A statistical theory of cascade multiplication

The secondary emission electron multiplier is chosen to illustrate the phenomenon of ‘cascade multiplication’. A method is given for deriving the semi-invariants of the probability distribution for the number of output electrons after any number of identical stages of multiplication, in terms of the corresponding semi-invariants for a single stage. The output distribution is not, in general, either of the Poisson or Gaussian types, though it tends to a limiting shape as the number of stages becomes very large. The special case in which each stage replaces a single primary electron by a Poisson distribution of secondaries is considered. The overall output distribution after many stages is still not Gaussian unless the mean amplification per stage is large compared with unity.

Shower production by penetrating cosmic rays

The transition curve, giving the cosmic-ray shower intensity under increasing thicknesses of lead, rises to a maximum at about 1.6 cm., falls fairly rapidly to 5 cm., and then falls off more slowly, maintaining a finite intensity at very great thicknesses. Further, the occurrence of showers deep underground has long been established (Follett and Crawshaw 1936; Ehmert 1937). The showers forming the initial part of the transition curve (up to about 5 cm. of lead) are adequately accounted for by cascade multiplication from incident electrons or photons (Bhabha and Heitler 1937). Some other mechanism, however, is required to explain the occurrence of showers under much greater thicknesses. It is generally recognized that the showers forming the tail of the transition curve are associated with the penetrating component, and the theory developed by Bhabha (1938) suggests a probable mechanism, whereby a mesotron knocks-on an electron in a direct collision; the electron subsequently producing a shower through the normal cascade process. It has already been shown that the production of secondaries (small showers) by the penetrating component can be accurately explained by this knock-on mechanism (Wilson, J. G. 1938; Trumpy 1938; Hopkins, Nielsen and Nordheim 1939).