Eigenmodes of Decay and Discrete Fragmentation Processes

Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. This representation is based upon a triangular matrix of transition rates. We expand the state vector of mass multiplicities, which describes the process, into the biorthonormal basis of eigenmodes provided by the triangular matrix. When the transition rates have a scaling property in terms of mass ratios at binary fragmentation vertices, we obtain solvable models with explicit mathematical properties for the eigenmodes. A suitable continuous limit provides an interpolation between the solvable models. It gives a general relationship between the decay products and the elementary transition rates.