PHOTOIONIZATION OF GASES

A. Terenin, Leningrad

Difficulties of an experimental nature and the limited choice of objects have not allowed the optical ionization of gases to develop to the same extent as other related fields of investigation. Meanwhile, the results obtained are of primary importance for understanding the process of recombination of an electron with an ion, for the interpretation of astrophysical phenomena, and, finally, the ionization of molecules by light can provide a number of valuable data on their structure.

The present article gives a review of the available material. In the first part the results obtained with vapors of alkali metals are set forth; in the second, the comparatively few data on the photoionization of molecules.

I. PHOTOIONIZATION OF ATOMS

When light of ever increasing frequency acts on a monatomic gas in the region of its line absorption spectrum, the phenomenon of re-emission, or fluorescence, is observed (at sufficient rarefaction of the gas), associated with the transfer of atoms to ever higher energy levels. With the attainment, however, by the frequency \(\nu\) of the incident light of a limiting value \(\nu_0\), corresponding to the boundary of a series and initiating the region of continuous absorption, the light ionizes the atoms; that is, the electrons, which previously manifested themselves only indirectly—in the processes of absorption and emission—are now separated from the atoms in the free state, according to the elementary process

\[ h\nu + A \to A^{+} + e_v \qquad (\text{for } h\nu \geq h\nu_0); \]

where the sign \(v\) for the electron indicates its velocity, uniquely related to the frequency \(\nu\) by the equation:

\[ \frac{1}{2}mv^2=h\nu-h\nu_0. \tag{1} \]

With the loss of the neutral state, atoms become accessible to detection by sensitive electrical methods, which make it possible very simply and directly to count the number of elementary processes caused by light—a quantity obtained from optical data only by indirect calculations.

The threshold ionization frequency \(\nu_0\), like the ionization potential, is determined most accurately from the series analysis of the atomic spectrum, where it corresponds to the deepest of all the existing terms. In those cases where such an analysis has not been carried out, there are, for the most part, values of the ionization potentials obtained by the electron-impact method. Table 1 gives the ionization potentials of the most common atoms.

Table I

\(\nu_0\) (volts)

In ordinary experiments on photoionization, before reaching the gas, the light from the source must pass through a layer of air and through quartz or fluorite walls. The shortest \(\lambda\) still transmitted by air is \(1850\ \text{Å}\), which corresponds to a maximum quantum energy of \(6.7\ \text{V}\). Removal of the air and the use of fluorite would make it possible to advance to \(10\ \text{V}\) (approximately \(1200\ \text{Å}\)), but most elements require heating, sometimes considerable, in order to be converted into the gaseous state; moreover, at high temperature metal vapors act destructively—

act on the walls. It is therefore understandable that experiments on photoionization had to be limited to alkali metals as elements with the lowest ionization potentials and the greatest volatility. The objects of the experiments described below were almost exclusively vapors of K, Rb, Cs. The limiting wavelengths \((\lambda_0)\) for the onset of photoionization for them are: Cs 3 183, Rb 2 967, K 2 856, Na 2 412 Å.

Experimental method. In experiments on the photoionization of gases, the following three types of apparatus are used:

1. A condenser is placed in a vessel with the gas under investigation, and a voltage is applied to it; the conduction current arising in the gas when the space between the electrodes is illuminated is measured (Fig. 1). Such an apparatus was used in all the older works on photoionization, the results of which, however, are not very reliable: photocurrents from the electrodes and walls, caused by scattered light, were of the same order as, or even exceeded, the volume ionization current in the gas [1, 2, 3, 7, 45].* At the present time this simple apparatus is also rather often used [8, 20, 16, 46], especially for absolute measurements of photoionization, i.e., measurements of the number of ions produced by light of a given intensity [21, 31]. A particularly advantageous form and arrangement of the electrodes are shown in Fig. 2 [31]. A drawback of this apparatus is the circumstance that the electrodes are immersed in the vapor and are heated together with it; the resulting thermionic current interferes with the observations.

Fig. 1.

Fig. 2.

1. The most irreproachable method is the use of a molecular or atomic beam, i.e., a bounded stream of vapor in a high vacuum (Fig. 3). In this case the electrodes remain cold and can

* The numbers in square brackets refer to the bibliography at the end of the article.

PHOTOIONIZATION OF GASES

may be most advantageously arranged with respect to the incident light intersecting the molecular beam either in the space between the electrodes or below it. The uncertainty in the value of the vapor density in the beam makes it difficult, in this arrangement, to carry out exact measurements of the spectral distribution of the photosensitivity. Usually it is used to establish the limiting wavelength—the onset of photoionization [9, 12, 15, 23, 35]. *

