A Model for Nuclear Fission — Question 6

Question 6

Neutron capture supplies excitation through separation energy

A heavy target absorbs a neutron. Neglect target recoil, so compound-nucleus excitation is $E^*=S_n+K_n$. Two hypothetical nuclei have $(S_n,B_f)=(6.4,6.0)$ MeV and $(4.8,6.0)$ MeV. Here $B_f$ is the fission barrier above the compound ground state.

1. For negligible neutron kinetic energy, decide which compound excitation lies above its barrier.

2. Find the minimum neutron kinetic energy needed to reach the barrier in each idealized case.

Question 6 - Solution

Neutron capture supplies excitation through separation energy

(a) Method and calculation

$$K_n\simeq0:\quad\boxed{E_A^*-B_A=+.4\,\mathrm{MeV},\quad E_B^*-B_B=-1.2\,\mathrm{MeV}}.$$$$\boxed{A:\text{ above barrier};\qquad B:\text{ below barrier}}.$$

(b) Interpretation and further calculation

$$S_n+K_n\ge B_f\Rightarrow\boxed{K_{n,\min}=\max(0,B_f-S_n)}.$$$$\boxed{K_{n,\min,A}=0,\quad K_{n,\min,B}=1.2\,\mathrm{MeV}}.$$

Physical check

Above-barrier excitation does not guarantee fission: neutron emission and photon emission may compete. Quantum tunneling can permit below-barrier decay.