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Nuclear evaporation is statistical particle emission from an excited compound nucleus after energy has been redistributed among many nuclear degrees of freedom. It is the nuclear analogue of preferentially losing particles energetic enough to escape a bound system, rather than a direct knockout by the initial projectile.

For a particle separation energy $S$ and relative kinetic energy $ϵ$, the daughter excitation is $E_f^{\ast }=E_i^{\ast }-S-ϵ$. The emission probability depends on the available daughter nuclear level density and the inverse reaction probability. Neutron emission avoids a charged-particle Coulomb barrier, while proton or heavier-particle emission competes under different thresholds and barriers. The emitted spectrum is therefore not determined by temperature alone.

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.