Abstract
The behavior of the neutron energy spectrum in a bare homogeneous moderator after the introduction of a burst of neutrons has been studied theoretically. The problem is reduced to an eigenvalue problem for a self-adjoint integral operator governing the neutron thermalization.In an infinite system, it has been shown that the Maxwellian component of the spectrum does not couple with higher modes which are orthogonal to the former and contribute nothing to the actual neutron density when integrated. The asymptotic neutron spectrum and the diffusion cooling are formulated most conveniently in the present scheme.The formalism is a general one and may be applied to any scattering model with due labor of computations. Numerical calculations has been done for heavy gaseous moderators.
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