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The polarization factor for the interference between Rayleigh scattering and Mossbauer scattering from 57Fe is shown to be cos θ for both an unsplit scatterer and a non-aligned split scatterer, a result which differs from that recently published by Wong. Polarization factors have no effect on the ratios of the absorption cross sections for the hyperfine components of a non-aligned split scatterer.

1. Summary of Paper .—The main object of this paper is to apply Nordheim’s theory of the emission coefficient of electrons from metals so as to explain the remarkable relation between the constants A and X of the thermionic emission formula, first recorded by O. W. Richardson and recently reformulated by Du Bridge. This theory regards the emission as due to the passage of electrons through simple surface potential steps and double layers, to be calculated according to the wave mechanics. We conclude that the theory gives a completely satisfactory account of the facts whenever it can be properly applied. The necessary conditions for its proper application are formulated. Certain apparent discrepancies in absolute magnitude between the observed and theoretical values of A are left outstanding and it is necessary to discuss possible explanations of these in some detail. It is concluded that though their precise cause cannot yet be specified they can certainly be explained and their existence is in no way antagonistic to the main theory. 2. The Experimental Facts .—Much attention has been devoted recently to the values of the constant A in the formula for the saturated thermionic (electronic) current I, namely, I = AT 2 e - x/k T , where T is the absolute temperature, X the work function and k Boltzmann’s constant. Particularly interesting measurements of A (and X ) have been recorded by Du Bridge for platinum when very severely outgassed. Du Bridge seems definitely to have established that for really clean platinum the photoelectric threshold and the thermionic work function agree at or near 6·35 volts, and that the corresponding values of A for various specimens range from 10,000 to 20,000 amp./cm. 2 .

Rudorf, in a paper on the rare gases and the equation of state, has drawn attention to the high value found by Ramsay and Travers for the density of liquid xenon at its boiling point. As is well known the atomic volume in any group of elements in the periodic table either increases regularly with rise of atomic weight or remains approximately constant, so that it is to be expected that the atomic volume of xenon would be greater than of krypton, since the value for krypton exceeds that of argon. If Rudorf's calculated value for the density of neon is taken into account, this anomaly becomes more striking, as is shown from the following table taken from his paper

1. In a previous paper the writers showed that a considerable number of discontinuities which had been detected in the excitation of the soft X-rays from these elements by the photo-electric method could be arranged on the assumption that they were due to transitions from two levels not far from the M I and M II III , as these had been deduced from hard X-ray emission data, and a series of virtual levels falling, with a close approximation into a Rydberg series. The present paper is an attempt to arrange the remaining discontinuities which have been observed into the same scheme. Although the identity of a level formerly referred to as A with the hard X-ray M I level and of the higher level with M II III seems probable ultimately, it is not certain, and we do not wish to be dogmatic about it, so that for the present we shall refer to these levels provisionally as X 1 and X 2 respectively.

The present paper contains an account of an investigation of the effects of electron collisions with neon atoms by a method similar to that used with helium and with argon. The apparatus employed is practically the same as that described in the account of the experiments with argon, the only difference being that one of the lower gauzes (C) was removed and that two small platinum plate electrodes were sealed into the ionisation chamber, so as to provide an electric field at right angles to the direction of the electron stream. The arrangement will be understood by reference to fig. 1, in which the lettering corresponds to that used in the earlier paper. The object of introducing the side electrodes, G and H, was to enable a second test of the production of ionisation to be made by means of a delicate galvanometer included in a subsidiary circuit. The usual precautions for ridding the glass and the electrodes from occluded gases were taken, and in all the observations recorded in the paper a magnetic field parallel to the axis of the discharge tube was used to prevent the electron stream from spreading laterally.

In a previous paper published by the authors which dealt with the L emission series of mercury, the wave-lengths of four lines were given the ν /R values of which corresponded with transitions between energy levels disallowed by the Bohr Selection Principle. In a further investigation, to discover if corresponding lines could be found in the L spectra of elements close to mercury in the Periodic Classification, the spectra of lead and bismuth were examined. In each case the corresponding four lines were found, and in addition several other “non-diagram” lines. The present paper gives a brief account of the results obtained. Several other investigators have found lines which correspond with transitions contrary to the Selection Principle. Dauvillier found many such in the L emission series of the heavy elements from ytterbium to gold, and Rogers in the spectra of tungsten and platinum. Crofutt also found several for tungsten, and the existence of a tungsten line γ 11 (L 3 N 4 ) has been confirmed by Dershem and by Overn.

In a recent paper, it has been shown, using the expansion method, that the simple relativistic expressions govern the transfer of momentum and energy during the close collisions of fast β-particles with electrons. The present paper gives an account of an investigation of the scattering of fast β-particles by electrons, using the expansion method. Among the many formulæ which have been proposed to express the interaction of two electrons, the relativistically invariant expression due to Möller appears to be the most satisfactory theoretically. Möller has referred the scattering for all velocities to a Lorentz frame of co-ordinates in which the momenta of the two electrons are equal and opposite. The observed angle of scattering θ is connected with θ*, the angle of scattering in the Lorentz frame, by the relation x =cos θ*=2-(γ+3) sin 2 θ/2+(γ-1) sin 2 θ (1) where γ=1/(l-β 2 ) ½ and β= v/c , v being the relative velocity of the two particles before collision and c the velocity of light.

The purpose of the present paper is to apply the quantum theory of spectrum emission by atomic systems containing an aspherical nucleus, given in my recent paper, to the Balmer series of hydrogen. Although, in working out the general formulæ of the said theory, I have had in view chiefly the more complicated, non-hydrogenic, spectra as a possible field of its application, yet it has seemed worth while to compare also the aspherical nucleus formulæ with the Balmer spectrum of hydrogen, the more so, as recent measurements have revealed a notable deviation of at least the first six members of this series from the simple Balmer formula. The measurements alluded to were made by W. E. Curtis in 1914, and their newly revised results are tabulated in his paper of 1919, for a copy of which accompanied by helpful explanations, I am indebted to Prof. Fowler. 1. It will be sufficiently general for the purpose in hand to assume an axially symmetrical nucleus of unknown asphericity (to be determined from the observations). Then the series will be given by the formulæ (28), (28·1), with k = 1 ( i. e. , nucleus charge = e ), with n' = 2 written for the constant term, and n = 3, 4, 5, etc., for the members H α , H β , H γ , etc., of the series. Thus, if N be the Bohr value of the Rydberg constant, and if (retaining all other symbols of my quoted paper) we write for brevity σ = (2N ch / e 2 ) 2 . (A - B), (1) the frequency formula will be v = N/4 {1 + 4σ g' /(2 - n' 3 ) 6 } - N/ n 2 {1 + n 2 σ g /( n - n 3 ) 6 }, (2) where g = g ( i, ϵ ) for the initial, and g' for the final orbit, are as on p. 55 ( loc. cit. ). It will be kept in mind that A — B, and, therefore, σ, may be either positive or negative, according as the nucleus is “oblate” or “prolate” in the generalised sense of these words, as explained in the quoted paper. The variable number n is the sum of the three independent integers n 1 , n 2 , n 3 , introduced through the quantum integrals, and, similarly, n' = n 1 ' + n 2 ' + n 3 ', the quantised eccentricity ϵ and inclination i of the electronic orbits, appearing in g ( i', ϵ ), being given by (21·3), loc. cit .

