  The partial width for decay of a resonance into three fragments is largely
determined at distances where the energy is smaller than the effective
potential producing the corresponding wave function. At short distances the
many-body properties are accounted for by preformation or spectroscopic
factors. We use the adiabatic expansion method combined with the WKB
approximation to obtain the indispensable cluster model wave functions at
intermediate and larger distances. We test the concept by deriving conditions
for the minimal basis expressed in terms of partial waves and radial nodes. We
compare results for different effective interactions and methods. Agreement is
found with experimental values for a sufficiently large basis. We illustrate
the ideas with realistic examples from $\alpha$-emission of $^{12}$C and
two-proton emission of $^{17}$Ne. Basis requirements for accurate momentum
distributions are briefly discussed.

Nuclear Theory