1. A very sensitive method, widely used for investigating the spectral distribution of photosensitivity, is based on the neutralization by positive ions of the negative space charge that limits the strength of the thermoelectron current from a heated cathode [14]. In Fig. 4 is shown the apparatus of Foote and Mohler: in a sealed vessel with Cs vapor, a thermoelectron current goes from the heated cathode filament to the cylindrical anode; the applied potential difference is less not only than the ionization potential, but even than the resonance potential of the vapor; therefore the electrons exert no action on the vapor atoms. However, the appearance in the space between the electrodes of even an insignificant number of positive ions, produced by illumination of the vapor through the left-hand window and the mesh wall of the anode, causes neutralization of the space charge, accompanied by a significant change in the electron current, which exceeds the ion current that has arisen by \(10^4—10^5\) times and, within certain limits, is proportional to it. Such a large effect is connected with the small probability of neutralization of the ion and its low velocity compared with the velocity of the electrons. Moreover, owing to the small dimensions of the cathode, the ions describe long spiral orbits before falling onto it. Under these conditions one ion can neutralize the charge of \(10^3—10^6\) electrons [30, 31, 37]. Illumination of the electrodes by the stray light of the source and the photoeffect thereby produced do not affect the experiment, since it only slightly increases the number of electrons already present in excess. The convenience

Fig. 3.

Fig. 4.

* Recently, in such an apparatus it was shown that, in the photoionization of K atoms, the electrons fly out predominantly in the direction of the electric vector of the incident light wave (47).

The advantage of this peculiar amplifier arrangement consists in the fact that it replaces the direct measurement of a photoionization current of the order of \(10^{-10}\) A by measurements of changes in an electron current of the order of \(10^{-5}\) A, accessible to an ordinary galvanometer. If one also takes into account that the vapors in a sealed and uniformly heated vessel are in a stationary state in the sense of elasticity, then the advantage of this method is obvious. All the most accurate measurements of the dependence of photosensitivity on wavelength have been made by this method. Its imperfection, however, is the deviations from proportionality between the ionic current and the change in the electron current, which occur at large values of the former. Fluctuations in the electron-current intensity caused by fluctuations in the heating of the filament can be compensated by means of a corresponding circuit proposed by Lawrence and Edlefsen (Fig. 5) [30]. The heated cathode filament is situated symmetrically with respect to two cylinders—anodes; only the space inside the left cylinder is illuminated, causing a deflection of the galvanometer \(G\), previously set to zero with the aid of the resistances \(R_1\) and \(R_2\); the deflection of \(G\), within certain limits, is proportional to the ionic current that arises. The figure also shows a monochromator, which decomposes the light from the source before it is directed into the vessel with the vapors; simultaneously with the measurement of the photoionization current, relative measurements of the incident energy are made with the vacuum thermoelement \(V\), which is necessary for determining the curve of the distribution of photosensitivity over the spectrum.

Fig. 5.

Probability of photoionization. The number of elementary ionization processes produced each second by a monochromatic light flux \(I_\nu\,d\nu\) \([\mathrm{erg}\cdot \mathrm{cm}^{-2}\cdot \mathrm{sec}^{-1}]\) in a vapor layer of length \(l\), containing \(N\) atoms in each cubic centimeter, is determined by the absorbed light energy, namely by the quantity \(k_\nu Nl I_\nu\,d\nu,\)* where \(k_\nu\) is the monochromatic—

* In this expression \(l\) is used instead of the usual \(dl\) in view of the small magnitude of the absorption.

PHOTOIONIZATION OF GASES

the atomic absorption coefficient may be taken as a measure of the effectiveness of the given radiation. The number of ionization acts is equal to the number of quanta contained in the absorbed energy, i.e.

\[ \frac{k_\nu N l I_\nu d\nu}{h\nu}. \tag{2} \]

The probability of the process of ionization of an atom by a given frequency, defined as the number of ionizations per second, referred to one atom and to a unit light flux,* is obtained equal to

\[ P_\nu=\frac{k_\nu}{h\nu}. \]

In view of the negligible absorption of ionizing light by rarefied vapors (elasticities of the order of \(10^{-3}—10^{-2}\) mm), the determination of \(k_\nu\), and consequently also \(P_\nu\), by direct spectrophotometric measurements is very difficult: the change in light intensity reaches only a few percent and thus lies at the limit of accuracy of photometric methods. Increasing the vapor pressure by heating causes undesirable chemical action of the vapors on the transparent walls and, moreover, favors the appearance of molecular absorption overlapping the region of atomic absorption. It is therefore understandable that by direct measurement of absorption it has been possible to establish only the order of magnitude of the atomic absorption coefficient at the limit of the principal series, which for Cs and K proved to be equal to \(10^{-19}\) [5,25]:

\[ k_0 \approx 10^{-19}. \]

However, in the case of photoionization there is, in addition, the possibility of directly counting the elementary processes from the saturation photocurrent \(i\), since the number of ionization acts occurring each second is \(\frac{i}{e}\), where \(e\) is the elementary charge. Equating this number to expression (2),

\[ \frac{k_\nu N l I_\nu d\nu}{h\nu}=\frac{i}{e}, \]

we obtain that the “photosensitivity” (i.e. the photocurrent, referred—

* A quantity proportional to this probability is denoted in the literature by the letter \(B_\nu\) or \(\psi(\nu)\).

