Pseudo-exponential decay of a neutron pulse in small beryllium systems

Abstract

The decay of a neutron pulse in beryllium is studied by solving, numerically, the homogeneous Boltzmann equation and fitting the amplitudes to an instantaneous slowing down source. The kernel used is the multi-phonon expansion, with a Debye phonon frequency distribution. It is found that for B 2 < 0·033 cm 2, the neutron evolution is soon dominated by a single, exponentially decaying mode; but for B 2 > 0·033 cm −2, it is likely that only a continuous spectrum of eigenvalues exists. However, this continuum exhibits an almost exponential behaviour and is interpreted as possessing an effective decay constant. This effective decay constant is compared with experimental values, for B 2 up to 0·1 cm −2, and is suggested as an explanation of those measured decay constants which exceed [ νΣ] min.