ELEMENTARY PROCESSES IN THE IONIZATION BY IMPACT OF MATERIAL PARTICLES*

G. Kalman and B. Rosen, Berlin

CONTENTS

Part One

Introduction

I. Electron impact. 1. Experimental methods. 2. Experimental data: a) Simple ionization of atoms, b) Simple ionization of molecules, c) Ionization with excitation, d) Formation of multiply charged ions, e) Velocity of secondary electrons in the elementary ionization process, f) Ionization by fast electrons.

INTRODUCTION

For the ionization of any body—gaseous, liquid, or solid—there are two ways: either one illuminates this body with sufficiently “hard” light, or one bombards it with a beam of material particles sufficiently rich in energy. In what follows we shall deal only with this latter process, i.e. ionization by particle impact. In doing so we shall confine ourselves mainly to the consideration only of the primary elementary act of ionization in gases. We shall discuss secondary processes quite briefly, and shall also touch upon the ionization of solids only in part.

There are three kinds of ionization by particle impact: ionization by electron impact, by ion impact, and by impact

* Physikalische Zeitschrift, 14, 521, 1931. Translated by A. B. Shekhter.

neutral particles. Ionization by electron impact experimentally plays the principal role, since the yield of ions under electron impact is, generally speaking, considerably higher than under the impact of ions or neutral particles.

I. ELECTRON IMPACT

1. EXPERIMENTAL METHODS

There are, first of all, two different experimental methods used to study primary ionization under electron impact.

The original electron-impact method—the method of Franck, Hertz, Lenard, Foote, and Mohler—confines itself to establishing the fact that, at a certain electron velocity in a given gas, ionization occurs.

The second method, in addition, makes use of a mass spectrograph, owing to which it becomes possible to establish in each individual case exactly what kinds of ions are obtained in ionization. In the present review we shall mainly describe the mass-spectrographic method of investigation. We shall regard the ordinary electron-impact method as known, referring to the detailed monograph of Franck and Jordan. Here we shall mention only the essential corrections introduced into this method in recent times.

Mass-spectrographic method. Dempster first pointed to the mass-spectrographic method²¹, after which this method was improved by a whole series of investigators*. Although this method has been described rather often and in detail, we shall nevertheless give here a brief description of the mass spectrograph in the form in which we used it for some of our investigations. We shall dwell in greater detail on the details of this apparatus elsewhere.

* Detailed references in papers 20a, 52, 56, 60, 61, 63, 66, 67, 68, 72.

The layout of the apparatus is shown in Fig. 1. Electrons emitted by a hot cathode \((GK)\) (for many studies it is advantageous to use an equipotential cathode), with the aid of two grids \(N_1\) and \(N_2\), are accelerated to the desired energy (voltage \(V_1\)) and enter the ionization space \(IR\), where they collide with gas atoms. A weak field \(V_2\) draws the ions formed toward the plate \(P\), after which they fly through the slit \(S_1\), and then acquire, between the slits \(S_1\) and \(S_2\), a stronger acceleration by the field \(V_3\) \((V_3 \gg V_2)\) and, finally, through the second slit \(S_2\) enter the space \(MR\), where they are deflected in a circular path by a strong magnetic field \(H\), whose lines of force are perpendicular to the plane of the drawing. The radius of curvature of their path \(\rho\) is

\[ \rho = c \sqrt{\frac{m}{e}\,\frac{2V_3}{H}} . \tag{1} \]

Fig. 1. Mass spectrograph.

With the aid of very narrow slits and several pumps, which make it possible to evacuate different parts of the installation separately, the pressure conditions in the separate parts can be varied independently of one another.* Having passed through the magnetic field, the ion beam (indicated in the figure by a dashed line) enters the space \(ER\) and finally reaches the receiver. In the space \(ER\) there are various auxiliary electrodes for further deflection of the ion beam; we shall discuss them later. In an ordinary measurement the ions fall on a small plate \(A\) (the receiver), located in a Faraday cylinder. The dependence of the intensity of the ion beam on the voltage \(V_3\) between \(S_1\) and \(S_2\), or on the strength of the magnetic field \(H\), gives what is called the mass spectrum. Ions with differ—

* See more details in Appendix 2. Ed.

with equal values of \(\frac{m}{e}\) reach the receiver at different magnetic fields or, respectively, electric fields \(V_3\). This is self-evident from Fig. 2.

The accelerating voltage for the electrons (\(V_1\)), at which a definite maximum of the ionic current first appears, is, generally speaking, the sought ionization potential of the corresponding ion. The dependence of the intensity of the ionic current on the voltage \(V_1\) is called the ionization function (several such functions are plotted in Fig. 3).

Fig. 2. Example of a mass spectrum (after Hogness and Kvalnes).

Another type of mass spectrograph was developed by Bleakney\(^{22}\), who himself carried out a whole series of investigations with it. The apparatus is shown in Fig. 4. The essential difference from an ordinary mass spectrograph consists in the fact that the electron current is directed perpendicular to the ionic current and, with the aid of a longitudinal magnetic field \(H\), is focused into a narrow beam.

Fig. 3. Example of an ionization function (after Bleakney).

Fig. 4. Mass spectrograph (after Bleakney \(^{22}\)).

