Energy Transfer and Resonance in Neutron-Nucleus Interactions
Neutron-Nucleus Interactions and Compound Nucleus Formation
When neutrons interact with a nucleus (which could be an element like carbon in construction materials, or fuel), several reactions can occur:
Capture (Absorption): The neutron is absorbed by the nucleus.
Inelastic Scattering: The neutron's kinetic energy is converted to excitation energy of the nucleus.
Elastic Scattering: The neutron's kinetic energy is conserved.
Upon neutron absorption, a compound nucleus is formed, which becomes excited.
This excitation energy must be released for the nucleus to return to a stable state.
If the nucleus is a fissionable material (e.g., fuel), nuclear fission can occur as a primary mode of energy release.
If the nucleus is a non-fissionable material (e.g., shielding), other forms of energy release, such as gamma emission, will take place.
Sources of Excitation Energy in a Compound Nucleus
The excitation energy of the compound nucleus originates from two main components:
Kinetic Energy of the Incoming Neutron (E_{\text{CM}}):
Incoming neutrons are not stationary; they possess initial kinetic energy, whether they are slow (thermal) or fast (fission) neutrons.
Fission spectrum neutrons, for example, are fast and possess energies in the mega-electron volt (\text{MeV}) range.
This kinetic energy contributes to the excitation energy of the compound nucleus.
Center of Mass (CM) Energy (E_{\text{CM}}): In a two-body collision between an incoming neutron and a target nucleus, the kinetic energy is distributed, with a portion contributing to the compound nucleus's excitation. This is often described through the conservation of momentum and energy.
Conservation of Momentum: If mn is the mass of the neutron, vn its initial velocity, mN the mass of the target nucleus (initially at rest, vN=0), and V{CN} the velocity of the combined compound nucleus, then: mn vn = (mn + mN) V{CN}.
The excitation energy is related to the difference in kinetic energies before and after the formation of the compound nucleus.
Binding Energy (E_B) of the Neutron in the Compound Nucleus:
When a neutron is captured by a nucleus, a certain amount of binding energy is released and contributes significantly to the excitation energy.
Even very slow neutrons, such as thermal neutrons with energies of approximately 0.02 \text{ eV}, can contribute to excitation energy.
The binding energy of a neutron in a nucleus is typically much larger than the kinetic energy contribution from slow neutrons, often ranging from 1 \text{ MeV} to 2 \text{ MeV} (1,000,000 \text{ eV} to 2,000,000 \text{ eV}). This makes EB \gg E{\text{CM}} for slow neutrons.
However, if the incoming neutron is highly energetic (e.g., 5 \text{ MeV}), its kinetic energy can become a more dominant factor.
Resonance Cross Sections
Nuclear Energy Levels: Atoms and isotopes possess discrete (quantized) energy levels, not continuous ones, governing their quantum states.
Resonance Phenomenon: When the kinetic energy of an incoming neutron precisely matches one of these discrete quantum energy levels of the target nucleus, the interaction cross section (for both scattering and absorption) exhibits a dramatic increase, known as a resonance.
Effects on Cross Sections: Resonances cause characteristic sharp peaks in the nuclear cross section as a function of neutron energy. These peaks represent energy regions where the probability of neutron interaction (capture or scattering) with the nucleus is significantly enhanced. The shape of these resonances is often described by the Breit-Wigner formula, which models the narrow energy range over which the interaction probability is maximized. The presence and characteristics of these resonances are critical in reactor physics, influencing neutron moderation, fuel utilization, and reactor control, as different isotopes exhibit resonances at different neutron energies.