This paper is mainly a report of further observations on the Stark-effect in helium made with a view to establishing various definite Stark patterns for the series lines. It thus appears as an extension to an earlier paper in which it was pointed out that a plan for Stark patterns is contained implicitly in the Bohr perturbation theory of the Stark-effect as developed by Kramers to predict connections between the hydrogen fine structure and the components observed in high fields. This plan, which on the perturbation theory might be expected to make its appearance in helium, receives somewhat detailed support from the present data, and will be outlined in later paragraphs. It should be stated now, however, that while the detailed analyses here given may be regarded as an extension to the observations by Stark and Nyquist, they offer definite reasons for a rather extensive revision of the complex analyses reported by Takamine and Kokubu. Soon after his discovery of this effect Stark suggested that it might be found to be of the same nature for the various members of a single spectral series. He noted, in particular, that on the early plates certain principal and sharp series lines of helium were merely displaced without being split by the applied electric field. In the following paper Stark and Kirschbaum gave the results of a more complete examination of the Stark-effect for the series lines of orthohelium, parhelium, lithium, and the doublets of calcium. With the single exception of the parhelium line λ 3614, which appeared to be double, they found all principal and sharp series lines simply displaced. The two components of each calcium doublet were shifted in the same direction, and by nearly the same amounts.

The experimental work described in the present paper suggested itself to the writer in connection with an earlier investigation on the law governing the temperature variation of the complete photo-electric emission from a hot body, i. e . the photo-electric emission from a body in equilibrium with the full (black body) radiation corresponding to its temperature. By making use of hypotheses contained in the quantum theory, the writer obtained the following expression for the current per unit area C = AT (1+2 k T/ Ф +2 k 2 T 2 / Ф 2 ) e -Ф / k t, where Ф is the work done in removing an electron from the hot body, and is equal to hv, v being the lowest frequency of the radiation capable of producing a photo-electric emission, and h being Planck’s constant. The quantity k is the "gas constant” reckoned for one molecule, and A is a quantity independent of T, and characteristic of the substance. As the expression inside the brackets in the above formula does not differ appreciably from unity, the latter is substantially of the same type as Richardson’s equation C = AT λ e -Ф / k T , (1) for the thermionic emission. Richardson* has also shown that it follows, from thermodynamic considerations, that this law governs the complete photo-electric emission. There is reason to believe that the thermionic emission is not wholly photo-electric in origin, but it is clear that some portion of it is the complete auto-photo-electric emission of the substance concerned, and that the law governing its temperature variation should be the same as that for the whole thermionic emission. We are thus led to expect that, when a body is exposed to an external source of full radiation, the same law will govern the variation of its complete photo-electric emission with the temperature of the source of the radiation. This expectation has been confirmed by experiments on the alloy of sodium and potassium, the description of which constitutes the subject of the present paper.

The original theory of the origin of the electron emission from glowing solids, which is based on the electron theory of metallic conduction, has recently been subjected to criticism on account of the manner in which the emission can be reduced by continually removing impurities from the discharge tube. The critics maintain that the emission occurs as a result of chemical action between the hot cathode the hot cathode and the surrounding gas, or between the constituents of the cathode itself. In a recent paper the author has summarised the evidence in favour of this latter view, and has described experiments which show that the results which it leads us it expect do not always occur. In particular it has been shown that the chemical action theory of the origin of the activity of a Wehnelt cathode, as propounded by Fredenhagen and by Gehrts, cannot be accepted. The experiments described in the present paper were designed to test further the theory that the electron emission is due to chemical action. The experiments consisted in studying the ionisation produced by Nernst filaments heated in various gases, of different chemical affinities for the material of the cathode. The apparatus and method of experiment were similar to those described in the paper already referred to, and its temperature was determined by means of a specially standardised Féry optical pyrometer which was kindly lent to me by Prof. T. Mather, of the City and Guilds Engineering College, London. The anode consisted of two parallel platinum plates, fixed in the discharge tube at equal distance on opposite sides of the filaments, and connected together outside the apparatus. The potential difference applied to the ends of the filaments was measured by a Siemens alternating voltmeter, which was used in series with a resistance of equal magnitude, the total resistance in parallel with the filament being 4572 ohms. The junction of the voltmeter and series resistance was connected to earth, and thus the mid-point of the glowing filament was kept at zero potential. The platinum plates forming the anode were connected through delicate galvanometer to the positive pole of a high potential battery, the negative pole of which was earthed. A diagrammatic view if the arrangements is given in fig. 1, which for simplicity the discharge tube is not shown. The filaments experimented with were all of the same type and were intended for use on a 100-volt alternating circuit. The thermionic currents in air under similar conditions varied slightly for different filaments, but in every case the currents measured after heating for some time were remarkably constant. In this respect the electron emission from a Nernst filaments is very different from that obtained with a metal cathode, which usually decreases continuously with time. Measurements of the thermionic currents in air, nitrogen, oxygen, and hydrogen were made. In each case the variation of the current with the pressure of the gas under a constant applied potential difference with a constant gas pressure in the discharge tube. The observations were usually made with the filaments at a temperature of 1525° C., but measurements were also made at other temperatures.

In a previous paper, the results of a series of measurements of the wavelengths of the first six lines of the Balmer series of hydrogen were given, together with a determination of the Rydberg constant for spectral series. It has recently been pointed out to me by Prof. Fowler that the value of the series constant there obtained is not quite correct, in consequence of errors in the corrections applied to the observed wave-lengths to reduce them to vacuo , the data employed for this purpose having been taken from a Table appropriate to wave-lengths in air at 20°C., whereas the tertiary standards of iron upon which the wave-length determinations were based referred to 15°C. Before the introduction of the International system, wave-lengths had always been given for air at 20°C., and there was no explicit mention of the change of standard temperature in the paper by Burns, from which the iron arc wave-lengths used as standards were taken. The oversight might possibly have been detected earlier but for the author’s absence on military service from September, 1914, to January, 1919. In any case, however, a revision of the previous work would have been necessary in view of the recent accurate determinations at the Bureau of Standards of the refractive index of air, and also of other work, both theoretical and experimental, on the Balmer series, which has been carried out since 1914. The correction in question is of the order of + 0·02 A., and results, as will be seen, in a decrease of nearly one unit in the value of the Rydberg constant.