The ions are drawn away from the path of the electron beam by the weak field \(V_2\) and, through a slit, enter a space in which (perpendicular to the magnetic field) there is located another electric field (field strength \(E\)). Under the influence of this

of the electric field and the magnetic field \(H\) the ions describe a complicated path. But, after passing through slit \(S_1\), they will also pass through slit \(S_2\) only when the force \(\frac{e}{c}[vH]\) (where \(v\) is the velocity of the ions) with which the magnetic field acts on the ions is exactly compensated by the electric field. Since, at a given accelerating voltage \(V_2\),

\[ v=\sqrt{\frac{2e}{m}V_2}, \]

the electric field that makes the ions pass through slit \(S_2\) depends on the value of \(\frac{e}{m}\) for these ions, i.e.

\[ \mathbf{E}=\frac{H\sqrt{2}}{c}\sqrt{\frac{e}{m}}\sqrt{V_2}. \]

The curve expressing the dependence of the ionic current on the electric field is used in the usual way as a mass spectrum.

In this apparatus a whole series of interfering processes is eliminated. First of all, it is possible here to avoid the electrons from the metallic walls, which are often very harmful. Further, one can work at very low pressures, so that even in the space filled with gas the results cannot be appreciably distorted by any secondary processes, above all by any selective recharging. Moreover, with such apparatus a very high intensity of the ion beam is obtained.

Another method of investigating the ionization process consists in directly measuring the losses of velocity that electrons undergo in inelastic collisions. For this purpose the electric or magnetic spectrum is recorded of an electron beam that has become inhomogeneous after collisions. This method has recently been applied by various authors \(^{115,120}\). An example of the apparatus used in this case is given in Fig. 5 (see p. 110). Bartels \(^{23,24}\) uses another method for measuring the ionization potential, based on the diffusion of ions. Kalman and Rosen \(^{26}\) give a method for the approximate measurement of the ionization—

unknown potentials of chemically unknown or experimentally difficult-to-access molecules by means of studying selective recharge.

Fig. 5. Apparatus for measuring the loss of electron velocities (according to Uddin and Dzhonson[^15]). The magnet pole, \(M\), is directed perpendicular to the plane of the drawing.

Finally, let us mention here one more new type of mass spectrograph, proposed by Bartky and Dempster[^25], which, according to the authors’ calculations, makes possible a sharper focusing of the ion beam than the usual circular deflection of the spectrograph. The method consists in the ions flying through a radial electric and a transverse magnetic field. We do not know whether experiments have already been carried out with such an apparatus.

2. Experimental Data

a) Simple Ionization of Atoms

Let us now turn to the discussion of individual ionization processes. The simplest such process consists in an electron striking an atom and tearing another electron from it. The electron torn out will in general acquire a not very large kinetic energy. The minimum energy of the incident electron at which ionization first occurs is practically equal to the ionization energy of the gas under investigation, at least for monatomic gases. It is thereby assumed that the matter in question is always the removal of the most weakly bound electron.

Most elementary ionization acts are based on this simplest process. In experiment, the onset of ionization is characterized by the sudden appearance of an ionic current, which increases sharply beginning with a definite electron energy. The ionization curve, i.e. the curve expressing the dependence of the intensity of the ionic current on the velocity of the elec-

trons, at first increases very sharply, then gradually becomes more gently sloping, reaches a maximum (at a voltage exceeding the ionization potential by approximately 100 V), and then decreases very slowly. Ionization may set in more or less sharply depending on a whole series of circumstances.

In monatomic gases, in which the rise of ionization is expressed most sharply, the accuracy with which the moment of appearance of the ionization current can be measured is approximately \(1/10\) V. It depends above all on the uniformity of the velocity of the impacting electrons.

Table I contains all the ionization potentials of atoms known up to now. It should be noted, however, that most of the values in Table I were obtained not from direct measurements by electron impact, but by the spectroscopic method*.

We have entered these spectroscopic data in the table, since they are more accurate than the data obtained by electron impact. In the table, an asterisk marks those values that have been confirmed by direct measurements by the electron-impact method. A large part of such measurements was made by the old method, without a mass spectrograph, since in the investigation of a monatomic gas there can be no doubt as to the nature of the ions formed.

Potentials of ultra-ionization. In addition to the ionization potentials entered in Table I, by means of ordinary electron impact it has been possible to find still other ionization potentials—so far for K and Hg \(^{32—39}\). Namely, if the ionic current is measured as a function of the energy of the electrons, it turns out that ionization begins at a certain definite electron energy. This energy coincides with the ionization potentials determined spectroscopically. But at energies somewhat exceeding the ionization potential, the ionization curve has

* Spectroscopic values, with a few exceptions, are obtained by extrapolating very accurately known spectral terms to the limit of the series. Thus these values often are not the result of direct measurements. The accuracy of these values depends on the correctness of the assignment of the spectral terms,

TABLE 1

Ionization potentials of atoms*

* The table in its essential features was compiled according to ^28. Additions to the numbers given there, kindly supplied to us by Dr. E. Tilo, correspond to the situation as of April 1931. For the literature, see ^28—^31. Values placed in parentheses are unreliable. Values marked with * were obtained by electron impact.

inflection points which, by analogy with the data obtained by the electron-impact method, may be interpreted as higher stages of ionization (ultra-ionization potentials). First of all the question arises whether these inflection points are connected with excitation of the atomic ion. Since the excitation potentials of atomic ions are for the most part known, it can be established that the inflections do not coincide with the known excitation stages. Such ultra-ionization potentials have been found in a large number of works. Lawrence^32 developed for this purpose a special electron-impact method in which the electrons, before ionizing, are spectroscopically analyzed in a magnetic field, so that only electrons with a relatively homogeneous velocity enter the ionization space.