...relative to the incident energy: \(\dfrac{i}{I_\nu d\nu}\)), is proportional to the quantity \(\dfrac{k_\nu}{h\nu}\), or, in other words, gives directly the probability \(P_\nu\). Owing to the great sensitivity of electrical methods, the photocurrents obtained in rarefied vapors are quite sufficient for both absolute and relative measurements of \(P_\nu\), and consequently also of the quantity \(k_\nu\). The most accurate data for the atomic absorption coefficient were obtained by measuring photosensitivity. The absolute values \(k_0\) at the boundary of continuous absorption, corresponding to the term \(1S\) (the boundary of the principal series), proved to be:

\[ \mathrm{Cs}\quad k_0 = 2.3\,(\pm 0.2)\cdot 10^{-19} \qquad \mathrm{Rb}\quad k_0 = 1.1\cdot 10^{-19} \quad [5,31]. \]

Theoretical calculations by the methods of wave mechanics give, for the boundary of continuous absorption of the Lyman series in the hydrogen atom, a value 100 times larger, namely of the order of \(10^{-17}\):

\[ \mathrm{H}\quad k_0 \approx 10^{-17} \quad [5,24]. \]

In the case of the alkali metals, not only the magnitude \(k_0\) but also the law of decrease of the absorption coefficient \(k\) with increasing frequency \(\nu\) is anomalous (in comparison with the hydrogen atom). It is known that for the absorption of X-rays, which is likewise connected with photoionization of atoms, there is a proportionality of \(k\) to the cube of the wavelength \(\lambda\), or \(k\sim \nu^{-3}\). This law was derived theoretically for a one-electron atom by Kramers [10], proceeding from the concepts of the old quantum mechanics with the application of the correspondence principle. The new quantum mechanics [22, 24, 32, 33] leads, for those cases which were considered (H, Li), to a fractional exponent \(y\), close to \(-3\).*

* For example, for the continuous absorption of the Lyman series, \(k\) changes at the boundary itself as \(\nu^{-3.3}\); with increasing frequency the exponent takes the value \(-2.5\) and finally, in the region of high frequencies, \(k\sim \nu^{-3.5}\). For absorption beyond the boundary of the Balmer series, i.e. ionization of the excited state of the H atom, fractional exponents close to \(-3\) are likewise obtained [24]. The same is true for the normal state \(1S\) of the Li atom, where, however, the calculation led to a departure from the monotonic decrease of \(k\), not observed experimentally [33, 34].

leads to a much more rapid decrease of \(k\) with increasing \(\nu\) than inverse proportionality to the cube of the frequency. The change of \(k\) in these cases (the initial state of the atom is \(1S\)) can be expressed by the empirical formula:

\[ k_{1S}=\frac{\mathrm{const}}{\nu^2(\nu-\nu_0)} \ [30]. \]

In Fig. 6 various dependences of \(k\) on \(\nu\) are shown graphically [4, 5]. The anomalous behavior of alkali atoms may be attributed to the circumstance that the orbit of the outer electron for the \(1S\) state is penetrating.*

Recombination of an ion with an electron. The process of photoionization of an atom corresponds to the inverse process of recombination with an electron possessing an arbitrary velocity \(v\):

\[ e_v + A^+ \longrightarrow A + h\nu, \]

a process accompanied by the emission of a frequency \(\nu\) connected with the electron velocity by relation (1). The spectrum of recombination radiation must be continuous and must constitute, according to the requirements of statistical equilibrium, the complete reverse of the absorption spectrum: the absorption maximum at the edge \(\nu_0\) must correspond to an identical emission maximum, whence it follows that recombination is most probable for very slow electrons (\(v \approx 0\)). Indeed, such continuous bands, adjoining

* In this connection it has been noted that the total (line \(+\) continuous) absorption for all atoms with one (outer) electron is the same and is equal to the absorption of a classical oscillator. The transfer of intensity into the first line of the principal series in comparison with the remaining lines of this series and the continuous region, observed in the case of alkali metals, must therefore be connected with the small magnitude of absorption at the edge (\(k_0\) is small). In hydrogen, where such an anomaly is not observed, \(k_0\) also has a large value [5].

The connection between the line and continuous parts of the spectrum is manifested also in the fact that the mean value of the absorption coefficient over a definite interval \(\Delta \nu\) in the line region, as one approaches the series limit, tends to the value \(k_0\). This makes it possible, on the basis of measurements of the absorption coefficients of the lines of the principal series, to estimate \(k_0\). Calculations lead to the same order of magnitude as before: \(k_0 \approx 10^{-19}\) [5].

For the alkali metals investigated (K, Rb, Cs), an edge at the limits of series (both principal and subordinate), with a maximum lying at the edge, was observed in certain types of electric discharge: electrodeless discharge, glow in a hollow cathode, etc. [4]. A favorable condition for obtaining them is not only a large concentration (of the order of \(10^{13}\) per \(\mathrm{cm}^3\)) of ions and electrons, but also their low velocity. A characteristic feature of the spectrum of recombination radiation is the presence of high members of series, associated with the presence of a large number of atoms

Fig. 6. I—\(k\sim\nu^{-2}\) \((\nu-\nu_0)^{-1}\); II—\(k\sim\nu^{-4}\);
III—\(k\sim\nu^{-3}\) (for \(\nu>\nu_0\)).

in high energy states.* Under the cleanest conditions, recombination radiation was obtained by Mohler in an apparatus analogous to that shown in Fig. 4. Figure 7 shows curves of the intensity distribution in the continuous emission bands adjoining the limits of the Cs series [28].