In two preliminary papers we have recorded the discovery that when monochromatic light is scattered in a transparent medium (be it gas, vapour, liquid, amorphous solid or crystal), the diffused radiation ceases to be monochromatic, and several new lines or sometimes bands (associated in many cases with a continuous spectrum) appear in the spectrograms of the diffused radiation. Further, the new radiations are, in general, strongly polarised. That the phenomenon is entirely distinct from what is usually known as fluorescence is clear from the fact that the effect is observed when both the exciting radiation and the new radiations generated by it are far removed from the characteristic ultra-violet and infra-red frequencies of the medium. As an illustration we may mention the case of transparent crystalline quartz in which the effect is very well shown with the 4358 A. U. line of mercury as the exciting line, the new lines also appearing in the indigo-blue region of the spectrum. Our preliminary studies have proved conclusively that the effect arises in the following way: The incident quantum of radiation is either scattered as a whole, in which case we have the classical scattering, or else is absorbed in part by the molecules of the medium, the remaining part appearing as a scattered quantum. The part absorbed shifts the molecule to a level of energy different from the initial state. The possibility of a process of this kind, in respect of the electronic state of an atom, was first contemplated by Smekal, and figures prominently in the theory of dispersion due to Kramers and Heisenberg, and in the papers of Schrödinger. Our experiments furnish definite proof of the possibility of such processes, and show that they may occur also in such complicated systems as the molecules of a vapour or a liquid or even in a complete crystal. In the series of papers of which this is the first our further studies of the new radiations will be discussed.

In a previous paper results of measurements of the angular distributions of slow electrons scattered elastically in argon were described. The appearance of maxima and minima in the curves obtained suggested the analogy of the scattering of electrons by atoms to the scattering of light by small spheres. This idea was given further credence by the results obtained by Arnot for the angular distributions of electrons scattered elastically in mercury vapour. However, a number of important and interesting phenomena occur in the scattering of electrons by atoms which are not present in the scattering of light by small spheres. Thus there is no optical analogy to the distortion of the de Broglie waves of the electrons by the potential field of the atom, nor to the exchange of electrons between the atoms and the colliding beam. The relative importance of such phenomena in determining the scattering of slow electrons will depend on the properties of the scattering atoms, so we may expect to be able to sort out the individual effects by comparing the results obtained with different atoms in the light of available theory. In order to do this the previous angular distribution measurements have been extended to helium, neon, nitrogen, hydrogen and methane, and as a consequence the interpretation of the phenomena has been much clarified. In this paper the results obtained in the above-mentioned gases are described and discussed. 2. Method and Results . The apparatus used was, except for minor modifications, the same as that described in paper I. Electrons from a tungsten filament were accelerated through a pair of slits by a suitable potential giving a homogeneous beam of known energy. This beam was fired through the gas under investigation at low pressure (1⋅5 X 10 -3 mm. Hg) in a field free space and the scattered electrons collected by a Faraday cylinder. This cylinder could be rotated by a ground joint so enabling the intensity of the scattered beam to be measured at different angles of scattering.

1. The present paper may be divided into two parts. In the first, some experiments on the intensity of reflexion of X-rays by rock-salt crystals at low temperatures are described. The results of these experiments, when combined with data obtained previously at high temperatures, are compared with the theoretical formulæ of Debye and Waller for the temperature factor of X-ray reflexion. In the second part of the paper we have attempted to get some idea of the actual amplitude of the heat-motions of the atoms in the rock-salt lattice, by analysing the F curves, or curves showing the variation of the atomic scattering power with angle of scattering, using the method of Fourier analysis introduced by Duane and Havighurst, so as to obtain the distribution of electrons in the crystal unit at different temperatures. In connection with this work a new set of absolute determinations of intensity of reflexion has been made, and, from these, the F factors at different temperatures have been calculated, using the results of the experiments described in the first part of the paper.

The difficulties connected with the continuous β-disintegration are well known. The fact that a given isotope of any element has a definite atomic weight suggests that the energy of the normal state of any nucleus is quantized ; further evidence is afforded by the alternating intensities in band spectra. Evidence from the fine structure of α -rays and from the γ-rays, proves that nuclei are capable of existing in quantized excited states. In fact, in all transformations where α -particles, γ-radiation or protons are ejected from nuclei, the evidence suggests, (i) that the nuclear energy is quantized, and (ii) that energy is conserved. On the other hand, when a nucleus P transforms itself into a nucleus Q by emission of a β-particle, the β-particle has all energies between zero and a definite upper limit. One may either conclude that the energy either of P or of Q is not quantized, or that energy is not conserved in the transition. Since the a-transitions leading up to P , and starting from Q , show no sign of any indefiniteness in the energy, it is difficult to accept the former alternative ; and it is thus usual to suppose that energy is not conserved. In this paper we make the suggestion that the sharp upper limit of the β-rav spectrum is a significant parameter with which to classify a β-disintegration. We suggest the following hypotheses : two elements P , Q , such that P -> Q is a β-disintegration, both possess definite atomic weights, and hence definite binding energies. Following Heisenberg* we assume that β-disintegration can only take place if the energy E P of the nucleus P is higher than the energy E q of the nucleus Q. We make the new assumption that the energy difference E P — E q is equal to the upper limit of the i. e., to the maximum energy with which a β-particle can be expelled. According to our assumption, the β-particle may be expelled with less energy than the difference of the energies E P — E q , of the two nuclei, but not with more energy . We do not wish in this paper to dwell on what happens to the excess energy in those disintegrations in which the electron is emitted with less than the maximum energy. We may, however, point out that if the energy merely disappears, implying a breakdown of the principle of energy conservation, then in a β-ray decay energy is not even statistically conserved. Our hypothesis is, of course, also consistent with the suggestion of Pauli that the excess energy is carried off by particles of great penetrating power such as neutrons of electronic mass.

