Experiments on molecular scattering in gases. II.—The collision of sodium and potassium atoms with mercury

An important parameter in the quantum theory of molecular scattering as developed by Massey and Mohr is a quantity Q which corresponds roughly to a collision cross-section in classical theory. Of the quantities related to Q, that which is most directly accessible to observation is the decay constant of the intensity of a molecular beam traversing a scattering medium; the reciprocal of this constant corresponds to the mean free path of classical theory. Thus if I is the intensity of a beam which has passed through a distance d of a scattering medium, and I0 is the original intensity, measured at the same distance from the source as is I, then I = I0e-d/λ, (1) where 1/λ is the decay constant; and we define Q by the relation λ = 1/Qv2 √1 + m1/m2 where m1, m2 are the masses of the scattered and scattering molecules respectively, and v2 is the molecular concentration of the scattering medium. The intensity I in equation (1) refers to those molecules which have suffered no deviation whatsoever in traversing the scattering medium. It is justifiable to assign this meaning to I, since quantum theory shows that if the interaction energy vanishes at infinity faster than 1/(distance)2, the ratio I/I0, and hence Q, is finite. Direct observation of the value of I/I0 is, however, impossible, since it presumes an apparatus of infinite resolving power. Nevertheless, by using long narrow slits to define the beam, it is quite feasible to obtain angular apertures of only some 10-4 radians without serious loss of intensity; and it is therefore pertinent to enquire how far the theory allows the deduction of the desired value of I/I0 at zero angle from measurements made with beams of ribbon cross-section possessing small but finite apertures.