The process of recombination can be described quantitatively

* Under these conditions it has repeatedly been observed that the continuous spectrum (of absorption or emission) extends appreciably beyond the limit \(\nu_0\) into the region of lower frequencies. This is explained by the fact that, at the large distance of the electron present here, the external field created by the ions of the discharge is comparable in magnitude with the Coulomb field in the atom, and quantum orbits cease to exist [42].

with the aid of the recombination coefficient \(\alpha\), entering into the equation for the rate of decrease of the number of ions:

\[ -\frac{dn_+}{dt}=\alpha n_+ n_- \]

where \(n_+\) and \(n_-\) are the numbers of ions and electrons in \(1\ \mathrm{cm}^3\).

In addition, the recombination process, like any interaction of two particles, can be described visually by means of the notion of the effective cross section of an ion with respect to an electron flying past it with velocity \(v\).

Denoting by \(f(p)\) the probability that an electron flying at a distance \(p\) from the ion will recombine with the latter, the number of such recombination acts will be proportional to \(f(p)\cdot 2\pi p\,dp\), where \(2\pi p\,dp\) is an annular element of area passing through the ion.

Fig. 7. (The scale in the right-hand part of the figure is enlarged 10 times.)

Assuming that there is some finite distance \(p=p_0\), beyond which the interaction of the electron with the ion ceases, we take

\[ \int_0^{p_0} f(p)\cdot 2\pi p\,dp \]

as the effective cross section \(q\) of the ion with respect to electrons of a given velocity (\(f,p_0,q\) depend on \(v\)) [10, 13]:

\[ q=\int_0^{p_0} f(p)\cdot 2\pi p\,dp . \tag{3} \]

With this definition, every entry of an electron into the region \(q\) entails recombination, since by multiplying by \(f\) we have reduced each element of area to the same value of the probability of the process, equal to unity.

The introduction of the effective cross section makes it possible to pres-

compare the number of recombinations per second, or \(-\dfrac{dn_+}{dt}\), with \(q n_+ \cdot v n_-\):

\[ -\frac{dn_+}{dt}=qvn_+n_- \]

whence the recombination coefficient \(a=qv\). The maximum of the recombination rate observed at small values of \(v\) must be connected with the fact that for slow electrons the effective cross section is greatest.

A direct determination of the effective cross section \(q\) from the recombination rate for given \(v, n_+\) (\(n_-\) usually \(=n_+\)) by electrical measurements encounters great difficulties, since the ionized gas recombines completely in \(10^{-3}—10^{-4}\) sec. However, such a time interval still provides sufficient scope for an experiment making it possible to determine \(a\), and consequently also \(q\). Experiment [26] gives, for argon ions Ar\(+\) and slow electrons \(v=0.4V\), the value \(a=2\cdot10^{-10}\), whence the effective cross section is obtained as \(5\cdot10^{-18}\ \mathrm{cm^2}\):

\[ q(\mathrm{Ar}+) = 5\cdot10^{-18}\ \mathrm{cm^2}. \]

Another experiment carried out for the same purpose [27] was based on passing a beam of ions (Cs\(+\)) through an electron cloud and measuring the depletion of the beam by ions resulting from recombination. The insufficient sensitivity of the apparatus, as well as a number of other incidental circumstances, made it possible in this difficult experiment to indicate only very roughly an upper limit for \(q\), which turned out to be \(5\cdot10^{-18}\ \mathrm{cm^2}\)—a number that is clearly exaggerated.

This exhausts the attempts at a direct determination of the effective cross section of recombination.

Optical determination of \(q\) from the recombination spectrum. The emission energy on a given segment \(dv\) of the continuous spectrum (Fig. 7), divided by \(hv\), gives the number of recombinations per second with electrons whose velocity \(v\) is determined by equation (1). Denoting the function

of the electron distribution over velocities by \(F(v)\), and the total number of electrons in \(1\ \mathrm{cm}^3\) by \(n_-\), we obtain:

\[ \frac{I_\nu\,d\nu}{h\nu}=qv\,n_+ n_- F(v)\,dv. \]

Measurement of the intensity distribution in the continuous spectrum \(I(\nu)\), combined with simultaneous measurement of the electron velocity distribution \(F(v)\) \((n_+=n_-=\mathrm{const})\), makes it possible to determine the form of the dependence of \(q\) on \(v\). By supplementing these measurements with a determination of the concentration \(n_+\) of ions, one can also obtain absolute values of \(q\). Experiments carried out with great care [29] gave, for the continuous band (the brightest one), corresponding to recombination of an electron onto the \(2P\) level of the Cs atom, the following dependence of \(q\) on \(v\) (or \(\nu\)):

\[ \mathrm{Cs},\ 2P.\qquad q \sim \frac{1}{v v_0^2}\sim \frac{1}{v^2(\nu-\nu_0)}. \]

The intensity of the band adjacent to the boundary of the \(1S\) principal series and corresponding to recombination onto the normal level of the atom proved to be, in comparison with the \(2P, 3D\) bands, much smaller (see Fig. 7). The following absolute values of \(q\) were obtained for slow electrons \((v=0.2\,V)\):

\[ \mathrm{Cs}\qquad q_{1S}=1.5\cdot 10^{-23}\ \mathrm{cm}^2\qquad q_{2P}=6\cdot 10^{-21}\ \mathrm{cm}^2, \]

i.e. the probability of recombination onto the normal level is approximately 100 times smaller than onto the nearest higher-lying one. Thus the electron, when recombining with an ion, gives predominantly excited atoms [5].