1. Summary of Paper .—It is now widely believed, for the reasons recounted in 2 below, that when the spectrum emitted by a luminous body is of the banded type, the small vibrators which give rise to the radiation are the molecules of the substance, as distinguished from atoms or ions. This result is applied in 3, which constitutes the main body of the present paper, in order to suggest a dynamical system which is formed of two members in the same way as a diatomic molecule may be supposed to be formed of two atoms, and which has free periods of vibration related to each other by the same formula as holds in the case of banded spectra. This formula presents a certain peculiarity, in that the frequency of vibration occurs in it linearly; whereas in the equation for determining the free periods of dynamical systems in general, the frequency enters by its square. It is shown that from this peculiarity in the radiation of a molecule, certain inferences may be drawn regarding the dynamical character of the connection between the atoms within the molecule, namely, that the kinetic potential of a molecule consists of the kinetic potential of the atoms, together with certain gyroscopic terms: and it is suggested that the exchanges of heat in chemical reactions are due to the necessity for readjusting this gyroscopic energy when the molecules are altered. In 4 it is shown that a mechanism somewhat modified from that of 3 would emit radiations connected by the same law as that which Balmer found for the hydrogen lines.

As I have shown in numerous publications, the vapour of mercury in vacuo , even at temperatures below the solidifying point of the metal, when illuminated by the light of a water-cooled quartz mercury lamp, emits the monochromatic radiation of wave-length 2536. According to Bohr’s theory, this resonance radiation results from the fall of an electron from the 2 p 2 orbit, to which it has been raised from the IS orbit by the absorption of one quantum of 2536 radiation, back to the IS orbit, the orbit occupied by the electron when the atom is in its normal state. An atom in which the electron has been brought to the 2 p 2 orbit is in a condition to absorb the radiation of any other line produced by the fall of electrons from outer orbits to orbit 2 p 2 , and Fuchtbauer has shown, in an extremely interesting and important paper (‘Physik. Zeit.,’ 1920), that a large number of the arc lines of mercury are radiated by cold mercury vapour illuminated by the mercury arc. He showed that, if the 2536 radiation was screened off by glass, none of the other lines appeared, and explained their presence as the result of the absorption by excited atoms with electrons at the 2 p 2 level, of the radiations terminating at this level, by which the electrons are carried out to other-orbits, from which they can fall back in various ways, giving rise to emission lines in the process. Though Fuchtbauer‘s experiment did not prove that this process actually took place, his explanation was the only one possible on modern theory, and the experiments which are to be considered in the present paper show that it was correct. Twenty years ago the most that could have been said would have been that the absorption of the 2536 radiation “shook” the atom in some way, causing it to emit its other frequencies as a sort of fluorescence, since Fuchtbauer’s experiment did not show that excitation by lines other than the 2536 line was necessary for the emission of the arc spectrum. To demonstrate experimentally that the step-by-step transfer of electrons from orbit to orbit actually takes place, it is necessary to illuminate the mercury vapour with various combinations of monochromatic light, and study the resultant emission spectrum.

in order to obtain good agreement between experimental and theoretical data for the selfbroadened line widths of oxygen in the microwave”’ and for the oxygen-broadened line widths of carbon monoxide. (2) The problem of calculating the latter has already been discussed, in considerable detail, elsewhere. (3) Therefore, we need only note here that the values used for the quadrupole and hexadecapole moments of oxygen in Ref. (3) are indeed the same as those considered in the present paper. The value of e(O,) = 1.21 D A is three times as large as the value 0.4 D 8, reported by BUCKINGHAM and much larger than any of the values considered reliable by STOCRYN and STOGRYN(~) among all of the available estimates for this constant. The value obtained by MURPHY and BOGGS(~’ is 0.58 D A and not 1.16 D A, as has been wrongly quoted in Ref. (1). The quadrupole moment defined in Ref. (6) is twice that defined in Refs. (4) and (5) and employed in Refs. (l-3), and in the present paper. Our line width computations are performed under the premise that the quadrupole moment of oxygen is known and is equal to the value 0.4 D 8, measured by BUCKINGHAM. The computation is based upon an expanded version (3) of ANDERSON-TSAO-CURNUTTE theory (7) which includes terms in the interruption function due to the hexadecapole moment of oxygen and due to an empirical anisotropic repulsive force. Although our treatment of the quadrupole-hexadecapole, hexadecapole-quadrupole, hexadecapole-hexadecapole and of the repulsive forces is approximate, the main thrust of our calculation is to argue that the value 0.4 D A for the quadrupole moment of oxygen is consistent with a calculation similar to that of YAMAMOTO and CATTANI(‘) and of BOUANICH, .(2) that is, we wish to demonstrate that by not considering these additional interactions of much shorter range, which are

In a previous paper 1 ) we analyzed the coefficients occurring in the polynomial in the scalar product S A · S B , representing an effective-spin hamiltonian for the direct first-order exchange interaction energy of two weakly-coupled atoms A and B in the state of highest multiplicity. No assumption of orthogonality between the orbitals on A and B was made, but contributions due to closed shells of electrons on A and B were neglected. In this paper, the analysis is extended to include phenomena of so-called “indirect valence-shell exchange” between two magnetic atoms A and B and “superexchange” between these atoms via a diamagnetic atom C. Cross terms between the two types of indirect exchange are not considered. Using the technique of symmetric double-coset expansions of permutation groups and a recursion relation of the expectation values of interatomic exchanges of unpaired electrons in spin space, the influence of closed-shell electrons on the coefficients in the polynomial in S A · S B , up to and including double and triple interatomic exchanges for the indirect valence-shell exchange and superexchange, respectively, can be given in a relatively simple form. As an example, the coefficients are listed in detail for the special case of three unpaired electrons on A and B.

The method of superposition of configurations is applied to the singlet sigma states of HeH+ which correlate to the separated atom states of principal quantum number less than or equal to 3. The calculations are carried out for internuclear separations in the ranges 0(.1)34.5, 35.0(.5)50.0 bohr. Energy eigenvalues and the expectation values of the electron coordinate along the internuclear line are discussed in this paper. Dipole transition matrix elements and radial coupling matrix elements are presented in a companion paper. The quality of the calculations is exhibited by comparisons of the length and velocity forms of the dipole matrix elements, by the Hellmann‐Feynman theorem, and by the approach to atomic properties at large internuclear separations. Supplementary calculations of higher quality wavefunctions for the lowest states are also reported. These are used to help estimate the extent to which the results of the main calculations have converged toward the exact values. Comparisons with other work are given. It is shown that for internuclear separations greater than about 3 bohr a one‐electron electron model potential approach is quite successful for the excited states. At smaller internuclear separations, and as the united atom limit is approached, current model potential methods cannot be trusted. In this region the model potential, being based on the separated atoms, cannot describe the actual changing charge distributions of the core electron. This work demonstrates the feasibility, for simple systems, of the ab initio structure calculations required for the quantitative description of low‐energy atom‐atom collisions.

