A new formalism for (n, 2n) AND (n, 3n) cross-sections of heavy mass nuclei

Simple analyses of (n, 2n) and (n, 3n) cross-sections are based on compound nucleus decay without branching. The result is an effective level-density parameter which is much smaller than the actual level-density parameter. Simple approximations of the energy distributions of the first and second neutrons in a multiple inelastic process (n, M) yield simple, closed-form formulae for the reduced (n, 2n) and (n, 3n) cross-sections, namely ( σ_n,2n σ_n,M) (E) and ( σ_n,3n σ_n,M) (E). Aiming at the needs of the neutron data evaluator, σ_n,M(E) is determined by normalization of the reduced (n, 2n) cross-section at a single experimental point. This is a more accurate alternative to using systemized ( σ_n,M σ_ne) (N, Z) and σ_ne(N, Z), although the application of the formalism to heavy-mass elements presupposes a knowledge of σ_n,f(E). The (n, 2n) and (n, 3n) cross-sections of nine nuclides with A > 150 are accurately reproduced by the formalism. This accuracy, in face of evidence of some non-compound processes, may be attributed to the ability of effective level-density parameters to account for the spectrum hardening effect of the non-compound processes.