Theoretical calculations [36] for the case of the hydrogen atom also show that for two \(s\) and \(p\) orbits with the same principal quantum number* the effective cross section \(q\), and consequently also the probability of recombination for \(p\), is approximately 4 times greater than for \(s\).

* Such orbits correspond to the \(1S\) and \(2P\) states of alkali-metal atoms. However, the probability of recombination into the normal (one-quantum) state \(1s\) of the H atom is greater than the probability of recombination into any other higher-lying state. See [36, p. 22].

Determination of the effective cross section from the absorption coefficient. The statistical consideration of the equilibrium of two opposite quantum processes, applied to the case of photoionization and recombination:

\[ h\nu + A \underset{q}{\stackrel{k}{\rightleftarrows}} A^+ + e_v \]

leads to the following dependence between the probabilities of these processes [5, 10, 13],

\[ \frac{q}{k}=2g\left(\frac{h\nu/c}{mv}\right)^2, \tag{4} \]

where \(q\) and \(k\) refer to definite values of \(v\) and \(\nu\), connected by equation (1), and \(g\) is the statistical weight of the state whose photoionization, or recombination into which, is considered here.*

Thus \(q\) and \(k\) are related to one another as the amounts of motion of the quantum and the electron, and knowledge of the absorption coefficient makes it possible to determine the effective cross section.

Let us first of all dwell on the form of the dependence of \(q\) on \(\nu\), obtained for various laws of the decrease of \(k\) with \(\nu\) [4, 5]. In the case of inverse proportionality of \(k\) to the cube of the frequency \((k\sim\nu^{-3}\), absorption of X rays), \(q\) is obtained from (4) proportional to \(\frac{1}{v^2}\) (Kramers); for frequencies \(\nu \gg \nu_0\) this gives inverse proportionality to the fourth power of the velocity:

\[ q\sim\frac{1}{v^4} \]

(since \(\nu=\frac{mv^2}{2h}+\nu_0\) from equation (1)).

The empirical dependence \(k\sim\frac{1}{\nu^2(\nu-\nu_0)}\), obtained for normal states of alkali atoms, after substitution into (4) gives

\[ q\sim\frac{1}{(\nu-\nu_0)v^2}, \]

or likewise \(\sim\frac{1}{v^4}\). The inverse proportional—

* Relation (4) has a general significance, independent of the detailed mechanism of the phenomenon. In Milne’s theory, instead of \(g\) there stands \(\frac{g}{\sigma}\), where \(\sigma\) is the number of equivalent external electrons realizing the normal state of the atom [13, 14] and capable of being ionized. See also the correction introduced into Milne’s second paper.

ionality of the effective cross section to the fourth power of the velocity is an inverse proportionality to the square of the kinetic energy of the recombining electron. Such a law of recombination was proposed by Thomson (J. J. Thomson),*; a similar dependence is obtained from quantum mechanics for the recombination of a slow electron with a proton into the deepest (normal) state of the H atom [24′]. It is very remarkable that an approximate inverse proportionality to \(v^4\) is obtained in a direct experiment for a process much more complicated than simple recombination, namely for the neutralization of \(\mathrm{H}^+\) ions, flying in the form of a canal-ray beam, by electrons torn away by these ions from other gas molecules with which they collide on their path (charge-exchange processes—Umladung—of canal rays); \(v\) is here the velocity of the ions [4, 11′]. Under the conditions of simple recombination of free electrons with ions, this dependence, owing to the difficulty of direct measurements, has not been verified.

Conversely, on the basis of relation (4), a definite form of the dependence of \(q\) on \(v\) leads to a definite functional dependence of the absorption coefficient \(k\) on the frequency, which can then be compared with experimental data. The assumption of the theory of Milne (13) and Eddington [10′, 4] that \(q \sim \dfrac{1}{v^2}\) leads to a slower decrease of \(k\) with \(\nu\) than any observed experimentally, namely \(k \sim \dfrac{1}{\nu^2}\). The character of the change of the effective cross section with velocity in the case of the normal state (\(1S\)) of an alkali-metal atom was discussed above; it was also indicated that the empirical dependence for the excited state (\(2P\)) has the form

\[ q \sim \frac{1}{\nu^2 v^2} \sim \frac{1}{\nu^2(\nu-\nu_0)} \]

(i.e., for large \(\nu \gg \nu_0\), inverse proportionality to \(\nu^3\)). Substituting this expression into (4), which may be rep—

* Phil. Mag. 47, 337, 1924.

posed as \(\dfrac{k}{q}\sim\dfrac{\nu-\nu_0}{\nu^2}\), we obtain \(k\sim\dfrac{1}{\nu^4}\) (see Fig. 6). Observations of absorption by excited atoms present great difficulties, and the dependence cannot be directly checked. In any case, it does not differ greatly from that obtained theoretically for the hydrogen atom.

