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An intermediate excited atomic nucleus formed when the reactants' available energy is redistributed among nuclear degrees of freedom before decay. Its resolved levels can appear as resonances. An isolated level's formation and decay into particular channels are described by partial decay widths in the Breit-Wigner resonance cross section; direct reactions and overlapping resonances need not obey that simple one-level description.

The contribution of a specified decay channel to the total decay width. In an exponential-decay description, its probability rate is ${\lambda }_i={\Gamma }_i/\hslash$, the total width is $\Gamma ={\sum }_i{\Gamma }_i=\hslash /\tau$, and its branching fraction is ${\Gamma }_i/\Gamma$. Channels must be specified consistently, including any inclusive treatment of unresolved radiation. A partial decay width has energy units rather than inverse-time units.

The partial decay width ${\Gamma }_x$ is the energy width associated with decay of the compound nucleus back into the entrance channel $x+X$; by time reversal it also controls formation from that channel. The partial decay width ${\Gamma }_y$ describes the selected exit channel $y+Y$. The total decay width sums all energetically accessible channels, including these: $\boxed{\Gamma =\sum _i{\Gamma }_i=\hslash /\tau }$. The branching fraction for channel $i$ is ${\Gamma }_i/\Gamma$. Widths have energy units, whereas ${\Gamma }_i/\hslash$ is a decay probability per unit time. The isolated-resonance formula assumes approximately constant widths over the resonance and neglects a nonresonant interfering background.

Compare two entrance channels feeding the same isolated resonance and the same selected exit channel, each at its own resonance energy. The exit partial decay width and the resonant denominator cancel. Different entrance momenta, spin weights and entrance widths remain. The formula assumes the same resonance, the stated unpolarized spin average and negligible nonresonant interference; a ratio at one shared laboratory energy would generally be different.