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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 nuclear level density $\rho (E)$ is the number of distinct nuclear energy levels per unit excitation energy, after specifying which spin and parity classes are included. In a small interval, the expected level count is approximately $\rho (E)\Delta E$. It is commonly expressed per MeV.

At high excitation, individual levels can be too numerous to resolve, so reaction models use a statistical density instead. A density counting each level once differs from a state density that includes every magnetic substate with multiplicity $2J+1$. Known low-lying levels and average neutron-resonance spacings provide experimental normalization constraints.^[ref]

Victor Weisskopf developed a statistical treatment of particle emission from highly excited heavy atomic nuclei. His 1937 paper compares the process with evaporation: the excitation energy is shared among many internal quantum states, and the available final states constrain which particles can escape with which energies. This connects nuclear level density with emission probabilities and approximately thermal-looking outgoing spectra. Nuclear evaporation supplies a way to predict the aggregate outcome of a complicated nuclear reaction without following every individual internal trajectory.^[ref]