In this paper initial‐distribution‐averaged escape probability has been calculated for a variety of compounds using the procedure developed in the preceding paper. The present method allows computation at any external field strength and temperature although the possible effect of very high external fields on the initial distribution of the ion pairs has been ignored. It has been found that no unique form of distribution function is the ``best'' under all circumstances even though in many cases an exponential or a Gaussian form suffices. An extended initial distribution function tends to reduce the ``temperature inversion effect,'' i.e., the decrease of escape probability with temperature at high fields. Nevertheless at suitably high fields the escape probability averaged over several distribution functions is predicted to be relatively insensitive to temperature over a wide range; such an effect should be observable.

The calculation of Van der Waals forces has acquired considerable interest recently through the work of Buckingham, Knipp and others (Buckingham, 1937; Knipp, 1939). In these papers the interaction energy between two atoms is expressed as a power series in i/R, where R is the nuclear separation, and the various terms in this series are known as dipole-dipole, dipole-quadrupole, quadrupole-quadrupole, etc… interactions. In most cases only approximate values are obtainable for the coefficients in this series, though for two hydrogen atoms in their ground states, Pauling and Beach (1935) have determined the magnitudes correct to about I in 106. In this paper we discuss the simplest possible problem of this nature, i.e. the force between a bare proton and a normal unexcited hydrogen atom. We shall show that a rigorous determination of the coefficients in the power series can be made.

The purpose of the paper is to discuss the inversion effect in ammonia in terms of a simple square-well approximation to the potential. This effect is of some present interest since two so-called inversion states have recently been used to achieve maser action in ammonia. A brief discussion of general mechanical features of the ammonia molecule and a semiclassical derivation of the rotational energy spectrum is followed by a discussion of inversion doubling in the vibrational spectrum and a brief treatment of the internal dynamics of the molecule. This is followed by a discussion of the Stark effect on the inversion doublets. The paper is then concluded with a brief description of the principle of the ammonia beam maser.

1. In order to explain the fact that the scattering of high velocity α-particles by the lighter elements does not obey the Rutherford scattering law, it is necessary to assume that the inverse square law does not hold for the force between an α-particle and a nucleus when the distance between them becomes exceedingly small. There is evidence to show that the inverse square law does hold down to distances of about 10 -12 cm., but that, as the distance is further reduced, the repulsive force changes to an attractive one, and it has been assumed by Gamow and others that the potential energy of an α-particle in the field of a nucleus varies with the distance, as is shown in fig. 1 by the curve t q p o .The divergence from Coulomb’s law, which is represented by the curve t q v u , does not become marked until a distance a is reached, but, for distances less than a , the force changes sign. Sexl has used a simplified form of such a potential field to calculate the decay periods of radioactive substances, and, in the present paper, an account is given of a method by which the anomalous scattering of α-particles by helium can be explained by assuming a potential field of the above type. In order to obtain a form for which the calculation is not unreasonably difficult, the field was simplified to the curve t q v w x of fig. 1. This field is defined by the two parameters a and d , and it is shown how the values of these parameters may be determined from the experimental results; the actual values obtained for the mutual potential energy of two α-particles are shown to scale in fig. 8. It is of interest to note that Sexl assumed the depth d of the “hole” to be zero in the case of the heavy elements, whereas it appears in this discussion that the depth is quite large in the case of helium (fig. 8), and that it is essential for the explanation of the experimental results to have the parameter d at our disposal.

It is known from the work of Fulcher, Merton, Richardson, and others, that definite groups of lines in the secondary spectrum of hydrogen are strengthened in certain types of discharge. The interpretation of these phenomena in terms of specific molecular excitations has been begun by Richardson, on the basis of his classification of associated groups into bands. In the present paper the grouping of lines in the secondary spectrum is studied by longitudinal observation of positive rays in hydrogen. The optical spectrum of positive rays may be used in the following ways to contribute to the elucidation of the mechanisms of this spectrum. Firstly, the grouping of lines when excited by the impact of positive ions falling through a potential of several thousand volts can be examined. This can be compared with the grouping due to the impact of electrons at low voltages comparable with the ionisation potentials, and with the grouping in the Geissler tube spectrum. Secondly, a large Doppler effect appears in the Balmer lines when the positive rays are photographed longitudinally. From this can be determined what proportion of the atomic spectrum is carried by neutralised positive rays, and what proportion is excited in the stationary gas by the impact of positive ions. Further, it is possible to decide in some cases which of the Balmer line carriers have been free atoms in the positive rays stream, and which are recently dissociated molecular positive rays. These proportions are found to vary along the Balmer series. They can thus be related to the intensity grouping of the adjacent regions of the molecular spectrum. Thirdly, previous investigators of the secondary hydrogen spectrum in positive rays have, with one exception, agreed there is no Doppler effect in that spectrum. The exception is Rau, who by an ingenious indirect method showed eight extremely faint components. In the present work some further Doppler components have been found, and the intensity indicated below which any other components must lie. Evidence is thus obtained as to which of the lines in the secondary spectrum are mainly due to the excitation of stationary molecules, and which are carried by neutralised positive rays. This can be compared with the phenomena of the Richardson electron discharges, for which other evidence is available as to the mode of excitation.

The investigations of the spectrum of fluorine which had been made up to the year 1923 are summarised in Kayser’s ‘Handbuch der Spektroscopie’ (vol. 5, p. 444; vol. 7, p. 401). They include measurements of lines attributed to fluorine by various workers, but there is no attempt to classify the lines of the neutral atom, the singly ionised atom, etc. Gale and Monk, however, have since published further measures of fluorine lines, and have made the beginnings of a classification by distinguishing the lines produced in vacuum-tube discharges through fluorine gas from those obtained only from a spark discharge in the gas at atmospheric pressure: Their work has been followed up by Carragan, who has made a study of the Zeeman effects for some of the lines of the former group, and, from the rules of Landé, has deduced the existence of multiplets of the first order and suggested certain term combinations. The results here recorded are the first-fruits of an investigation of the fluorine spectrum under different conditions of excitation. Evidence of at least three successive spectra has been obtained as the exciting agency is gradually intensified. Under the gentlest stimulus the lines which appear form an isolated group in the red and infra-red region of the spectrum. They are in the main identical with the vacuum-tube lines of Gale and Monk, and have been produced simultaneously with strong bands of silicon tetrafluoride when a discharge has been passed through this gas. They have accordingly been assigned to the neutral atom of fluorine. The identification, measurement and classification of these lines form the substance of the present paper. Data concerning the spectra produced by more intense discharges will be published in due course.