Lawrence’s results have recently been confirmed and supplemented by Morris^33 and by many other authors.^34–36

All the ultra-ionization potentials so far found in Hg are collected in Table II. Up to now it has not been possible to give these potentials a satisfactory interpretation. Gaunt^37 and Hippel^9 believe that the matter here depends on the excitation of metastable atoms. The supposition has also been expressed that the ultra-ionization potentials are related to the ionization of molecules. Against this it may be objected that the concentration of molecules in these experiments was evidently small, whereas the inflections obtained were rather sharply expressed. Moreover, an increase in temperature did not affect the sharpness of the inflections. It is interesting to note that in ionization by light, apparently, analogous inflections are obtained in the ionization curve.^39

In K an inflection of the ionization curve was found at an energy approximately 1 V greater than the ionization potential.

b) Simple ionization of molecules

Let us now turn to a discussion of the process of ionization of molecules. The ionization potentials of molecules are given in Table III. These values were obtained by the electron-impact method, since spectroscopic data here are very scarce.

Ultra-ionization potentials

somewhat. Therefore the accuracy of the values given in Table III is correspondingly lower. To this it should also be added that the moment at which ionization of a molecule sets in can be established less accurately than for atoms, and for the following reason. The ionization potential of a molecule is taken to mean the energy required in order to tear an electron out of an unexcited molecule and remove it to infinity without imparting kinetic energy to it. The molecular ion that remains in this process must also be unexcited. One of the difficulties hindering the determination of the ionization energy of a molecule consists in the fact that the bombarded molecules have already been excited as a result of thermal motion (rotational and vibrational energy). At room temperature this excitation is small (approximately only 1% of all molecules possess an additional energy of about 0.2 V). But one must not forget that, owing to the proximity of the hot cathode, molecules possessing an excitation corresponding to a higher temperature may penetrate into the ionization space.

The second, far more substantial difficulty consists in the fact that, in general, it is not known whether the process of ionization of molecules consists in the simple removal of an electron. It is quite possible that, simultaneously with ionization, excitation (nuclear vibration and rotation) of the molecular ion also takes place, occurring with appreciable probability. In this case an excited molecular ion would be formed upon ionization.

If the probability of formation of a molecular ion without excitation of nuclear vibrations is relatively small, while

...and Cd in Hg [32—39]. Ionization potential \(Hg = 10.4\ \mathrm{V}\)

the probability that excited molecular ions are formed upon electron impact is much greater, then strong ionization would have to occur at an energy lying above the true ionization energy. This, apparently, does occur in some cases. Thus, for example, from the optical excitation of band spectra it is known that, in a transition with absorption of light from a definite electronic state to a higher state, in this higher excited state the lowest nuclear vibrations are not always excited; often only higher nuclear vibrations are excited.

The probability of excitation for the very lowest nuclear vibrations is often very small; for certain nuclear vibrations this probability increases and then falls again. Analogous conditions also obtain when the question is not excitation but the tearing away of an electron. Theory shows that, at least for fast electrons, the probability of ionization is approximately characterized by the probability of an optical transition. Therefore one may think—and this can be justified theoretically—that analogous conditions also obtain for ionization by slow electrons. Consequently one must be prepared for cases in which the probability of ionization with excitation of nuclear vibrations will be much greater than the probability of ionization without such excitation.

A clear elucidation of this fact was given by Franck^40 and Condon^41. It is essentially based on the fact that electron impact is a process so rapid that the mutual arrangement of the nuclei does not have time to change appreciably during the time

*

of this impact. Therefore the excitation of one or another nuclear vibration depends above all on the difference in the internuclear distances, on the position of equilibrium in the normal and excited states, and on the force causing the nuclei to oscillate about their equilibrium positions in the normal and ionized state.

The ionization potentials placed in Table III, with the exception of the ionization potentials of the molecules H$_2$, N$_2$, and CS$_2$ and of the quantities placed in parentheses, were obtained directly by the mass-spectrographic method. In other words, these are the electron energies at which molecular ions of the indicated kind first appeared in the mass spectrograph. That is, the numbers given provide us with the true ionization potentials plus a certain unknown excitation of nuclear vibrations.

TABLE III

Ionization potentials of molecules (for literature see $^{50}$)

* See below.
* See p. 000.
* See $^{48}$ and $^{49}$.
* According to Bleakney and Tate $^{45}$, mass-spectrographic method.
* Average from older measurements by electron impact.
* Calculated value.
* Average from measurements by the electron-impact method.
** Calculated from spectroscopic data.
** Calculated from spectroscopic data.

The figures in Table III that are given in parentheses were obtained without a mass spectrograph. They assume that these figures correspond to ionization of molecules.

Determination of the true ionization potential. There are cases in which it is possible to decide whether, under electron impact, the true ionization energy is being measured, or the ionization energy plus the energy of excitation of nuclear vibrations. Namely, for hydrogen it is possible, by theoretical and spectroscopic means, to determine the true ionization potential exactly. Burrau42 calculated by quantum mechanics the ionization energy of H₂ and obtained the value 15.12 V. Horowitz and Finkelstein43 find a somewhat larger value—16.62 V, but this value should be regarded only as an upper limit. On the basis of optically known molecular terms Richardson and Davidson44, proceeding from formulae of the Rydberg type, obtained the value 15.235 V or 15.381 V, depending on whether the zero energy is included or not. This is probably the most accurate value of all those obtained so far.

