Collisions Of Slow Electrons Research Articles

Stark broadening of the overlapping 4471.48 Å hel line in a plasma

The purpose of this paper is to provide a comprehensive study of the generalized impact formalism as applied to overlapping neutral lines, especially to the 4471.48 Å HeI line emitted in a plasma. First, we will discuss the specific algebraic modifications needed to adapt the impact theory to partially degenerate lines. Secondly, we will review briefly the time-averaged dipole width and shift functions. The corresponding impact parameter averages and other properties are given and discussed at length. Thirdly, we will show that the various proposals made for the long range cutoff of the electron impact parameter do not lead to significant discrepancies in the final line shape. The short range cutoff is shown to be dependent on the static splitting and it is the smallest for the nondiagonal elements of the collision matrix. Moreover, the nonmarkovian corrections to the frequency-independent impact theory appear to be of only marginal importance for the 4471.48 Å line in the line core, in contradistinction to the wings where more significant discrepancies are exhibited. These results strongly suggest that the non-diagonal part of the collision operator is dependent on the close perturbers collisions (weak collisions with the smaller impact parameter), so that the extension of the impact formalism to off diagonal matrix elements appears as an acceptable approximation, as long as the impact theory retains its validity. The impact formulation is seen to be self-consistent with respect to slow electron collisions which are automatically excluded when the static splitting is introduced in the collision operator. Finally, our profile calculations are compared with the previous ones and additional results with 2 × 10 16 ⩽ N e ⩽ 6 × 10 16 e-cm −3 and T e = 2 × 10 4 K are presented. The dip between the two peaks is seen to be sensitively dependent on the perturber temperature. This effect combined with ion dynamic shielding and a self-consistent choice of the short impact parameter cutoff could allow for an important enhancement of the line intensity between the two peaks, and also a significent reduction of the theory-experiment discrepancy.

Vibrational Excitation of CO by Slow-Electron Collision

The cross section for the vibrational excitation v =0→1 of CO by slow-electron collisions is calculated using the close-coupling method. First, only the dipole interaction is considered to give rise to the vibrational transition and the result is compared with the Born calculation; it is found that the Born approximation gives a rather poor result in the present case. Next, the polarization effect of the molecule is taken into account. The contribution from the polarization term is shown to be comparable to that from the dipole interaction. Finally, the excitation cross section is evaluated by including both the dipole and the polarization interactions, and a comparison is made with experimental data.

Multiple ionization of mercury by successive electron impacts

Mercury ions of charge multiplicity up to n = 9 have been formed by repeated collisions of slow electrons (less than 150 eV) with ions trapped in an electron beam of high current density (~5 × 10−2 A cm−2). Ion current is observed at electron energies below the ionization potential for all multiply charged ions up to n = 8 and is ascribed to collision sequences involving metastable states of the ions (eN/eNm/ee(N + 1), where N represents an ion of charge multiplicity n). All the breaks observed in the ionization probability curves for [Formula: see text] can be explained in terms of collision sequences involving spectroscopically known metastable levels as limiting steps. Measured ionization potentials of the highly ionized species up to n = 9 are in reasonable agreement with extrapolation of spectroscopic values.

Scattering of Slow Electrons by Molecules

This paper is concerned with theory of collision of slow electrons with simple molecules. First, nature of the electron-molecule interaction is discussed. Then, for nuclear. position fixed in space, calculation of the scattering cross section of a diatomic molecule is formulated. Both one-center and two-center expansion methods are used, and comparison of the two methods is made. The rotational and vibrational transi­ tions are considered for non-polar and polar molecules. Finally, for electronic transitions, studies in the past are briefly summarized.

