Abstract
To describe neutron thermalization in solid media, two simplified models are formulated to describe the motions of atoms bound in solids. One atomic model postulates that the atoms of solids are linear, classical, randomly oriented, harmonic oscillators characterized by a single energy; and the other model postulates the same basic oscillator but permits a distribution of oscillator energies. With atom speed distributions derived from these models, energy exchange cross sections are evaluated analytically assuming a free particle neutron-atom interaction. With these energy exchange cross sections, integral equations are formulated describing thermalization of neutrons in infinite homogeneous media containing a 1/v absorber. The integral equations of both atomic models are solved numerically for the neutron density speed distribution. Numerical results for the single energy atomic oscillator of unit mass are compared with experimental results for neutron thermalization in zirconium hydride. Results for the averaged energy atomic oscillator of unit mass are compared with the neutron density calculated from the Wigner-Wilkins monatomic gas model. This comparison is made for three values of absorption. Numerical results for averaged energy atomic oscillators of masses 1, 2, 9, and 12 are examined to determine the effect of atomic mass upon the neutron density distribution.
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