All authors who worked both with a simple electron-impact apparatus and with the aid of a mass spectrograph experimentally found the ionization potential to be about 16 V. Only Bleakney and Tate45, with their new type of mass spectrograph, find that the formation of ions begins at 15.4 V. All this apparently indicates that, in the formation of molecular ions of hydrogen, certain vibrational quanta are excited with sufficient probability. But, according to Bleakney’s results, ionization without excitation of vibrational quanta also has an appreciable probability, whereas according to the earlier experimental data only a very small probability had been ascribed to it. For other gases the theoretical ionization potential is unknown. Nor can it be extrapolated from spectroscopic data. Nevertheless, in some cases it is possible to determine the true ionization energy rather accurately. Namely, for those gases for which band spectra of molecular ions are known, i.e., bands correspo-

resulting from transitions of molecular ions with electronic excitation into normal molecular ions, one can calculate the true ionization energy in the following way. These systems of bands are excited by electron impact. In this case it turns out that the bands of the molecular ion are excited by electron impact in a single act, i.e., in an electron impact a molecular ion is formed at once which, at the same time, already possesses electronic excitation (for excitation of this kind, see the following section).

To determine the excitation energy of the initial level of some group of a given system, corresponding to a definite electronic and nuclear excitation from the normal state of the neutral molecule, it is sufficient to analyze the band systems obtained upon excitation by electron impact in fluorescence light and to determine at what electron energy this group of band systems, corresponding to a state with a definite electronic excitation and a definite nuclear vibration, is first excited. Since, on the other hand, owing to precise knowledge of the band systems, the excitation energy of this level from the normal state of the molecular ion (i.e., of the molecular ion without nuclear vibration) is also known, then, by subtracting these two excitation energies from one another, one can determine the primary ionization energy^46. But such a procedure is applicable only in those cases where the term system of the molecular ion is sufficiently well known. Thus, for example, this is the case for the molecular ions of nitrogen, and Turner and Samson^47 obtained in this way, for the true ionization energy of nitrogen, the value 15.8 V, whereas by the usual mass-spectrographic method an ionization energy above 16 V was obtained.

c) Ionization with excitation

Up to now we have touched only upon those ionization processes in which, chiefly, molecular ions were formed that were either entirely unexcited or possessed relatively small vibrational excita-

... Now we shall examine ionization processes characterized precisely by the fact that excitation also occurs simultaneously with ionization. Excitation associated with ionization is manifested above all in the fact that the mass spectrograph registers not simple molecular ions, but products of the dissociation of molecular ions. Further, this excitation is manifested in the emission of light belonging to the spectrum of the molecular or atomic ion that has been formed. In these processes we are dealing chiefly with the excitation, occurring simultaneously with ionization, of more strongly bound electrons. The limiting case of the excitation of such electrons is the formation of multiply charged ions, which will be discussed below.

Ionization and dissociation. First of all let us examine the processes in which excitation of ions formed by electron impact is marked by the appearance of new kinds of ions.

In mass-spectrographic investigations it was found that, with a gradual increase in the velocity of the impacting electron, simple molecular ions of the gas present in the ionization space are formed first. With a further increase in the electron energy, at a certain value of this energy new ions appear, owing their origin to dissociation of the molecular ion. In Table IV, columns 2 and 3 give the energies of formation of such decomposition ions and indicate the kind of decomposition products.

These dissociations occur because, upon ionization, the molecular ion simultaneously receives either a vibrational quantum or a vibrational quantum together with electronic excitation; moreover, this excitation may sometimes be so strong that the molecular ion decomposes spontaneously, with one of the decomposition products carrying away the charge. One can also imagine the case in which excitation produces a molecular ion rich in energy, possessing energy sufficient for decomposition, but which nevertheless does not decompose spontaneously. We

TABLE IV

Dissociation of molecular ions associated with ionization*

* See literature 51–78.
** Minimal energies can be calculated only when the ionization potentials of the dissociation ions formed are known (cf. pp. 528 and 530).
*** The source is unreliable.

would then be the formation of a metastable molecular ion rich in energy. One may think that such formations, upon collisions with other molecules (or with the wall), decompose or react chemically with them. This would mean that the decomposition and formation of new kinds of ions would be caused by a secondary process. The question of which process causes dissociation—primary or secondary—can be decided in the following way. If the process is primary, then the ratio of the intensities of the ions dissociated to the primary molecular ions does not depend on the pressure in the ionization space. If, however, the formation of certain ions is the result of a secondary process, then the relative amount of these ions will increase with increasing pressure, for at low pressures the number of collisions decreases and, consequently, so does the number of ions formed in the secondary process. Apparently all the decomposition ions listed in Table IV are of a primary nature. Their relative amounts do not depend on the pressure (the values placed in parentheses are not reliable; their independence of pressure has not yet been investigated).

