New semiempirical formula for exotic cluster decay

A new semiempirical formula, with only three parameters, is proposed for cluster decay half-lives. The parameters of the formula are obtained by making a least squares fit to the available experimental cluster-decay data. The calculated half-lives are compared with the results of the earlier proposed model-independent scaling law and the empirically fitted analytical super-asymmetric fission model (ASAFM), showing more closeness to the ASAFM results.

Figure 1

${\log }_{10}{T}_{1∕2}\left(\mathrm{s}\right)$ for different clusters emitted from various radioactive parents, calculated by using the AZ formula (AZF) and compared with experimental data. Also, the results of calculations for AF $(b=0)$ and ZF $(a=0)$ truncations of AZF are shown for comparisons.

Figure 2

The experimental data on ${\log }_{10}{T}_{1∕2}\left(\mathrm{s}\right)$ for the emission of ${}^{14}\mathrm{C}$ and ${}^{24}\mathrm{Ne}$ clusters from different radioactive parents, compared with the results of calculations using AZ formula (AZF) proposed here, the scaling law [16] and the ASAFM [8].

Figure 3

The calculated ${\log }_{10}{T}_{1∕2}\left(\mathrm{s}\right)$ values for the emission of ${}^8\mathrm{Be}$, ${}^{12}\mathrm{C}$, and ${}^{16}\mathrm{O}$ clusters from different Hg parents using AZ-formula (AZF), compared with the calculations of ASAFM [8] and the scaling law [16].