Cluster Decay

Cluster decay (also named heavy particle radioactivity or heavy ion radioactivity) is a type of nuclear decay in which a parent atomic nucleus with A nucleons and Z protons emits a cluster of N_e neutrons and Z_e protons heavier than an alpha particle but lighter than a typical binary fission fragment (although ternary fission into three fragments produces products which overlap cluster decay). A chemical transformation of the parent nucleus leads to a different element, the daughter, with a mass number A_d = A - A_e and atomic number Z_d = Z - Z_e where A_e = N_e + Z_e. For example:

223
88Ra → 14
6C + 209
82Pb

This type of rare decay mode was observed in radioisotopes that decay predominantly by alpha emission, and it occurs only in a small percentage of the decays for all such isotopes.

The branching ratio with respect to alpha decay

is rather small (see the Table below). T_a and T_c are the half-lives of the parent nucleus relative to alpha decay and cluster radioactivity, respectively.

Cluster decay, like alpha decay, is a quantum tunneling process: in order to be emitted, the cluster must penetrate a potential barrier. This is a different process than the more random nuclear disintigration that precedes light fragment emission in ternary fission, which may be a result of a nuclear reaction, but can also be a type of spontaneous radioactive decay in certain nuclides, demonstrating that input energy is not necessarily needed for fission, which remains a fundamentally different process mechanistically.

Theoretically any nucleus with Z > 40 for which the released energy (Q value) is a positive quantity, can be a cluster-emitter. In practice, observations are severely restricted to limitations imposed by currently available experimental techniques which require a sufficiently short half-life, T_c < 1032 s, and a sufficiently large branching ratio B > 10 −17.

In the absence of any energy loss for fragment deformation and excitation, as in cold fission phenomena or in alpha decay, the total kinetic energy is equal to the Q-value and is divided between the particles in inverse proportion with their masses, as required by conservation of linear momentum

where A_d is the mass number of the daughter, A_d = A – A_e.

Cluster decay exists in an intermediate position between alpha decay (in which a nucleus spits out a He4 nucleus), and spontaneous fission, in which a heavy nucleus splits into two (or more) large fragments and an assorted number of neutrons. Spontaneous fission ends up with a probabilistic distribution of daughter products, which sets it apart from cluster decay. In cluster decay for a given radioisotope, the emitted particle is a light nucleus and the decay method always emits this same particle. For heavier emitted clusters there is otherwise practically no qualitative difference between cluster decay and spontaneous cold fission.