1. In a recent note I have called attention to the degree of correspondence between W. L. Bragg’s estimates (based on X-ray crystal measurements) of the dimensions of certain atoms, and those deduced by means of the kinetic theory of gases from determinations of viscosity. I was not then fully aware of the modern work of Chapman‡ in relation to the latter subject, and made calculations by means of a formula which has been definitely superseded. The result was that the comparison gave only qualitative agreement. A closer examination of the data, in the light of Chapman’s results, together with a new aspect of the matter which forms the main subject of the present paper, reveals certain interesting facts regarding the probable arrangement of atoms in molecules, and, in addition, leads to substantial quantitative agreement with Bragg’s values. 2. From the very close agreement between the values of the atomic radius calculated by means of Chapman’s formula, and from van der Waal’s law, there appears now to be no room for doubt that, in the case of monatomic gases, at any rate, the atoms, when in thermal agitation, behave like hard spheres which exert mutual attraction on one another. It is also evident that the absolute diameters of these spheres are now known with considerable accuracy, sufficient to justify quoting to three significant figures. They are given for four monatomic gases in column 3 of Table I for comparison with Bragg’s values, which appear in column 2. They differ to a slight extent from those calculated by Chapman himself, owing to the adoption in the present calculation of Millikan’s|| recent value 2.705 x 10 19 for the number of molecules per cubic centimetre at N. T. P. This differs by about 2 per cent, from that used by Chapman, and the substitution results in an increase of about 1 per cent, in the estimated atomic diameter.

On the basis of the theory of singlet ground state for a localized spin developed so far, the total charge and spin localized around the impurity are calculated in detail. It is shown that for ¢a-component associated with the localized up-spin state half of a down-spin electron and half of an up-spin hole are trapped by the impurity. This leads to a conclusion with the aid of the Friedel sum rule that a phase shift of the conduction electrons at the Fermi level is ±n/2. It is further shown in general that the localized charge in the ground state completely vanishes for the present s-d exchange Hamiltonian. 111 non-magnetic metals forms a singlet (non-degenerate) state coupled with the conduction electrons by the s-d exchange interaction. In this singlet state, the spins of the. conduction electrons are localized around the impurity spin, and form a singlet bound state with it. The energy of the singlet ground state is lower by the binding energy IE I than the normal-state energy JE which can be obtained by the usual perturbation calculation which starts from the doubly degenerate free state of a localized spin and the conduction electrons. Our theory dealing with the present system consisting of a localized spin and the conduction electrons is based on the perturbation method.*> It starts from a singlet state in which one electron (or hole) excited above (or below) the Fermi sea is coupled with the localized spin instead of starting with the doubly degenerate free state, and calculates the ground-state energy and the wave function (and also other quantities) perturbed by the s-d exchange interaction in a power series of the exchange coupling among which the most divergent terms are retained. As particularly shown in a previous paper by the present authors,7) the charge density at the impurity center which is :finite in the start­ ing approximation completely vanishes in the :final stage of pertu:rbation. This fact indicates that the localized charge around the impurity vanishes and only the spin-correlation density remains to be localized. The main purpose of this paper is to calculate the total localized charge

In this paper we discuss the neutralization rate of an isolated ion pair in a polar medium as obtained from the prescribed diffusion solution of the Smoluchowski equation. Specifically, we consider the cases of water, methanol, and ammonia. A specific model with two diffusion constants and a time‐dependent dielectric constant has been employed. The time dependence of the dielectric constant is taken, as in the previous paper, for the situation of fixed charge rather than for fixed external field. Numerical results have been obtained for the probability that the ion pair remains unneutralized at a given time and for the rate of change of this probability with time. A critical review is presented for the time–distance relationship.

This paper records various observations on the frequency, intensity and polarisation of the Raman line of frequency shift 1332 cm.-1 in diamonds. The scattering has been considered as a monochromatic reflection by phase-waves, and the consequences are discussed. No change in the frequency within 1 in 1000, nor any difference in intensity was found by varying the setting of the crystal or the angle of scattering. The depolarisation value was found to be 1, in disagreement with the supposed theoretical value of 2. The intensities and frequencies of the line in crystals varying enormously in their fluorescence and absorption properties were compared quantitatively and found to be sensibly the same. An interesting case of an irregularity of the spectral line noticed in an imperfect crystal is illustrated in the paper, and a suggestion is made that an intense local stress of the order of 1000 atmospheres is responsible for such an effect.

The pressure shift of spectral lines, unexplained by the usual theories of pressure broadening, can be adequately treated on the basis of a theory which considers the perturbations produced by neighboring atoms on the two states between which transitions occur. The analysis presented in the paper is directly applicable only to absorption lines, but its consequences are qualitatively correct for emission lines as well. The forces acting on the unexcited atom are the usual van der Waals forces; the perturbations of the excited state are produced by interactions of the same character (dispersion forces) but of different magnitude. The energy increments for both cases can be roughly computed by means of spectroscopic data, which renders possible the evaluations of the mean energies of transitions and hence of pressure shifts. Details are worked out mainly for the shift of $\ensuremath{\lambda}2537$ (Hg) in foreign gases, and are compared with the experimental data of F\"uchtbauer, Joos, and Dinkelacker. In this case, the energy increments are negative both for the excited and for the normal state of Hg, but larger for the former. Hence there results a red shift, whose magnitude agrees well with observations. The line width produced by the perturbations here considered is an appreciable portion of the total experimental half-width. It is no longer necessary, therefore, to explain the total broadening effect of foreign gases by an appeal to Lorentz collisions. Main results of the theory are: the shift is proportional to the density of the perturbing gas; it is usually to the red, but may, under conditions discussed in the paper, be to shorter wave-lengths; a dependence of the shift on the temperature exists, but is slight at ordinary temperatures; the "standard deviation" of frequencies within the broadened line is proportional to the square root of the density of the perturbing gas.

In previous papers we developed techniques for the accurate calculation of dipole moments using moderate‐sized (200 configuration) CI calculations. In this paper we consider the modifications necessary to treat higher excited states of a symmetry. It is shown that states below the state of interest must be considered simultaneously to a similar degree of accuracy. Calculations were performed on the 2Σ+ states of CN. For the X 2Σ+ state the SCF, CI, and experimental dipole moments (in debye) are 2.301, 1.465, and 1.45±0.08; for B 2Σ+ the CI and experimental values are −0.958 and −1.15±0.08. Spin hyperfine constants, and in particular spin density at the nucleus, are considered in the context of one‐electron operator properties which may be calculated by the same methods used for the dipole moment. SCF and CI values for the spin density are compared with experimental values for several diatomic molecules.

