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Gregory Breit and Eugene Wigner explained strong variations in slow-neutron capture through resonant nuclear excitation. In modern notation, an isolated nuclear resonance has a contribution proportional to ${\Gamma }_n{\Gamma }_{\gamma }/[(E-E_r{)}^2+{\Gamma }^2/4]$, apart from spin and kinematic factors. Here ${\Gamma }_n$ and ${\Gamma }_{\gamma }$ describe the entrance and radiative channels, while $\Gamma$ is the total decay width. With slowly varying prefactors, moving $\Gamma /2$ to either side of $E_r$ halves the peak, connecting its observed width with the unstable intermediate state.^[ref]

A nuclear resonance is an enhanced nuclear reaction or scattering response near the energy of an accessible quasi-bound nuclear state. For an isolated resonance, a common energy dependence is ${\sigma }_{ab}(E)\propto {\Gamma }_a{\Gamma }_b/[(E-E_r{)}^2+(\Gamma /2{)}^2]$, where $E_r$ is the resonance energy, $\Gamma$ the total width and ${\Gamma }_a,{\Gamma }_b$ partial widths for entrance and exit channels.

The lifetime scale is $\tau \sim \hslash /\Gamma$: narrower states persist longer. Spin factors, wavelength factors and interference with background amplitudes complete a cross-section model. Resonance spacings and widths provide input to statistical nuclear-reaction calculations.^[ref]