The Boltzmann equation can be written in an integral form. This can be done by mathematical manipulations on equation (3.18). Here we give a physical derivation of the integral form based on physical arguments, in the simplify­ing case where the macroscopic cross-sections are time independent, the scattering cross-section is isotropic, the medium homogeneous and the system is stationary in time. Then the flux at position r is due to neutrons created elsewhere, be they scattered neutrons or fission neutrons with the right velocity. The probability that a neutron with velocity v at position r’ reaches position r is

e ^T (v)lr — r’l
r — r’|2

The number of neutrons scattered and created at position r 0 is

‘(r, v)(^(?, v! v) + mpf(v)Xf(r’, v’)) dv’.

Thus, the flux at position r reads:

xCSs(r’, v! v) +mpf(v)Xf(r’, v )) dv’ . (3.19)