consequent overestimate of a, because this increase was not considered in its evaluation. The existence of a stronger magnetic field at the cathode than along the axis of the interaction region minimized the effect. As an electron proceeded from the cathode through the magnetic field gradient, the ratio of electron velocity transverse to the magnetic field to velocity parallel to the field decreased. From Section VI,A, it is observed that the Hagen system could be converted to a true mb apparatus by the substitution of a several hundred

105

EXPERIMENTS WITH MERGING BEAMS

kiloelectron volt ion-source power supply for the 1 keV supply. Hagen's 6E2= kO.1 eV. This is smaller than that chosen for the merging beams examples, and would result in smaller 6 W's. As shown by these examples, for the same W, better resolution could be obtained in an mb experiment. In addition, W's less than 0.1 eV would be practical in an mb experiment. As a result, a range of W could be achieved which would overlap the W's of the Kasner and Hagen experiments. VII. Current or Very Recent Studies

To make this review of merging beams experiments as up-to-date as possible, a few brief remarks will be made about some very recent studies. Belyaev et al. (1968) have measured cross sections Q for the symmetric C + C C + and N + N N resonance charge transfer processes C' + N + in a range of W from 7 to 100 eV. They used a method similar to their single source, mb technique described in Section 111,A,2. As expected, for each of the processes a straight line will fit their experimental points on a vs In Wplot. Examples of the Q values for the C + + C reaction are about cm2 and 3.5 x cm2 for W=7 and 100 eV, respectively. For 7.5 x the N + + N reaction, Q z 3 . 6 ~ cm2 and 2.3 x cm2 for W = 9 and 100 eV, respectively. Rol and Entemann (1 969) have studied the ion-molecule reactions Na + N O + --* NaO' + N and Na NO' -+ NaN" + 0 at W' s down to 0.05 eV. The method was similar to that described in Section 111,B,2, except that increased sensitivity of the detector to product ions was obtained by using counting techniques. It appears that only metastable states of NO+ were responsible for the observed NaO+ and NaN'. There were no measurable signals due to these product ions when NO+ was entirely in the ground state. Rol and Entemann have also measured W' as a function of W for the Na +NO+ reactions and find that W' is considerably higher than can be explained, for example, by the spectator-stripping model. The high W' effect is more pronounced for the N a + N O + reactions than for the process -+ NaO+ 0 (see Section III,B,2). Na 0 2 + Rozett (1968) is engaged in developing a merging beams system to study collisions of hydrocarbon ions with free radicals. Neynaber and colleagues are studying the reactions Na 0 +Na+ + 0and Na 0 -+ Na' 0 + e in a manner similar to that described in Section V. The results should be easier to interpret than those for the Na + O2 reactions since there will be fewer excited states of 0 than there were of 0 2 .

+

+

+

+

+

+

+

+

+

-+

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VIII. Concluding Remarks From the foregoing discussion, we have seen that the merging beams technique has been successfully used to study several types of reactions in an energy range heretofore inaccessible. The fact that chemical bond and activation energies are in an energy range in which mb experiments can be conducted should stimulate use of the method for studying collision dynamics. In the opinion of Fite (1968) the method can be uniquely used at low energies to investigate reactions having small rate coefficients. He observes that flowing afterglows, for example, while useful in determining large rate coefficients, cannot be used to determine coefficients smaller than about lo-" cm3/sec. This limitation is the result of competing processes and of impurity effects in flowing afterglow experiments. There are, of course, limitations to the mb method and problems associated with it. Obtaining differential cross sections by measuring laboratory angular distributions would be difficult because the maximum laboratory solid angle for reaction products is relatively small in mb experiments. Identification of the states of the reactants and products poses a problem with mb techniques as well as with many other methods for studying two-body collisions. However, excited species in the primary beam can be partially controlled and their abundance studied through the use of electron-bombardment ion sources in which only single collisions between electrons and molecules occur (see Section III,B,2). Turner et af. (1968b) have developed a method for measuring the abundances of specific states of ions in a beam. This method has been used for several ionic species. The ion beam is attenuated by passing it through a cell of gas; abundances are determined from an analysis of the attenuation as ? function of gas pressure in the cell. It is conceivable that a generalization of this method for other ions and neutrals could be applied in the analysis of excited states of particles in an mb experiment. Additional problems with mb experiments include, for example, those associated with making absolute measurements of fast neutral currents and determining the overlap integral It is hoped that solutions to these and other problems will be found with increasing use of the mb technique. ACKNOWLEDGMENTS I wish to thank those people whose work I discussed in this chapter for their assistance in sending me up-to-date reports of their research. I also want to acknowledge useful discussions with E. A. Entemann, R. K. B. Helbing, P. K. Rol, E. W. Rothe, and S. M. Trujillo. I give special thanks to B. F. Myers who kindly read the manuscript and gave many helpful suggestions during its preparation. My work on merging beams has been supported by the Advanced Research Projects Agency through the Office of Naval Research.

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