Equation (4) makes it possible to obtain the absolute value of the absorption coefficient \(k_0\) (at the boundary) on the basis of the above-given (p. 113) values of \(q\) for the \(1S\) and \(2P\) states of the Cs atom [5, 31]. We have

\[ \mathrm{Cs}\quad k_0(1S)=0.5\cdot 10^{-19}\qquad k_0(2P)=8\cdot 10^{-17} \]

The first number agrees with the previously cited direct determinations of the absorption coefficient; as for the second number, it shows that the excited state of the alkali atom (Cs), like the hydrogen states, is similar not only in the character of the decrease of \(k\) with increasing frequency, but also in the absolute magnitude of the absorption coefficient (as was indicated above, \(k_0\) for the various states of the hydrogen atom is a quantity of the order of \(10^{-17}\), which corresponds to values of the effective cross section \(q\) of the order of \(10^{-21}\ \mathrm{cm}^2\)).

Thus, on the basis of various data, the upper limit of the effective cross section for recombination of an electron with an ion into a definite state of the atom is a quantity of the order of \(10^{-21}\ \mathrm{cm}^2\) and even smaller. Meanwhile, the gas-kinetic dimensions of ions, determined by direct experiments on collisions of ions with various gas molecules [40], are quantities of the order of \(10^{-15}\ \mathrm{cm}^2\) (for \(\mathrm{Cs}^+\)). Hence there follows the unexpected conclusion that the effective cross section of an ion is many times (approximately \(10^6\) times) smaller than its dimensions, whereas it would have been more natural to suppose that the ion interacts with the electron over a distance exceeding its dimensions. Nor is the situation saved by direct determinations of \(q\) (for \(\mathrm{Ar}^+\)), which lead to a value of the order of \(10^{-18}\ \mathrm{cm}^2\). Such a result is a consequence of the definition of the effective

cross section given in (3): \(q\) is not the actual area of interaction, but a “reduced” area, i.e. multiplied by the probability \(f\). The negligible magnitude of \(q\) is evidently due to the negligible magnitude of \(f\). If one describes the recombination process pictorially with the aid of an actual area (or volume) surrounding the ion, within which alone the interaction can in general take place, then this cross section \(\bar q\) undoubtedly has an extent exceeding the dimensions of the ion; however, only a negligible fraction of the entries into this region leads to recombination. The decomposition of the effective cross section \(q\) into two factors: the “proper” cross section (area) \(\bar q\) and the (mean) probability \(\bar f \leq 1\), however, introduces an element of arbitrariness in estimating their relative magnitude, depriving these pictorial representations of any physical reality.*

It remains to say a few words about the difference between the values of the effective cross sections: that obtained by indirect methods and by calculation, \(q \approx 10^{-21}\ \mathrm{cm}^2\) \((\mathrm{Cs}^+,\ \mathrm{H}^+)\), on the one hand, and the only reliable value obtained by direct measurement, \(q \approx 10^{-18}\ \mathrm{cm}^2\) \((\mathrm{Ar}^+)\), on the other. First of all, the latter number represents the total effective cross section for recombination into all states of the Ar atom, whereas in the first case certain, and the very lowest, states are considered. Since there are very many high quantum states in the atom and the probability of recombination decreases only slowly with increasing principal quantum number,** one may expect also in the first case \((\mathrm{Cs}^+,\ \mathrm{H}^+)\) that the total effective cross section will be of the order of \(10^{-18}\ \mathrm{cm}^2\). It should not be forgotten, however, that the “affinity” for elec—

* Assuming \(\bar q \geq 10^{-15}\ \mathrm{cm}^2\) (the dimensions of the \(\mathrm{Cs}^+\) ion), we obtain, for example, from the value quoted above \(q = 10^{-21}\ \mathrm{cm}^2\), that \(\bar f \leq 10^{-6}\); assuming for \(\mathrm{Ar}^+\) \(\bar q \geq 10^{-16}\ \mathrm{cm}^2\) and using the value obtained for it of the total effective cross section \(q = 10^{-18}\ \mathrm{cm}^2\), we obtain a more probable value \(\bar f \leq 10^{-2}\).

** See the theoretical estimates in [36, p. 22]; the presence in the spectrum of recombination radiation of intense lines corresponding to high levels of the atom also confirms this conclusion.

the ion \(\mathrm{Ar}^{+}\), similar to the electronegative atom Cl, may turn out to be quite different than for the ion \(\mathrm{Cs}^{+}\) with the closed shell of a noble-gas atom, and therefore one cannot freely use the value for \(\mathrm{Ar}^{+}\) for \(\mathrm{Cs}^{+}\). It should also be noted that up to now we have been operating with the maximum values \(k=k_0\) (at the boundary) and \(q=q_0\) (recombination with electrons \(v\approx 0\)). To calculate the total number of recombinations for photoionization it is necessary to take into account the entire extent of the curves \(q(v)\) and \(k(\nu)\). A calculation of the integral absorption shows that photoionization of the hydrogen atom is 700 times more probable than excitation of the first line of the principal series (for the same intensity of the incident light over the entire extent of the spectrum) [24].

