Cluster decay

Parent Cluster Daughter Cluster decay a-Decay 1 /2 cluster / l/2 d... 

Equation 19.17 may be interpreted in a simple way. If the equilibrium concentration of critical clusters of size Afc were present, and if every critical cluster that grew beyond size Mc continued to grow without decaying back to a smaller size, the nucleation rate would be equal to J = (3CNexp[-AQc/(kT)]. However, the actual concentration of clusters of size Mc is smaller than the equilibrium concentration, and many supercritical clusters decay back to smaller sizes. The actual nucleation rate is therefore smaller and is given by Eq. 19.17, where the first term (Z) corrects for these effects. This dimensionless term is often called the Zeldovich factor and has a magnitude typically near 10-1. 

The existence of cluster substructure in nuclei is supported also by the observation of cluster decay. Besides a particles, the heavy nuclei can emit Ne, Mg, Si clusters, too. The partial half-lives for these decays depend on the penetrability of the Coulomb barrier in a way very similar to a decay (Mikheev and Tretyakova 1990 see Geiger-NuttaU-type relations in O Sect. 2.4.1.1). The heavy cluster decay is a very rare phenomenon. For example, in the decay of Ra there were 65 x 10 a particles observed, while only 14 cluster emissions during the same time (Rose and Jones 1984). For the detection of rare clusters solid state track detectors are very suitable. 

A charged particle heavier than an a particle but hghter than a fission fragment, such as C, O, F, Ne, Mg, and Si isotopes, is spontaneously emitted in a cluster decay of a heavy nucleus. The cluster decay was first predicted by Sandulescu et al. (1980) and experimentally discovered by Rose and Jones (1984) in the decay Ra -I- Pb. Theoretical study of the cluster... 

His research field is nuclear theory reactions, clustering, cluster decay and light exotic nuclei. He is a coauthor of the monograph Structure and Reactions of Light Exotic Nuclei (2003). 

At times t tw the distribution function of undercritical clusters (i < icr) is described by the quasistationary distribution function (11.1.12) (g = g ). For overcrit-ical nuclei (i > Zq > z cr) one can neglect fluctuation processes of clusters decay and formulate the following initial-boundary value problem for g i,t) instead of (11.1.2)... 

In Figure 5.43 the comparison of values of calculated according to Equation 5.77 and experimental values for an epoxy polymer [172] are adduced. Curve 1 was calculated according to the values of and received experimentally (174). As one can see, the shapes of the experimental and theoretical dependences % P) are in agreement, hut the absolute values of received experimentally systematically exceed the calculated ones (hy approximately 3 times). This discrepancy can he removed as follows. It was shown earlier [72, 127] that free volume in crosslinked epoxy polymers consisted of two components -fluctuation free volume fg connected with clusters decay (formation), and the constant component fg ( 0.024) connected with chemical crosslinking nodes (see Figure 5.17). 

Fig. 11. Natural logarithm of the cluster decay coefficient (in units of s ) at energy 500 K as a function of cluster size. The results are for averaged impact parameters. The solid line is a least-squares fit to the computed values. Reproduced with permission of copyright holder.

Fig. 15. Cluster decay rate coefficient as a function of fixed energy for "harmonic noncollisionally formed four-atom clusters. Decay rate as computed from trajectory calculations for harmonic clusters are represented by A and those for anharmonic hot clusters are represented by O. The solid lines are the best fits of the RRK equation to the results.

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