• Tags: beta, neutrino, continuous-spectrum
• Difficulty: Moderate

Beta-minus decay: a neutron converts to a proton inside the nucleus, emitting an electron and an antineutrino: n -> p + $e^-$ + $antineutrino_e$. The nucleus changes: _$Z^A$ X -> _{Z+1}^A Y + $e^-$ + antineutrino. A unchanged, Z increases by 1. The beta particle energy spectrum is continuous (from 0 to Q-value) because the energy is shared between the electron and antineutrino. The neutrino was postulated by Pauli (1930) precisely to explain this continuous spectrum and conserve energy, momentum, and angular momentum. Beta-plus decay: p -> n + $e^+$ + $neutrino_e$. Z decreases by 1. Requires the parent to be at least 2$m_e$*$c^2$ = 1.022 MeV heavier than the daughter (in atomic mass units). Electron capture: the nucleus captures an inner orbital electron: p + $e^-$ -> n + neutrino. Z decreases by 1. Only a monoenergetic neutrino is emitted (no continuous spectrum). Electron capture competes with beta-plus decay but has no energy threshold.