Photoionization in two stages. Photoionization can also occur under the action of frequencies smaller than the limiting one \((\nu_0)\), namely for the frequencies absorbed by the atom in the lines of the principal series, if the energy lacking for ionization is supplied in a collision of the excited atom with other particles.* The source of such energy may be both the thermal motion of the atoms and the store of excitation energy carried by another particle. The first possibility—the participation of thermal energy—was invoked by Foote and Mohler [14] to explain the fact they observed, that photoionization of Cs vapor takes place not only in the continuous region, but also for the lines of the principal series lying close to the boundary.

The second possibility—ionization of an excited atom in a collision with another, likewise excited one—explains the equally obscure fact of ionization of dense \((p\approx 1\ \mathrm{mm})\) mercury vapor upon illumination by the resonance line \(2537\ \text{\AA}\) [2,3 16,20]. Even twofold absorption of this line \((2\times 4.9=9.8\ V)\) is insufficient for ionization of the Hg atom \((10.4\ V)\). Nevertheless, since the number of ions formed is proportional to the square of the intensity of the acting light,

* Secondary absorption of exciting light of the same or another frequency, although possible, does not, however, play an essential role in the phenomenon considered here.

undoubtedly ionization in two stages, if not by the double absorption of the same quantum, then by a combination of the excitation energies of two atoms upon their collision. The presence in mercury atoms of excited states with anomalously long lifetimes (metastable ones) and the comparatively large concentration of such particles are of primary importance for processes of energy transfer. However, even with such a combined action of two excited Hg′ atoms, their total energy is insufficient for ionization. The assumption that the deficiency (of the order of 1 V) is made up from the kinetic energy of thermal motion is unlikely. A more plausible explanation is based on the fact of multiple accumulation of energy in collisions with metastable mercury atoms [41]: in this interpretation the energy deficiency is more than made up in the collision of a doubly excited mercury atom with a metastable atom
(\(\mathrm{Hg}' + \mathrm{Hg}' = \mathrm{Hg}'' + \mathrm{Hg}\)).

In explaining photoionization by frequencies \(\nu < \nu_0\), it is also necessary to take into account the possibility that a molecule is formed from colliding atoms, followed by its ionization, i.e. a process of the following type:

\[ A' + A = A_2^{+} + e. \]

Such a process becomes possible if the energy of excitation of the atom plus the energy of formation of the molecule is greater than the energy of ionization of the latter. This, evidently, is how one should explain the above-mentioned photoionization of alkali-metal vapors (Cs) upon absorption in the lines of the principal series [3,43].*

II. PHOTOIONIZATION OF MOLECULES

If the photoionization of monatomic gases has reached the stage of quantitative investigation of the phenomenon, albeit for a limited number of objects, then the ionization of di- and polyatomic gaseous molecules by light is still at the initial stage of development. The absence or incompleteness of infor-

* Indeed, in the recently published work [48] this interpretation of the phenomenon has been substantiated quantitatively.

A. TERENIN

of data on electronic levels does not make it possible to calculate the ionization frequency $\nu_0$ or the ionization potential of the molecule, as was possible in the case of atoms. Thus there remain the data obtained by the electron-impact method, which, however, do not always permit an unambiguous interpretation, owing to the complication of the ionization process by the onset of dissociation of the molecule. Direct determinations of ionization potentials must therefore be supplemented by magnetic or electrical analysis of the ions obtained. Table II gives the ionization potentials of a number of molecules.

Table II

$\nu_0$ (volts)

If one recalls that quartz (crystal) is transparent down to approximately 1800 Å ($\simeq 7 V$) (air begins to absorb even earlier), while fluorite is transparent approximately down to 1200 Å ($\simeq 10 V$), it becomes clear that for most molecules there is no possibility of observing photoionization in an apparatus in which the active light has to pass through a transparent wall. The exceptions are NO, J$_2$ (partly also Br$_2$, H$_2$S, NH$_3$, HgJ$_2$), which do allow this possibility. Nevertheless, in a number of older works [1, 2, 3, 6] the existence of photoionization of N$_2$, O$_2$, CO$_2$ was established under conditions in which the light of the source (hydrogen tube, Al spark in air) passed not only through a fluorite wall but also, in some cases, through a thin layer of air. The observations were carried out in a low-sensitivity apparatus$^{1,*}$ which was improved by Lenard (Lenard) in

* See beginning: Experimental method.

in the sense that the condenser—usually cylindrical in shape and of great length—was located outside the space in which the illumination was carried out [6]. The gas, for the most part at atmospheric pressure, was rapidly drawn by a pump from the latter space into the condenser, where the conductivity retained in it was measured. It should be noted that the effects obtained were extremely weak, and could easily have been caused by the photoelectric effect from dust particles suspended in the gas or from impurities of every kind, present despite the measures taken to purify the gas.* It is also characteristic that the weak currents observed were found to be proportional to the square of the light intensity, which would indicate ionization in two stages and would explain ionization by such low frequencies.