In a previous paper it was shown that the usual model for second-order decay predicted the correct form for the decay in many thermoluminescent crystals but gave the wrong behavior for the parameters involved. Specifically, it was shown that $b$ and $m$ in the decay expression, $I={I}_{0}{[\frac{b}{(b+t)}]}^{m}$, should behave differently as functions of the decay temperature and the degree of trap filling than is observed experimentally at temperatures near or below the glow peak. In the present paper it is shown that the discrepancies can be accounted for by assuming a first-order decay from a distribution of trapping levels. Most of the results are based on a Gaussian distribution but it is shown that other distributions can produce similar results. The first-order mechanism is justified by considering the relative magnitudes of the rate constants for trap emptying, retrapping, and recombination. At temperatures well above the glow peak this assumption is no longer justified, but in this range the second-order decay predicts the observed results for $b$ and $m$. The effects of retrapping and of crystal dimensions are considered. Also, the effect on the glow peak of having a distribution of levels rather than a set of discrete levels is worked out and it is shown that the peak is broadened appreciably even for relatively narrow distributions.

This paper is a report of observations on H a which show an asymmetry in the displacements as well as in the intensities of its Stark components. The early theoretical treatments of the Stark effect in hydrogen neglected the fine structure and gave symmetrical displacements of the components in moderate electric fields (about 40,000 v./cm.). So far as the writer is aware, no observations have been made which would lead one to deny this symmetry. Using the wave equations of Darwin and Dirac, Schlapp has reconsidered the hydrogen-like atom in an external electric field and under the influence of the forces which cause fine structure. In the case of H a numerical results were calculated for two limiting cases, (i) where the effect of the electric field is small compared with the fine structure (for fields less than 300 v./cm.), and (ii) where the fine structure is small compared with the Stark effect (fields above 10,000 v./cm.). The displacements were not calculated for the inter­mediate region, but the connections between the two sets of components are given.

In previous papers the values of rotational momenta for certain polar liquids in rotating electric fields having frequencies ranging between 0.125 and 8.5 MHz and between 8.5 and 23.0 MHz, were determined. In this paper however, are reported the rotational momentum values for some polar liquids (toluene, nitrobenzene, ethyl alcohol, amyl alcohol, distilled water, acetic acid) in a rotating electric field at much higher frequencies, that is 100.0; 120.0; 150.0 MHz, in order to determine in a different way the viscosity coefficient values. The values of the viscosity coefficient η, obtained by comparing the experimental rotational momentum with that given by the Born formula—in whichM is substituted by the values of the electric momentum measured in the Debye polarization processes—are relatively in agreement with those obtained by classical methods.

When an alternating potential, whose frequency is fairly lower than the electron plasma frequency, is applied to a probe, dc component of the probe current varies according to the nonlinear characteristic of the sheath around the probe.This fact is well known and many papers have been presented. However in this lower frequency range, sinusoidal potential which is applied to the probe seems to heat the electrons in the plasma around the probe from the fact that the measured electron temperature increases.So the theories which have been presented so far seem to need some corrections. In the present paper, a new expression of the characteristic curve of the radio frequency probe is presented. In this expression, effect of the penetration of R. F. electric field through the ion sheath is taken into consideration. A theory derived by Margenau was applied here to explain the experimental result.

The success of the hollow cathode discharge in helium in exciting the spectra of various metals suggested that a similar method might be applied to excite the spectrum of arsenic. It was in the course of this work that plates were obtained which revealed with remarkable intensity the Lyman series of hydro­gen, extending down to the 15th member. The most interesting feature of the series, however, is the anomalous distribution of intensity among its members. Instead of the intensity gradually falling off as we go to higher members, a sudden enhancement is observed in the intensity of the 10th and 11th members and then an abrupt fall so that the remaining members are only just observable. The appearance of the series is such as immediately to suggest the occurrence of a kind of resonance effect. The experiments were therefore repeated under various conditions in order to investigate the cause of this observed anomalous intensity and to discover, if possible, the type of impact involved in the production of such a phenomenon. In two preliminary notes, the main conclusions which have been obtained have been reported and it is the purpose of this paper to describe these investigations and the conclusions reached. Experimental . The experimental use of the hollow cathode source is well known and has been described previously by various writers but on account of the importance of the phenomenon that has been observed, it is considered worth while to present details of the method employed. Some metals, like aluminium, are generally used directly as the cathode, but Paschen has found that the source can be adapted also for metals of low melting points or those which vapor rapidly, in which case the metal in question may be placed in a carbon (or tungsten) hollow cathode. The cathode in these experiments, was a thin hollow cylinder of carbon, C, fig. 1, of length 3·5 cm. and diameter about 1·5 cm. The cylinder was closed at one end N, which terminated in a kind of box of length 0·5 cm., the inner wall W of which was perforated. This box served as a reservoir to contain metallic arsenic, whose vapour entered the cathode through the perforated wall. A similar cathode was used by Takahashi* in his experiments on Zn and Cd.

EXPERIMENTAL Information on the Interaction of atoms of a gas with a solid surface Is at present somewhat scarce. Nevertheless, there are experimental methods which make It possible to evaluate the Influence of various factors, such as the temperature and structure of the surface, the density and temperature of the gas, and others, on the exchange of energy between the gas and the solid surface [1]. There are some Indications that the transfer of energy In solid bodies is faster than that due to collisions in a gas. Quantitative estimates of the accommodation coafficients were obtained in experiments with molecular beams [2, 3]. However a satisfactory description of the interaction phenomena can be achieved only by a joint utilization of experimental results and of a realistic the iretical model of the interaction between the gas particles and the crystal lattice. The theoretical Investigations are, however, in view of the great mathematical complexity, and also because of the obscure physical nature of the collision phenomena, usually confined to specific simplified problems. One of these simplifications is the modelling of the solid surface by a linear chain of atoms, linked together by harmonic forces. Such a model Is considered In [4–6]. In [4] specific values of the interaction parameters are Investigated, and In [6] the solution is obtained in the form of a series In terms of Bessel functions. However, the authors of these papers confined themselves to the case when the lattice is Initially at rest. In [5] the equations of mofcion of the chains are integrated numerically; the analysis of the results obtained in that paper indicates the dependence of the solution on the non-zero Initial perturbations of the lattice.