Collisions of Slow Electrons and Positrons with Atomic Hydrogen

We investigate the scattering of electrons and positrons by atomic hydrogen for projectile energies in the range from 11.0 to 54.4 eV. We calculate (a) the differential and total cross sections for elastic and inelastic scattering, (b) quantities related to polarization and correlation of electron spins, and (c) the polarization of radiation emitted in various electromagnetic transitions. A close-coupling approximation is used in which the total wave function is expanded in hydrogen eigenstates and only terms corresponding to the $1s$, $2s$, and $2p$ states are retained; the wave function is symmetrized or antisymmetrized explicitly in the case of electron collisions. In positron interactions, positronium formation is neglected. The coupled integro-differential equations that result from the approximate wave function are integrated numerically on an IBM-709 or 7090 computer, subject to standard boundary conditions, to yield the reactance matrix elements in each total spin and total angular-momentum state. In the case of electron scattering, the integral terms are treated by means of an iteration procedure. We find for elastic $1s\ensuremath{-}1s$ electron-hydrogen scattering that the inclusion of the $2p$ state in the close-coupling wave function modifies some partial-wave contributions at lower energies; however, the effect on the total cross section is small. The $1s\ensuremath{-}1s$ cross section has a maximum computed value of about $6\ensuremath{\pi}a_{0}^{}{}_{}{}^{2}$ at the second quantum excitation energy, and the differential cross section is strongly peaked in the forward direction. For elastic $2s\ensuremath{-}2s$ scattering of electrons, calculated total cross sections are exceptionally large, attaining values of the order of $400\ensuremath{\pi}a_{0}^{}{}_{}{}^{2}$ at 11.00 eV; here, too, the differential cross section is strongly peaked in the forward direction. Our calculated inelastic electron-hydrogen $1s\ensuremath{-}2p$ cross sections are in disagreement with experimental results, sometimes by as much as a factor of two. The calculated cross section reaches a maximum of $1.3\ensuremath{\pi}a_{0}^{}{}_{}{}^{2}$ at about 20 eV. The predictions for polarization of photons emitted by hydrogen atoms excited by electron bombardment yield a result that, near the $n=2$ threshold, is a rapidly varying nonmonatomic function of energy; again, over-all agreement with experimental results is poor. We support our belief that these discrepancies probably can not be reconciled by any close-coupling calculation. We also present results for the $1s\ensuremath{-}3p$ excitation cross section calculated with a $1s\ensuremath{-}3p$ close-coupled wave function; there are no experimental data for comparison here but we point out the consequences these results have for $1s\ensuremath{-}2s$ excitations. Our calculated total $1s\ensuremath{-}2s$ excitation cross sections show little difference as a result of including the $2p$ state in the close-coupling wave function. Agreement with experiment is again poor although measurements are subject to possible errors in normalization and we suggest further investigation of normalization procedures. As in the elastic case, the differential $1s\ensuremath{-}2s$ cross section is strongly peaked in the forward direction. Measurements of the spin-flip cross section and our calculation of it are in fair agreement at the $n=2$ threshold. The effect of the $2p$ state on elastic positron-hydrogen scattering is quite pronounced, especially for energies immediately above the $n=2$ threshold. For $1s\ensuremath{-}2s$ excitations by positrons, the same effect is seen, but it manifests itself over a wider energy range. Calculated values of reactance matrix elements are provided in tabular form for electron-hydrogen scattering at six energies above threshold.

The Low-Energy Scattering of Electrons and Positrons by Hydrogen Atoms

The elastic and inelastic (excitation, pickup, or ionization) collisions of slow electrons or positrons with hydrogen atoms are reviewed. A survey of the experiments that have been reported is given, and the theoretical attempts to calculate the relevant cross sections within the framework of nonrelativistic wave mechanics are reviewed. (L.T.W.)

The Numerical Solution of the Exchange Equations for Slow Electron Collisions with Hydrogen Atoms

Numerical methods are used to calculate phases in the exchange approximation for the s-, p- and d-wave scattering of electrons by hydrogen atoms, using small energy intervals. There is a discussion of experimental results.

Momentum Transfer Cross Section and Fractional Energy Loss in the Collisions of Slow Electrons with Nitrogen Molecules

The momentum transfer collision cross sections, ${q}_{m}$, of nitrogen molecules for slow electrons and the mean fractional electron energy loss, $\ensuremath{\lambda}$, in these collisions have been determined by the method of microwave interaction in gaseous discharge plasmas. The mean energy of the electron was varied from 0.04 to 0.46 ev. The cross section, ${q}_{m}$, was found to be \ensuremath{\sim}17\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ at 0.04 ev. It decreases to \ensuremath{\sim}8\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ at 0.46 ev. The mean fractional energy loss of the electron, $\ensuremath{\lambda}$, in the energy range investigated, was found to be \ensuremath{\sim}5.5 in units of $\frac{2m}{M}$. These results lend strong support to the theory of rotational excitation of ${\mathrm{N}}_{2}$ by slow electrons.

Formulae for the Mean Losses of Energy in Collisions of Slow Electrons Moving in Diatomic Gases

Formulae are derived for the mean losses of energy in collisions with molecules by electrons moving in a steady state of motion in a diatomic gas in an electric field. Although the theory is incomplete and crude, yet the formulae describe the experimental measurements closely in the smaller ranges of electronic energy.

Microwave Determination of the Probability of Collision of Slow Electrons in Gases

A microwave method is given for determining the collision probability for momentum transfer for electrons in thermal equilibrium with a gas. An integral equation is developed which gives the ratio of the resistive and reactive components of the microwave conductivity in terms of the collision frequency for electrons with the gas atoms. Two approximate solutions are given for the collision frequency as a function of electron energy. An experimental procedure is described in which the conductivity ratio is determined from the shift in the resonant frequency and the change in conductance of a resonant cavity. Measurements are made during the decay of a pulsed discharge after the electrons have cooled to the gas temperature. Preliminary results are given for several gases.