Secondary processes. The formation of ions in secondary processes has been proved by a whole series of investigations. True, for the most part what arise here are conglomerates of ions (one ion adheres to several neutral molecules), formed with sufficient frequency only at higher pressures. In mass-spectrographic investigations, up to now secondary ions whose origin is known with sufficient reliability have been found only in H₂, I₂, and K. In hydrogen, H₃⁺ ions appear. A whole series of investigations has established that these ions, appearing at high pressures in very large quantities, are of secondary origin. The reaction leading to the formation of these ions is as follows: H₂⁺ + H₂ = H₃⁺ + H. This is consistent with the circumstance that H₃⁺ is formed at the same energy as the H₂⁺ ion, and that the intensity ratio H₃⁺ : H₂⁺ increases strongly with pressure⁵². An example of another secondary

process of this kind is the formation of \(J_3^+\) from \(J_2^+\) \(^{62}\). The reaction in this case is probably analogous, namely:

\[ J_2^+ + J_2 = J_3^+ + J. \]

In iodine, apparently, other processes also occur in addition, which may proceed according to the following scheme (charge transfer):

\[ J^+ + J_2 = J_2^+ + J. \]

The secondary processes leading to the formation of \(K_3^+\) in potassium vapors \(^{78}\) probably proceed according to a scheme analogous to the formation of \(I_3^+\).

Primary dissociation upon excitation of nuclear vibrations during ionization. The primary ions of the decomposition products, noted in Table IV, as has already been said, are the result of excitation of nuclear vibrations, perhaps also connected with electronic excitation. Dissociation as a consequence of nuclear excitation occurs as follows: when an electron is torn away, the nuclear vibrations of the molecular ion are simultaneously excited. If in this process a nuclear vibration is excited that already lies in the region of the continuous vibrational spectrum, then decomposition of the molecular ion takes place. If decomposition occurs into a normal neutral particle and a normal ion (in the case of a diatomic molecular ion this corresponds to a normal atomic ion and a normal neutral atom), then the formation of the decomposition ion will begin at an electron energy equal to the ionization energy plus the dissociation energy of the molecular ion into the normal decomposition ion and the normal neutral particle. The onset of ionization corresponds to excitation of the beginning of the continuous vibrational spectrum. In this case the ions fly apart without noticeable kinetic energy. The energy at which decomposition ions can first be formed can in many cases be calculated from the dissociation energy of the normal molecule and from the ionization energy of the atom or particle formed upon decomposition. As an example, let us give the calculation of the energy of formation of the ions CO and \(\mathrm{CO}_2\). \(\mathrm{CO}_2\) dissociates

on CO and O, absorbing an energy of 5.7 V. The true ionization energy of CO is 14.3 V. Thus, CO ions can be formed from neutral CO₂ only at an electron energy equal to at least \(5.7 + 14.3 = 20\) V. The energies calculated in this way are placed in the fourth column of Table IV for the various dissociation processes, while the processes themselves are indicated in the third column.

But the continuous vibrational spectrum of a molecular ion does not always correspond to dissociation into two normal unexcited particles. The continuous vibrational spectrum may also correspond to the dissociation of a molecular ion into a normal and an excited particle, the excited one being either the ion or the neutral particle (or both together). It may be thought that in this case the ion appears not at the minimum possible energy calculated in Table IV, but at an energy exceeding this minimum value by the excitation energy of the dissociating particle.

However, even in such cases the ions of the dissociation products may nevertheless appear at the minimum possible energy. Namely, when such strong nuclear vibrations are excited in the molecular ion that it can energetically dissociate into two normal unexcited particles, then for such a process there exists a certain probability by way of the so-called radiationless transition, in which the molecular ion dissociates from a high, quasi-discrete state with nuclear vibration into two separate particles 79–83. The difference from the case of dissociation by excitation of a continuous vibrational spectrum is that in this latter type of excitation the molecular ion dissociates instantaneously, whereas in dissociation by a radiationless transition the molecular ions, on average, dissociate only after some time following excitation. When the transition probability is very small, the molecular ion lives for a very long time, and practically no dissociation occurs. The experimental conditions in mass-spectrographic investigations are, generally speaking, such that such dissociation could be replaced

given a lifetime of these excited molecular ions equal to a minimum of \(10^{-6}\) sec. For atomic processes such a lifetime is relatively long.*

Consequently, one may expect that in this case as well, in which the continuous spectrum corresponds to decay into a normal and an excited particle, dissociation sometimes begins already at the theoretical limit for decay into unexcited particles.

A comparison of the measured and theoretical critical potentials for the appearance of dissociation ions shows that in most cases the dissociation ions do indeed appear near the very lowest of the expected values of the electron energy (see Table IV).

Excitation of states that have no equilibrium position\(^{84-89}\). There exist, however, still other dissociation processes, the most essential difference of which consists in the fact that the ions fly apart with considerable kinetic energy. Namely, it may happen that upon ionization such an electronic level of the molecular ion is excited which in general possesses only a continuous vibrational spectrum. Such electronic levels without a discrete vibrational spectrum mean that, in this state, the molecule or molecular ion in general has no equilibrium state.**

When such a level is excited, the molecular ion breaks up into its constituent parts. The duration of the electronic impact is of the order

\[ \frac{l}{v}, \]

(\(l\) is the diameter of the molecule, \(v\) is the velocity of the electrons). This time is so small that during it, owing to the large mass of the nuclei, the distances between them change—

* If the decay is caused by a nuclear vibration plus electronic excitation, then the time allowed for the transition without radiation is considerably shorter, for a particle with electronic excitation, generally speaking, in view of the possibility of radiation, lives only \(10^{-8}\) sec.

