Cluster Decay - Theory

Theory

The quantum tunneling may be calculated either by extending fission theory to a larger mass asymmetry or by heavier emitted particle from alpha decay theory.

Both fission-like and alpha-like approaches are able to express the decay constant = ln 2 / T_c, as a product of three model-dependent quantities

where is the frequency of assaults on the barrier per second, S is the preformation probability of the cluster at the nuclear surface, and P_s is the penetrability of the external barrier. In alpha-like theories S is an overlap integral of the wave function of the three partners (parent, daughter and emitted cluster). In a fission theory the preformation probability is the penetrability of the internal part of the barrier from the initial turning point R_i to the touching point R_t. Very frequently it is calculated by using the Wentzel-Kramers-Brillouin (WKB) approximation.

A very large number, of the order 105, of parent-emitted cluster combinations were considered in a systematic search for new decay modes. The large amount of computations could be performed in a reasonable time by using the ASAF model developed by Dorin N Poenaru, Walter Greiner et al.. The model was the first to be used to predict measurable quantities in cluster decay. More than 150 cluster decay modes have been predicted before any other kind of half-lives calculations have been reported. Comprehensive tables of half-lives, branching ratios, and kinetic energies have been published, e.g. . Potential barrier shapes similar to that considered within the ASAF model have been calculated by using the macroscopic-microscopic method.

Previously it was shown that even alpha decay may be considered a particular case of cold fission. The ASAF model may be used to describe in a unified manner cold alpha decay, cluster decay and cold fission (see figure 6.7, p. 287 of the Ref. ).

One can obtain with good approximation one universal curve (UNIV) for any kind of cluster decay mode with a mass number Ae, including alpha decay

In a logarithmic scale the equation log T = f(log P_s) represents a single straight line which can be conveniently used to estimate the half-life. A single universal curve for alpha decay and cluster decay modes results by expressing log T + log S = f(log P_s). The experimental data on cluster decay in three groups of even-even, even-odd, and odd-even parent nuclei are reproduced with comparable accuracy by both types of universal curves, fission-like UNIV and UDL derived using alpha-like R-matrix theory.

In order to find the released energy

one can use the compilation of measured masses M, M_d, and M_e of the parent, daughter and emitted nuclei, c is the light velocity. The mass excess is transformed into energy according to the Einstein's formula E = mc2.