Dr. F. L. Arnot

NEWS has been received from Sydney, Australia, of the sudden death early in October of Dr. Frederick Latham Arnot, for eight years lecturer in natural philosophy in the University of St. Andrews and, since 1939, lecturer in physics in the University of Sydney. He was born on September 29, 1904, at Sydney, of British parents, his father being Scottish and his mother English. He was educated in his home University, and after graduating with first-class honours in 1927, he was awarded an exhibition at Trinity College, Cambridge, and worked as a research student in the Cavendish Laboratory under the supervision of Sir Ernest Butherford (later Lord Rutherford). Two years later he was awarded an Isaac Newton studentship, and received the degree of Ph.D. in June, 1930, for investigations concerning the collisions of slow electrons with molecules in gases at low pressures. His later results at Cambridge on the scattering of electrons in gases and on the diffraction of electrons in mercury vapour were of great beauty and importance.

On the Cross Sections ofCl2andN2for Slow Electrons

Measurements of total cross section for collision of slow electrons between 2 and 40 volts have been carried out in ${\mathrm{N}}_{2}$ and ${\mathrm{Cl}}_{2}$ by use of a Brode type apparatus. The results for ${\mathrm{N}}_{2}$ compare well with those of previous investigators and with the theory of elastic scattering. The cross section of ${\mathrm{Cl}}_{2}$ is of order 2000 sq. atomic units with a maximum at $2.65\ensuremath{\surd}V$, the curve being similar to those for Na, K, Cs and Rb. Application of the theory of elastic scattering indicates that only a small portion of these collisions can be elastic.

The collisions of slow electrons with atoms—IV

The collision of a slow moving electron with an atom is known to be a very complicated phenomenon involving a number of processes which are themselves complex. To obtain even an approximate description of such phenomena the only method of attack is to consider the effects of the different individual processes separately in order of estimate the nature and magnitude of their contributions to the resultant scattering. In both elastic and inelastic scattering the principal processes occurring may be stated as follows:- 1-Scattering by the field of the atom considered electron as undisturbed by the incident electron, the latter being also thought of as only slightly affected by the collision. 2-The distortion of the incident and scattered electron waves by the potential field of the atom, the latter field being taken as the undisturbed atomic field. 3-The exchange of electrons between the incident and scattered electron waves and the atom. 4-The disturbance of the atomic field by the incident electron waves.

The collision of slow electrons with atoms. III.—The excitation and ionization of helium by electrons of moderate velocity

It has been shown that quantum mechanical methods are capable of providing a general explanation of the phenomena observed in the excitation of helium by the impact of low velocity electrons. Thus a well-known feature of the observations is that the probability of excitation of a triplet state attains a maximum for electrons of much lower velocities of impact than in the case of the singlet state and falls off very much more rapidly as the velocity increases. By using Born’s method of approximation and taking into account electron exchange the variation of excitation probability with velocity of impact has been calculated for various singlet and triplet levels of helium for energies between the resonance potential and 60 volts. When one compares the observed and calculated curves it is found that qualitative but not quantitative agreement is obtained. It is therefore necessary to improve the methods of calculation and an attempt was made to do this by taking into account the distortion of the incident and outgoing electron waves by the fields of the normal and excited atom respectively. As a result it was then found possible to explain the diffraction effects observed in the inelastic scattering of electrons at large angles but the calculated variation of cross-section with velocity is still not satisfactory. In order to improve the theory it is important to determine the range of validity of the simple method of approximation by extending the calculations to higher velocities of impact (up to 400 volts) where the method should be more accurate. This is of special interest in view of the recent experimental measurements of Lees and of Thiem who have measured the excitation functions of the various helium lines for electron energies up to, and in certain cases greater than 400 volts. In this paper we have extended the calculations in this way and have considered also ionizing collisions. Since the probability of ionization by electrons can be measured with considerable accuracy we can apply a very satisfactory test of the theory in this direction. In addition to the probabilities of ionization of hydrogen and helium the velocity and angular distributions of ejected and scattered electrons are also computed. The comparison of calculated and observed results is discussed in detail and it is found that Born’s approximation is valid for electrons with energies greater than 200 volts.

The collision of slow electrons with atoms. II.—General theory and inelastic collisions

Although a satisfactory theory of the collisions of fast electrons with atoms is provided by the method of Born-Dirac, a complete theory of slow collisions has not yet been developed. This is due to the large number of complicating factors which cannot be neglected when the time of interaction between atoms and the incident wave is considerable. These complications include the distortion of the incident and scattered waves by the atomic field, the exchange of electrons between atom and colliding beam, and the disturbance of the atomic wave functions by the incident wave. The effect of the second of these phenomena was considered in detail to a first approximation by us and found to be of considerable importance. In this paper, the accuracy of the calculation could not be regarded as high inasmuch as the other disturbing effects were neglected. It was then shown in a later paper how the effect of the disturbance of the incident wave could be included in the calculation, and it was found that for the elastic scattering the agreement with experiment was considerably improved. On applying the method to the calculation of inelastic collision probabilities, the effect of the distortion of the incident wave was found to be small in comparison with, say, the effect of exchange. However, when one considers physically the excitation of an atom by electron impact, it is clear that the distortion of the outgoing wave by the field of the excited atom will be of greater importance than that of the incident wave by the normal atom. This is due to the greater spread of the field of the excited atom and also to the increased wave-length of the outgoing wave. In the same way, the distortion of the outgoing wave may be important in the case of elastic exchange.

