Measures on phase space as solutions of the one-dimensional neutron transport equation

Summary The linear integral transport operator for slab geometry is formulated and studied as a mapping on the set of measures on the phase space of the underlying system, with the expected number of neutrons emergent from a collision represented by a measure on the space of outgoing velocities. Under appropriate assumptions it is shown that, if c represents the maximum number of secondary particles per collision, then there exists c ₁ ≥1 such that the system is subcritical for c≤c ₁ . An example shows that c ₁ ≥1 is sharp in general, but further assumptions are given under which one can deduce c ₁ >1. The idealized laws of elastic and inelastic scattering are shown to satisfy our assumptions. Entrata in Redazione il 27 ottobre 1975.