** The existence of such states is explained by the fact that, according to wave mechanics, two separate systems, generally speaking, can interact in different ways: they may attract or repel each other at any distance between them.

ELEMENTARY PROCESSES IN IONIZATION

are only very slightly changed. If the excited electronic level has no equilibrium position, then the nuclei in the excited state possess a positive interaction energy, the magnitude of which corresponds to the distance between them in the normal state. As a result of this positive interaction energy, the nuclei, under such excitation, fly apart, and moreover with finite kinetic energy.

For the molecular ion of hydrogen the conditions are theoretically known to some extent, and it has been calculated ^85,87 that, at approximately 27 V, an electron ionizes a neutral hydrogen molecule while simultaneously exciting it in such a way that the molecular ion decomposes into a normal hydrogen atom and a hydrogen ion, both of them possessing a kinetic energy of about 5 V. Such an appearance of fast dissociated ions is difficult to observe in a mass spectrograph. For, as a consequence of the fact that these ions, upon decomposition, acquire velocities in all possible directions, the ion beam passing through the diaphragms of the mass spectrograph becomes so blurred that it is no longer possible to determine the maximum accurately. (The ions usually recorded in the mass spectrograph acquire only small velocities upon decomposition, as is evident from the sharpness of the maxima; apparently this is explained by the fact that they are formed only upon excitation of the continuous spectrum.) And indeed, in all experiments with electron impact in hydrogen a critical potential at 28–30 V was observed. With the aid of his new mass spectrograph, Bleakney ^87 succeeded in showing that, at this ionization potential, the transfer of kinetic energy to the ion is involved. But the correctness of the theoretical considerations was finally proved only by Lozier ^88,89, who investigated ionization by electron impact by an entirely different method. His apparatus was such that, with the aid of retarding fields, it was possible to determine how many ions were formed that had acquired a definite kinetic energy upon ionization. It is true that in this case it was no longer possible to determine the mass of the ions. In this way Lozier found that in hydrogen, beginning at approximately 28 V, there indeed

hydrogen ions are formed which have velocities of about 5–6 V. The yield of such ions possessing kinetic energy is less than the yield of ordinary ions without kinetic energy. Analogous experiments with nitrogen[^89] showed that above 35 V ions with a kinetic energy of about 3 V appear in nitrogen. At high electron velocities in nitrogen the number of ions with kinetic energy apparently even exceeds the number of ions without kinetic energy.

Ionization and the excitation of light in a single act. Let us now turn to processes in which ionization is manifested not in the formation of dissociation ions, but chiefly in the emission of light originating from an atom or a molecule.

Fig. 6. Intensity of the negative band of nitrogen 3914 Å, produced by the electron beam, as a function of the electron velocity (both curves correspond to two different positions in the discharge tube), after A. Lind[^96].

In Table V several of the best-known excitations of this kind are given (for molecules). It is clear that here ionization and electronic excitation occur simultaneously. That this electronic excitation, which determines the emission of the observed fluorescence, takes place in a single act together with ionization is evident above all from the following circumstance (see p. 119). Light is emitted only beginning with an electron energy approximately equal to the normal ionization energy of the gas under investigation, plus the excitation energy of the corresponding bands present in the fluorescence spectrum. For atoms many such processes have been investigated. For molecules, among processes of this kind, the excitation mentioned on p. 118 of the bands of the molecular nitrogen ion has been best investigated.[^90],[^91] In nitrogen, Lind[^96] also investigated the intensity of fluorescence and, thereby, the probability of excitation of individual vibrational states of excited electronic levels of the molecular ion as a function of the electron velocity. It turned out that there is a remarkable wave-like dependence on the electron energy (see Fig. 6), for which no explanation has yet been found.

TABLE V

Ionization with simultaneous excitation

For atomic ions, the corresponding excitation function has recently been investigated by Larpe \(^{99}\) (see Fig. 7).

d) Formation of Multiply Charged Ions

We now pass to a special limiting case of ionization associated with excitation, namely to the case when the most weakly bound electron of the ion is excited so strongly that it too is torn away and flies off. In this process two secondary electrons and an ion with double charge arise. In this case the doubly charged molecular ion may sometimes dissociate into singly charged ions.

Fig. 7. Excitation function of zinc spark lines (after Larpe \(^{99}\)).

Direct formation of multiply charged ions. For atoms one may expect that ions with double charge, formed in this way in a single elementary act, will first appear at electron energies just sufficient to tear out both of the most weakly bound electrons and carry them off to infinity without imparting velocity to them. Analogously, the formation of ions with still higher charges must occur in the same way. And indeed, in electron impact with the aid of a mass spectrograph it was found that multiply charged

ions first appear at these energies (sometimes also known from spectroscopic data) ^100, ^101. (The circumstance that multiply charged ions do not appear at lower electron energies by direct impact of an electron on an ion is explained by the fact that, owing to the very low ion density in these experiments, the probability of collision between an ion and an electron is vanishingly small.) Table VI gives these ionization potentials for multiply charged atomic ions. But these values, like the values in Table I, are for the most part of spectroscopic origin. Only the values marked with an asterisk have been approximately confirmed by mass-spectrographic investigations. Only the values of the ionization potentials of $\mathrm{Ne}^{+++}$, $\mathrm{Hg}^{+++}$, $\mathrm{Hg}^{4+}$, and $\mathrm{Hg}^{5+}$ were found by electron impact. We shall speak below, in the general discussion of the question of yields, about the relative probability with which these multiply charged ions are formed.

