Cluster decay

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Cluster decay, also named heavy particle radioactivity, heavy ion radioactivity or heavy cluster decay,^[1] is a rare type of nuclear decay in which an atomic nucleus emits a small "cluster" of neutrons and protons, more than in an alpha particle, but less than a typical binary fission fragment. Ternary fission into three fragments also produces products in the cluster size. The loss of protons from the parent nucleus changes it to the nucleus of 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.^[2] 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.^[3]

The branching ratio with respect to alpha decay is rather small (see the Table below).

${\displaystyle B=T_{a}/T_{c}}$

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 disintegration 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.

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

${\displaystyle E_{k}=QA_{d}/A}$

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 ⁴He 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.