It is shown that the "two-libron" lines in the Raman spectrum of solid hydrogen result from the large cubic anharmonicity of the quadrupole-quadrupole Hamiltonian. A localized picture is used to describe the interaction of two librational excitations on neighboring molecules, and dynamic interactions with other molecules are treated perturbatively. In this approximation the average single-libron energy agrees with the anharmonic calculation in the accompanying paper. Using a value of the quadrupole-coupling constant obtained from the single-libron spectrum, the resulting two-libron energies and Raman transition probabilities are in excellent agreement with the observed spectrum. Disciplines Physics | Quantum Physics This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/416 PHYSICAL REVIEW B VOLUME 4, NU MBKR 8 Two-Libron Spectrum of Solid H2 and D2~ 15 OCTOBER 1971 A. John Berlinsky and A. Brooks Harris Department of Physics, University of Pennsylvania, Philade/podia, Pennsylvania 19104 (Received 19 January 1971) It is shown that the "bvo-libron" lines in the Baman spectrum of solid hydrogen result from the large cubic anharmonicity of the quadrupole-quadrupole Hamiltonian. A localized picture is used to describe the interaction of two librational excitations on neighboring molecules, and dynamic interactions with other molecules are treated perturbatively. In this approximation the average single-libron energy agrees with the anharmonic calculation in the accompanying paper. Using a value of the quadrupole-coupling constant obtained from the single-libron spectrum, the resulting two-libron energies and Baman transition probabilities are in excellent agreement with the observed spectrum.

In a previous paper the authors have given a preliminary analysis of the are spectrum of palladium. This has now been extended and brought into better agreement with the theoretical considerations of Hund. In addition, some progress has been made in the analysis of the second or spark spectrum of palladium. The work on the arc spectrum has been made possible by the study of the Zeeman effect of the palladium arc by Beals, by the experiments of McLennan and Cohen, and McLeannan and Liggett on the absorption spectrum of normal palladium vapour, and by the measurements of Meggers of the lines of the palladium arc in the region from 4500 to 9000 A. The ground Terms of Palladium I . On the basis of his experiments on the Zeeman effect, Beals assigned most of the strongest lines of the arc spectrum of combinations between a group of low terms designated by 1 S 0 , 3 D 321 , 1 D 2 (in the notation of Russell) and a group of singlet and triplet, P, D ¯ and F terms. This has been generally confirmed, although it has been necessary to rearrange the PDF group slightly in order to bring it into agreement with the theoretical grouping of these terms. The new arrangement of the lines involved is shown in Table I, and is supported by consideration of the relative intensity. Those lines for which the agreement between observed and calculated Zeeman effect is particularly good are not affected by the changes. Table I also contains other lines due to combinations with the low group, some of which have been identified as the second members of series of which the lines given by Beals are the first members. The nature of the other terms combining with the low group has not been ascertained.

If the terms of the hydrogen spectrum to which certain quantum numbers have been assigned are compared with corresponding terms in the spectra of other elements, the latter will be found to be greater. While all writers agree that this is due to the presence of other orbital electrons, the structural reasons for this discrepancy are still a matter about which there is considerable difference of opinion. The present paper is an effort to consider this subject from a slightly new point of view. We may call such spectra hydrogen-like as arise from the radiation of the valence electron when it is alone in the outer shell. The alkali metals have such spectra normally and other elements give it in higher states of ionization. In all the cases to be considered, the valence electron moves about an atomic kernel, consisting of the nucleus and a number of electrons which move in orbits much smaller than those of the valence electron. The kernel is probably a structure geometrically similar to the atoms of the inert gases, but somewhat smaller, due to the contracting influence of the greater nuclear charge; and, unlike the inert gas atoms, the atomic kernel has a net positive electric charge. There was formerly some doubt about the total quantum numbers to be assigned to the valence orbit of the elements, but the correlations of X-ray and visible spectroscopy by Bohr and others have settled upon 3 as the total quantum number of the normal orbit in the sodium group, 4 in the potassium group, and so on.

The Paper is mainly concerned with the possible existence and stability of atoms, and of molecules formed after the manner suggested by Stark, the link between the atoms in a molecule being provided by a stationary electron on the molecular axis. Atoms on the Rutherford model, though dynamically unstable, are stable for the simple vibrations ordinarily excited; but it is shown in the Paper that atoms with such a stationary electron have a much more limited degree of stability. Moreover, they cannot exist even in an undisturbed state unless they are endowed with a negative charge, for no steady motion is possible, and this conclusion extends even to atoms regulated according to a dynamics such as that of Bohr. Stark's conclusions do not, therefore, survive a quantitative treatment, and molecules cannot be formed in the manner he supposes. The Paper also discusses the more symmetrical problem, in which there are two such stationary electrons in an undisturbed atom, and it is shown that systems with a transitory existence, which are known by their spectra to occur in the solar corona, are apparently unaccompanied by the still more transitory systems which would be formed by the attachment of an electron after the manner of Stark. This is a further argument against the possibility that two atoms in a molecule can be linked by a single electron, or by two electrons, which attract both atoms.

In a previous paper we have applied quantum-theoretical considerations to the passage of positive ions through gases, but in certain circumstances, as for example the electric discharge in iodine vapour, negative ions are of importance. Very little has been done in discussing theoretically the behaviour of such ions, and in fact there has also been little experimental investigation of their properties. It is therefore of interest to discuss, by quantum-mechanical methods, the formation and neutralization of negative ions. Results obtained in this way should indicate the most profitable directions for further experimental research and assist in the interpretation of observations because of the close analogy presented by the attachment of electrons to neutral atoms to the capture of neutrons by atomic nuclei. Throughout the work of this paper we restrict ourselves to the consideration of atomic ions such as Cl - , O - , H - , Before considering the formation of these ions by various processes it is desirable to discuss in general terms how a negative processes it is to be regarded from the quantum standpoint. The existence of a stable negative ion ( i.e ., an atom of positive electron affinity) implies that there is a stationary state of negative energy for the attached electron in the average field of the atomic nucleus and the remaining electrons. This is itself is not remarkable, for a neutral atom exerts an attractive force on an electron and the existence of negative ions might be anticipated. However, the number of stationary states for attached electrons is limited and not infinite, owing to the short range of the effective attractive field in which the electron moves. The operation of this effect combined with the Pauli principle, which further limits the possible states into which an electron can be attached, results in the exclusion of a number of atoms from the list of those which form stable negative ions. For example the ion He - is not known to exist in stable form. The helium effective atomic field is sufficiently strong to give rise to a 1 s electron state of He - but no excited states. Such a state would involve 3 electrons in the same s level, and so would violate the Pauli principle. The third electron is thus left without a vacant state into which to go. Similar considerations apply to the other inert gases. For the halogen atoms, however, a vacant state exists in the incomplete outer shell. Thus an electron can be attached in a 3 p state to form C l , But, since Ne - is unknown, it is very unlikely that a second excited stationary state pf Cl - exists, for an electron in such a state would move in an effective field very similar to that in which an electron in Ne - would move (both in 3 d or 4 s states).