Let us note that, in addition to the ions listed in Table VI (p. 131), formed by direct electron impact, still other multiply charged ions have been observed in canal rays ^102. The cause of their formation in the discharge tube may be not only the process just described. They may also be formed there by ion impact. It is interesting that in canal rays certain particular multiply charged ions are formed especially often. Thus, for example, above all we find multiply charged atomic chlorine ions ^104 (up to fivefold charged) and multiply charged Hg ions ^103. According to some data, even 18-fold charged Hg ions exist ^105. True, the process of their formation has not yet been completely clarified. The high frequency with which multiply charged Hg appears in canal rays is reflected also in experiments with electron impact. $\mathrm{Hg}^{2+}$, $\mathrm{Hg}^{3+}$, $\mathrm{Hg}^{4+}$, and $\mathrm{Hg}^{5+}$ are formed by electron impact with comparatively large yields ^100 (with much larger yields than $\mathrm{A}^{++}$, etc.). No measurements with electron impact have yet been made for chlorine ions.

The conditions for the formation of multiply charged ions from

molecules are very complicated. Indeed, multiple ionization presupposes the simultaneous tearing out of many electrons from a molecule. But in doing so all the bonds in the molecule change completely, and often a doubly charged molecule immediately breaks up into singly charged ions.

Let us try to clarify this process for ourselves using the example of the hydrogen molecule \(^{84-88}\). In order to ionize a normal \(H_2\) molecule twice, a minimum energy of \(31.3\ \mathrm{V}\) is needed, namely the dissociation energy of the \(H_2\) molecule, \(=4.3\ \mathrm{V}\), and twice the ionization energy of the atom, equal to \(27\ \mathrm{V}\). However, with the aid of \(32\)-volt electrons it would never be possible to tear both electrons out of the \(H_2\) molecule. The electron impact proceeds very rapidly. Therefore, if two electrons are removed from the \(H_2\) molecule by electron impact, then there will remain two positively charged ions, the distance between which is approximately equal to the distance between the nuclei in the simple \(H_2\) molecule.

But these ions possess, relative to one another, a potential energy of approximately \(18\ \mathrm{V}\); therefore both these nuclei will fly apart with a kinetic energy of approximately \(9\ \mathrm{V}\) each. Thus, in order to remove two electrons from \(H_2\) molecules by electron impact, it is necessary, in addition to the already mentioned \(32\ \mathrm{V}\), to expend also the potential energy of repulsion, \(18\ \mathrm{V}\).

As a consequence of the short duration of the electron impact, about \(50\ \mathrm{V}\) is therefore required in order to tear two electrons out of an \(H_2\) molecule. Analogous conditions also hold for other molecules. One may suppose that molecules, when two electrons are torn out, predominantly break up into separate simple ions.

Nevertheless, one can very well imagine that sometimes a multiply charged molecular ion may also exist (if one starts from a doubly charged atomic ion and a neutral atom).

Until recently, experimentally, on the basis of measurements in canal rays, it was believed that multiply charged molecular ions exist only very rarely*.

* An exception is the existence of doubly charged \(BF_3\) ions in canal rays \(^{103a}\).

However, in more recent works it has turned out that other doubly charged molecular ions are also encountered in canal rays. Conrad \(^{104}\) showed that ions \(\mathrm{CO_2^{++}}\), \(\mathrm{CO^{++}}\), and also \(\mathrm{CH^{++}}\), occur with appreciable intensity in canal rays. Meanwhile it has also been possible, by means of electron impact \(^{106}\), to find the ions \(\mathrm{CO_2^{++}}\) and \(\mathrm{CO^{++}}\) and to determine the critical potential of their formation (about 50 and 45 V, respectively)*.

Recently it has also been possible to find, by the method of electron impacts, the ions \(\mathrm{CO_2^{++}}\) and \(\mathrm{CO^{++}}\) and to determine the voltage required for their appearance (approximately 50 and 45 V) \(^{106}\). It thereby turned out that these ions can energetically decay into two ions with simple charges, but that, nevertheless, they exhibit an appreciable lifetime. Further, with respect to decay into a singly charged ion and a neutral atom they are stable. In exactly the same way, by the electron-impact method \(^{106}\), the formation of multiply charged atomic ions from molecules was investigated, and it was found that \(\mathrm{C^{++}}\) ions arise from \(\mathrm{CO_2^{++}}\) at approximately 55 V, and from \(\mathrm{CO^{++}}\)—at approximately 45 V.

Formation of multiply charged ions by the Auger effect. Until now we have always reduced the formation of multiply charged ions to a process in which two electrons are simultaneously torn out of an atom or molecule. There is, however, still a quite different method of formation of multiply charged ions \(^{107-114}\). From a neutral particle an electron is torn out of an inner shell, i.e., a comparatively strongly bound electron. (Such ionization of the inner shell will be discussed one section later.)

In this way an ion arises which lacks an electron in the inner shell. In the general case, as is known from X-ray emission spectra, such a missing electron is replaced by another electron from a more distant shell. It is known that such a process

* Later the ions \(\mathrm{NO_2^{++}}\) and \(\mathrm{NO^{++}}\) were also found.

