The straggling of β-particles

Abstract

When a beam of electric particles is passed through a sheet of matter the energy of the individual particles is reduced. The loss of energy is not the same for all the particles so that particles incident on the foil with the same energy emerge with different energies. This dispersion of the energy caused by the foil is known as the "straggling" of the particles. The straggling of α-particles has been the subject of several experimental investigations, and the theory in this case was adequately developed by Bohr in 1915. In the case of β-particles, however, the straggling was not experimentally investigated until quite recently and no theoretical treatment of the phenomenon has been given, the calculations of Bohr being, as he showed, applicable only to α-particles. The purpose of the work described in this paper is to develop a theory of the straggling of β-particles by thin foils and by means of it to interpret the results of experiment. The paper is arranged as follows. In 2 an account is given of the state of the experimental work on the subject, and in particular the effect of the complications introduced by "scattering" are considered. The formula derived by Bohr for the straggling of electric particles is given in 3 and its inapplicability to β-particles demonstrated. The present calculations of the straggling of β-particles are given in 4. The theory of the straggling of electric particles resolves itself into two parts. The first deals with the dynamics of collisions between electric particles and atoms, and is the same whether we are concerned with the straggling or some other phenomena such as ionisation of "stopping power." This may be called the fundamental theory and its requirements may be summarised in the function ϕ (Q) which express the frequency of collisions in which the electric particle loses energy of amount Q. The second part of the theory is the process of calculating the straggling by means of probability theory from the function ϕ . This may be regarded as the straggling theory proper and it is the main subject of 4. When the present calculations were started it was intended to calculate the straggling on the basis of classical theory only, the value of the function ϕ on this theory being definitely known. However, after some practice with the type of calculation involved it was decided to calculate the straggling for other forms of ϕ . From the results obtained it is possible to deduce the straggling corresponding to any form which ϕ may reasonably have, and if a new theory leads to a value of ϕ different from the classical value, the straggling on the new theory may readily be determined. Alternatively this fuller treatment may be used for the reverse process of calculating from the observed straggling the value of ϕ to which it corresponds. This is considered to be the most convenient procedure and in 5 the form of ϕ which explains the experimental results is deduced. this is compared in 6 with the value of ϕ on classical theory. A brief outline is given in 7 of certain new ideas concerning the nature of collisions of electric particles with electrons and atoms.