The Collision of Slow Electrons with Atoms. I & II

The Collision of Slow Electrons with Atoms. I & II

The collision of slow electrons with atoms. I.—General theory and elastic collisions

An outstanding defect of the old quantum theory was its inability to treat the phenomena occurring in the collision of electrons with atoms, and Born’s theory showed how the new quantum mechanics was capable of removing this defect. The original theory of Born was a method of successive approximations to the solution of the wave equation representing the colliding systems, and could be applied to both elastic and inelastic collisions. In its actual applications, which could be worked out to the first approximation, the theory fell far short of expectations. The Ramsauer effect, the most interesting phenomenon exhibited in the elastic scattering of electrons, could not be explained, and in the field of inelastic collisions, it failed to provide a means of explaining the excitation of levels of a term system which does not combine with the ground state system, e. g. , the excitation of the triplet lines of helium. These failures are, of course, failures of the theory in its first approximation. The first approximation in Born’s method of successive approximations neglected the disturbance of the electron waves by the field of the scatterer, and also the possibility of exchange of electrons between the atoms and the colliding beam. The neglect of both these effects becomes important for low velocity impacts, and it was clear that the Ramsauer effect, which is only observed for low velocity electrons, could only be explained by more accurate theory. The question was whether both effects, the distortion of the electron waves by the atomic field, and the exchange of electrons was important, or only one of them.

Societies and Academies

LONDON Royal Society, Feb. 18.—D'Arcy W. Thompson: The geometry of the siliceous skeletons of the Radiolaria. The figures of equilibrium and minimal area which are assumed by soap-films in Plateau's experiments have proved helpful in explaining the configurations of various cells and simple tissues in plants and animals. Among the most curious and anomalous of cell-forms are those of certain Radiolaria. In some of these the skeleton resembles a minute spiked helmet with three curved lappets or straps below. Even such an anomalous configuration as this may be precisely imitated or reproduced by an artificial system of liquid films.—H. W. S. Massey and C. B. O. Mohr: The collision of slow electrons with atoms (1). The theory has been developed in which the zero approximation is not a plane wave but the wave representing the motion of the electron in the static field of the atom concerned. Exchange does not become very important until voltages lower than those obtained on Born's theory using the plane wave as first approximation. At lower voltages, strong interference effects occur between the incident and exchanged electron waves, giving peculiar angular distributions of the scattered electrons. These effects are observed experimentally.—H. C. Webster: The artificial production of nuclear γ-radiation. The production of nuclear γ-radiation by bombardment with α-particles has been observed for the elements Li, Be, B, F, Na, Mg, Al. Negative results were obtained with H, C, N, Ni, Cu, Sn. The absolute efficiencies of production of the various radiations range from about 0.5 quanta per million α-particles for magnesium to about 30 quanta for beryllium. In addition, the way in which the efficiency of production varies with the residual range of the α-particles was investigated. The processes probably responsible for the radiations are discussed: some appear to be due to the capture of an α-particle by a nucleus without proton emission, others are probably due to a secondary process following proton emission, others may arise from inelastic collisions without capture.

Elastic collisions

1. In a recent paper by Bullard and Massey on the “ Elastic Scattering of Slow Electrons in Argon,” the description they give of previous work on this subject is in many respects inaccurate and misleading. Similar faults also appear in some other papers published in the ‘ Proceedings,’ where effects obtained in collisions of slow electrons with atoms or molecules of gases are described. It is therefore desirable to make clear the objections that have been raised to these papers, by considering a few cases in detail, and to refer briefly to some of the principal experiments by which the properties of slow electrons were discovered. 2. The collisions of electrons with molecules of gases in which the electrons lose only a small part of their energy, are generally known as elastic collisions. They were first observed in the experiments on the motion of electrons in air and other gases at low pressures, which were made at Oxford. The experiments were interpreted by the ordinary principles adopted in the kinetic theory of gases. The mean energy of agitation, E, of the electrons was thus obtained from the partial pressure of the electrons. The theory of the motion was fully investigated by Pidduck. He gave a method of finding the coefficient of elasticity in the collisions of electrons with molecules or atoms of a gas, and he showed that in air the collisions were almost the same as the collisions of perfectly elastic spheres.