TABLE VI

Ionization potentials of ions *

* In columns 1, 2, etc., the potentials are given that are required in order to ionize monovalent, divalent, etc. ions. Values in parentheses are unreliable; values with * were found by the electron-impact method.

*

can also occur without radiation (Meitner ^107^, Auger ^108–110^). Then the energy released when an electron falls from a higher level to a lower one goes to the ejection of yet another electron from one of the more distant shells and to the transfer of this electron to infinity with the corresponding velocity. In this process a doubly charged ion is formed. If the shell from which the second electron is torn out is not the outermost one, the process may be repeated. Then triply and multiply charged ions are formed. These processes were studied in detail by Auger ^112^ in a Wilson chamber (although he produced the first ionization by X-rays). It turned out that, for atoms with small atomic number, such radiationless processes leading to the formation of multiply charged ions are relatively frequent. 93% of all argon atoms in which the K-shell is excited decay without radiation; at higher atomic number the frequency of radiationless processes becomes smaller; for krypton it is below 50%. It should be noted, however, that these ionization processes of the inner shell are in general not very frequent, since the probability of ionization of the K-shell, at least for fast electrons, is inversely proportional to the ionization energy. Thus ionization of the K-shell is much rarer than ionization of the most weakly bound electron.

d) Velocity of secondary electrons in the elementary ionization process

Above, we have essentially examined the most important primary processes arising in ionization by slow elec-

trons. Let us now consider another question: what velocity is acquired by the electrons torn away in these processes from atoms or molecules (secondary electrons). One may try to solve this question by directly measuring the energy losses of the primary electrons during ionization. Such measurements have been made, the spectrum being recorded of an electron beam of known energy that has passed through a gas1. After passing through the gas, the beam contains both electrons that have undergone practically no loss of energy and electrons that have undergone quite definite losses of energy \(E, E_1, E_2, E_3\), etc. It turned out that these energy losses correspond to various levels of excitation of the atoms or molecules of the gas under investigation. However, no selective maximum was found that would correspond to an energy loss equal to the ionization energy. On the contrary, in those cases when the initial energy of the electrons is considerably greater than the ionization energy, in addition to the discrete energy losses corresponding to excitation, apparently all possible energy losses greater than the ionization energy occur. This indicates that, in the process of ionization, the electron detached from the atom always carries with it a certain amount of kinetic energy[^117-119a].

True, in the velocity spectra of electrons selective maxima were also observed corresponding to energies exceeding the ionization energy. Rudberg[^121] found such a maximum in CO (an energy loss of 19 V) and believes that it corresponds to ionization simultaneously with excitation. Here, however, it is not clear why ionization simultaneously with excitation gives a selective maximum, whereas simple ionization does not. In hydrogen, Whiddington and Jones[^115] find, at a primary-electron velocity of 70 V, a weakly expressed maximum above the ionization energy—

…ionization, as though corresponding to an energy loss of 26 V. However, in their opinion, this maximum corresponds to repeated excitation.

Up to now no direct measurement has been made of the velocity of secondary electrons in ionization by slow electrons. But from measurements with fast ionizing electrons one may conclude that, in ionization, slow secondary electrons appear predominantly, as should also be expected from theoretical data.

e) Ionization by fast electrons

Let us touch briefly also on the ionization processes that occur when an atom is bombarded by very fast electrons.

By fast electrons we mean electrons with a velocity of approximately 10,000 V and above. The ionizing action of fast electrons, the theory of which is given in Appendix I, falls into two parts: first, ionization of the outer shell of the atom, i.e. the tearing away of the most weakly bound electrons, analogous to what occurs in ionization by slow electrons; secondly, ionization of the inner shells of the atom.

This latter type of ionization can be detected experimentally by the appearance of the corresponding hard fluorescence (K-, L-, and similar X-ray lines). It is already evident from purely quantitative experiments that the yield of such ionization processes is very small ^{160}. This is also in agreement with theoretical considerations, according to which ionization at higher levels must be inversely proportional to the ionization energy of the corresponding level. We shall return to the discussion of quantitative measurements of yields in processes of this kind in the last section, in the general consideration of the question of yields.

The question of the ionizing action of fast electrons on the outer shell has also been investigated experimentally, in particular for hydrogen ^{171}. In these experiments attention was directed first of all to the distribution of velo-

…of the velocities of the secondary electrons. Since the experiments were carried out with hydrogen, the secondary electrons could originate only from the outer shell; and since the experiments were carried out in the gas phase, the slow electrons detected could indeed only have been secondary electrons that had not yet lost velocity as a result of multiple reflection or braking.

TABLE VII

Distribution of velocities of secondary electrons in hydrogen (after Bethe\(^ {14}\)).

Table VII gives Ishino’s experimental data and, for comparison, the theoretical values according to Bethe’s theory\(^ {14}\) (cf. p. 524). The data presented are the number (in percent) of those secondary electrons that were able to overcome a given retarding potential. The velocity of the incident electrons was about 10,000 V. It is clearly seen that approximately 80% of all secondary electrons have an energy of 10 V or less, and only 5% have an energy above 100 V. The values obtained from Thomson’s classical collision theory do not agree so well with experiment.

(To be continued in the next issue.)

1. Recently Whiddington and Roberts[^121a] investigated velocity losses in \(O_2\) and found a clearly expressed maximum corresponding to ionization of \(O_2\), so that—at least in this case—the detached electron carries with it only a very small amount of kinetic energy. ↩