Other men's flowers: Classical treatment of collisions; Massey's adiabatic criterion and ionization in flames; ion-molecule reactions; bound-free and free-free transition of electrons in ambient atomic hydrogen

Abstract

The article is concerned with four different topics. 1. 1. Classical collision theory. Interest in the classical treatment of collision phenomena was twice aroused by the study of stopping power, firstly before wave mechanics was developed and secondly in 1959 by Gryzinski. The original interest waned because quantum theory (and only it) could in principal provide exact results. However a clasical treatment is often useful and indeed may, as in the case of electron capture from heavy atoms by fast light nuclei, give better results than can at present be obtained by attempting to find the appropriate solution of Schrödinger's equation. In connection with electron-atom collisions it is argued that the non-symmetrical version of the treatment is in practice superior to the symmetrized version and a reason for this is proposed. It is necessary to make allowance for the mean free path of the projectile electron while within the target system being in general less than the linear dimension of the system. The impact ionization cross sections obtained from the formula derived are in at least as close accord with laboratory data as are those obtained from the Born (exchange) approximation. 2. 2. Massey's adiabatic criterion and ionization in flames. Reliance may be placed on Massey's criterion that a collision between atomic systems is unlikely to cause an electronic transition if a certain parameter λ M be large compared with unity. The probability of a transition due to a dipole interaction, of one due to a quadrupole interaction and the Landau-Zener transition probability are functions of λ M and all fall off at around the same rate as λ M is increased. If Massey's criterion appears to be violated the physical interpretation adopted cannot be correct. Contrary to what might be initially supposed from the criterion it is in no way anomalous that the cross section for the ionization of atomic sodium in burnt flame gas mixtures at 2000 K to 3000 K should be as high as 2.5 × 10 −12 cm 2. 3. 3. Ion-molecule reactions. Exothermic ion-molecule reactions play a vital part in the ion-chemistry of the upper atmospheres of the Earth and planets and in interstellar clouds. For these and other reasons they have been the subject of many experimental investigations. Apart from the Langevin formula for the rate coefficient for close collisions, theory has contributed little. Far from enabling rate coefficients to be predicted it does not even provide a means of systemizing the laboratory data. However the transition state method at least enables the range and main features of measured results to be understood in general terms. The absence of activated energy E(act) must be taken into account properly: it does not suffice simply to let E(act) vanish in the standard formula for the rate coefficient. Moreover attention must be paid to the possibility that the transmission coefficient may be very small; to the effect of the peculiar nebular nature of the collision complex; and to Teller crossings of potential energy hyper-surfaces and electronic transitions. 4. 4. Absorption by H - and H + e atmosphere . Calculations on the absorption coefficient due to the combination of photo-detachment from atomic hydrogen negative ions and of free-free transitions of electrons in atomic hydrogen gas have been carried out over the past 40 years and are still continuing. The original object was to find whether an explanation could be provided for the variation with wavelength of the absorption coefficient of the solar atmosphere while the current object is to have accurate quantal results in order to utilized the variation to obtain information on different depths within the atmosphere. There were four, partly overlapping, stages in the photo-detachment work: the increase from 3 to 70 of the number of variational parameters in the Hylleraas type wave function representing the bound state; the change from the length to the velocity formulation of the transition matrix element to weigh more heavily the part of the bound state wave function which should be best determined by the application of the Rayleigh-Ritz principle; the refinement of the free state wave function; the addition of a tail function having the correct asymptotic form to the Hylleraas-type wave function for the bound state. Progress on the calculation of the free-free contribution has proceeded better partly because the problem is less difficult and partly because of the close connection with scattering theory which has rapidly become more sophisticated.