Nuclear Reactions (Q-value)

A nuclear reaction is when a projectile (n, α, γ, etc.) hits a target nucleus, producing a new nucleus + ejecta.

Standard notation: target(projectile, ejected)product. Example: ¹⁴N(α, p)¹⁷O = α-particle + N-14 → O-17 + proton.

Conservation laws: charge (Z), mass number (A), energy, momentum, and angular momentum are ALL conserved.

Q-value: Q = (initial rest mass − final rest mass)·c² = total kinetic energy released.

Endothermic (Q < 0): require minimum (threshold) KE of projectile. Exothermic (Q > 0): release energy.

Reaction cross-section σ measures probability — typical units: barn = 10⁻²⁸ m². Depends strongly on energy.

Compound nucleus model (Bohr): projectile is absorbed first, then a 'hot' compound nucleus decays.

Direct reactions: fast, single-step (e.g., pickup or stripping). Compound-nucleus: slower, statistical.