Slowing down of neutrons in beryllium from 1·44 eV to thermal energy

Abstract

The present paper attempts to study the slowing down of neutrons in beryllium in the energy range 1·44 eV to thermal. Taking beryllium temperature to be 300°K, the elastic scattering cross-section as a function of neutron energy and the cross-section for a neutron going, in a single collision, from any given initial energy to any other final energy, are calculated. For neutron energies less than 2 kΘ D , Θ D being the Debye temperature of beryllium and k the Boltzmann constant, the Debye model of a solid is used; whereas for energies greater than about 2 kΘ D the Einstein model is used. The mean logarithmic energy decrement ξ and the mean energy loss per collision have been evaluated in the two energy regions, and the respective curves are smoothly joined. ξ goes to zero at neutron energy 600 k, and the mean energy loss goes to zero around 780k. Assuming that the neutron distribution is very nearly Maxwellian, ξξ is averaged over this distribution. As expected, the averaged logarithmic energy decrement ξ goes to zero at characteristic temperature T 0 = 300°K. Knowing ξ the slowing-down age is determined as a function of the temperature of the neutron distribution. The time variation of the temperature of the neutron distribution has also been calculated. One finds that it exponentially approaches equilibrium at 296°K, with a relaxation time of 19 μsec. Assuming the distribution to be in equilibrium with the moderator when its temperature is 300°K, we find that the age from 1–44 eV to thermal is 20 cm 2, and that the time taken by neutrons to slow down in this energy interval is 100 μsec. The total calculated age from fission energy to thermal is 101 cm 2, and the total slowing-down time is 113 μsec.