When a free neutron enters a nucleus it experiences a sudden drop in potential energy, from V (x) = 0 eV outside to V (x) = −12 MeV inside. Suppose a neutron, emitted with kinetic energy E = 4 MeV by a fission event, strikes such a nucleus.

(a) Write down, with justification, a plausible form for the eigenfuctions in each of the regions defined by the potential.

(b) Determine an expression for the reflection coefficient.

(c) Using your result from (b), estimate the probability that the neutron will be absorbed, thus initiating another fission. Hint: This can be modelled as an abrupt potential step.