Question

. Suppose that neutrons are born with a kinetic energy 1 MeV from nuclear fission. Find the probability that a neutron will downscatter to a kinetic energy of 0.025 eV (after several collisions) with the following isotopes, having respective capture probabilities

p(gamma) per collision:

(a) A=1, Hydrogen with p(gamma)= 1×10−3,

(b) A=2, Hydrogen with p(gamma)= 2×10−5,

(c) A=12, Carbon with p(gamma)= 5×10−5,

(d)A=23, Na with p(gamma)= 8×10−3.

Use the results to discuss which of these isotopes are most effective at slowing down neutrons for use in nuclear fission reactors.

Answer 1

Due to the very high speed of neutron after fission, their speed must be slowed down. This done by virtue of elastic scattering with nuclei. When a neutron collides elastically with another nucleus at rest in the medium, it transfers some of its energy to it. So maximum energy is transferred when the mass of the nuclei is comparable to the neutron. Thus low mass isotopes have the number of collisions decreases a large amount of energy is less time. This slowdown should be fast to avoid captures by other nuclei as neutron are unstable freely and bound into the atomic nucleus. Thus, the projectile having large scattering cross section tend to effectively moderate the neutron speed.