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

Abstract

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.