Abstract
We report here the results of some calculations on the existence of a fundamental discrete mode of the neutron transport operator in a spherical medium. This mode represents the asymptotic exponential decay of a thermal neutron distribution following a neutron burst. It is known that such a discrete mode does not exist for a sufficiently small medium and that the fundamental mode decay constant cannot be less than −lim [ νE( ν)] where ν is the neutron velocity and Σ is the corresponding ν → 0 total cross section. In this paper we show that if the energy domain is bounded away from zero, the discrete eigenvalue exists for any radius of a sphere; and for λ < −( νΣ) min the eigenvalue can be made to lie arbitrarily close to −( νΣ) min by choosing an appropriately small cut-off energy. It is the latter fact which is important and brings out explicitly the importance of ( νΣ) min in the approach to equilibrium even in bounded media. Although the present calculations are based on a simple thermalization model with a separable scattering kernel; the main conclusions are expected to be valid for any realistic model in any bounded geometry.
Published Version
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