Relative stability and magic numbers of nuclei deduced from behavior of cluster emission half-lives

We calculated the half-life times ($T_c$) of the ${}^{14}\mathrm{C}, {}^{20}\mathrm{O}, {}^{20}\mathrm{Ne}$, and ${}^{24}\mathrm{Ne}$ cluster emissions from heavy and superheavy nuclei. The variation of $T_c$ with the neutron and proton numbers of daughter nuclei is studied to determine the minima in ${log}_{10}{T}_c$ at each neutron number for different daughter isotones. We found that each minimum for a given isotone corresponds to neutron magicity already indicated by other approaches. The proton numbers at neutron magic numbers were found to be also proton magic numbers or differ slightly from them. We arranged the different isotones at each neutron magic number according to their stability in the sense that the more stable daughter isotone corresponds to the lowest value of ${log}_{10}{T}_c$. The magic neutron numbers predicted by the present study are $N=126$, 148, 152, 154, 160, 162, 172, 176, 178, 180, 182, 184, and 200. The predicted magic proton numbers are $Z=82$, 98, 100 102, 106, 108, 114, and 116. The values of $N$ and $Z$ mentioned above agree with magic numbers deduced in other studies.

Figure 1

The decimal logarithm of the half-lives of heavy and superheavy nuclei ($Z_p=85–122$) against ${}^{14}\mathrm{C}$ cluster decay versus the neutron number of the daughter nucleus. Calculations are performed within the density-dependent cluster model based on the M3Y-Reid $NN$ interaction as discussed in the text. The vertical dotted lines correspond to the indicated possible neutron magic numbers.

Figure 2

The same as Fig. 1 but for ${}^{20}\mathrm{O}$ cluster decays.

Figure 3

The same as Fig. 1 but for ${}^{20}\mathrm{Ne}$ cluster decays.

Figure 4

The same as Fig. 1 but for ${}^{26}\mathrm{Ne}$ cluster decays.