It should be observed that experiments carried out under equally imperfect conditions nevertheless confirmed the expectations, in that photoionization was also observed for $\mathrm{J}_2$ [44] and $\mathrm{NH}_3$ [3]. It is obvious that, for substantial progress in this field, it is necessary to abandon the use of any transparent wall between the source and the illuminated gas. Protection of the observation space from the stream of ions diffusing from the source can be achieved by means of an electric field that removes the ions, or by means of a continuous counterflow of gas, creating a kind of gaseous wall.

The first possibility was used by Mohler (Mohler) [2, 17] to observe high ionization potentials of Ar, Ne, Cs, K. At one end of a vessel filled with one of these gases, a discharge with electrodes of variable speed was excited; at the other end, by means of the circuit in Fig. 4, the volume photoionization arising in the gas as a result of illumination was registered. In the medium-

* Usually what was measured, or even only ascertained, was the acceleration, caused by illumination of the gas, of the already existing fall of the potential of an electroscope or electrometer connected to one of the surfaces of the condenser.

** The instruments contained mercury, rubber, paraffin, and metallic walls.

of the vessel, the ions diffusing from the light source were caught by an electric field.

The second possibility—a counterflow of gas—was used by Oldenberg (38) for observing the glow produced in \(\mathrm{H}_2\) and \(\mathrm{N}_2\) by the shortest ultraviolet radiation. In \(\mathrm{N}_2\), a spectrum belonging to \(\mathrm{N}_2^+\) appeared in this case, which indicates photoionization of molecules; however, owing to the difficulty of the experiment, the effective frequency of the light was not determined.*

Returning to experiments on the photoionization of molecules, it should be mentioned that dense mercury vapors, when illuminated in the region of \(1850\ \text{Å}\) (by the lines Al \(1855\)—\(62\ \text{Å}\)), show, alongside intense fluorescence, also noticeable photoionization [2, 45]. Since this fluorescence is ascribed to diatomic mercury molecules \(\mathrm{Hg}_2\), apparently the observed photoionization should likewise be explained by the participation of these molecules. There has been no later study of this phenomenon. Under the same question mark stands the recently discovered [34], in potassium vapor, second maximum of photosensitivity, three times exceeding the normal maximum at the series limit and displaced from the latter toward higher frequencies by a distance of \(500\ \text{Å}\) (\(\simeq 1\ \mathrm{V}\)). Since the dissociation energy of the \(\mathrm{K}_2\) molecule is approximately \(0.6\ \mathrm{V}\), this second maximum may be ascribed to the process:
\(h\nu+\mathrm{K}_2=\mathrm{K}+\mathrm{K}^++e\), i.e. to dissociation of the molecule with simultaneous ionization of the atom. However, this explanation encounters the difficulty that the percentage content of \(\mathrm{K}_2\) molecules in potassium vapor is negligible and, moreover, no similar anomaly is observed in other alkali metals.

If to what has been set forth one adds the photoionization of vapors of complex organic compounds, observed long ago and under imperfect conditions [3], then this exhausts all the material on the ionization of molecules by light. Meanwhile,

* The application of a counterflow of gas as a kind of gas wall is the basis of the light source proposed by Cario and Lochte-Holtgreven (Cario und Lochte-Holtgreven) [39] for optical excitation.

In connection with the latest advances in the field of the structure and properties of molecules, the photoionization of the latter is acquiring considerable interest.

Spectral data that make it possible to determine the dissociation energies of molecules show that, with the ionization of a molecule, i.e., with the removal of an electron, the bond of the atoms in the molecule changes, increasing in some cases \((\mathrm{O}_2,\mathrm{CdH})\), decreasing in others \((\mathrm{N}_2,\mathrm{CO})\). Ionization of molecules by electron collisions has revealed, in some molecules \((\mathrm{N}_2,\ \mathrm{O}_2,\ \mathrm{NO})\), the existence of a second ionization potential at high voltages; in the latter case, removal of the electron causes such a considerable weakening of the bond of the molecule that it decomposes into an atom and an ion either at once or at the next collision.* There is no doubt that a more subtle method of optical action will be able to clarify more fully and accurately the participation of the various electrons in the bond of the molecule. For this it is necessary to extend observations toward the very shortest ultraviolet radiation, i.e., into a region of very difficult experiment.

However, it is also possible to find such molecules whose limiting ionization frequencies still lie in a convenient region of the spectrum, transmitted by quartz and air \((\lambda > 1850\ \text{\AA})\). It was shown by the author (46) that vapors of halide salts of various metals \((\mathrm{TlJ},\ \mathrm{TlBr},\ \mathrm{TlCl},\ \mathrm{PbJ}_2,\ \mathrm{PbCl}_2,\ \mathrm{BiJ}_3)\) exhibit considerable photoionization when illuminated by the light of various sparks. The limiting ionization frequencies correspond to 5.8 V for \(\mathrm{TlJ}\) and 6.0 V for \(\mathrm{TlBr}\). Such high photosensitivity of these molecules at comparatively low frequencies should apparently be attributed in part to the low ionization potential of the metal atom entering into the composition of the molecule.

From the fragmentary information set forth above it is clear how little the photoionization of gases, especially molecular gases, has been developed.

* See a more detailed exposition of this question in the author’s report at the Fourth Physico-Chemical Conference in Moscow in 1928.

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