Radioactive decay of radium and radon isotopes byC14emission

Estimates are given for half-lives of the radioactive decay of radium and radon isotopes by emission of ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ nuclei. The classical one-dimensional WKB approximation for penetration through a pure Coulomb barrier is used in the calculations. Results indicate that naturally occurring radon isotopes are ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ emitters like their parent radium isotopes, whose decay rates by emission of ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ nuclei have recently been measured. The predicted half-lives for decay of ${}_{}{}^{219}{}_{}{}^{}\mathrm{Rn}$, ${}_{}{}^{220}{}_{}{}^{}\mathrm{Rn}$, and ${}_{}{}^{222}{}_{}{}^{}\mathrm{Rn}$ by emission of ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ nuclei are in the range ${10}^{11}$–${10}^{14}$ yr. For radium and radon isotopes the minimum half-life is obtained when the double-magic ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ and the semimagic ${}_{}{}^{206}{}_{}{}^{}\mathrm{Hg}$, respectively, are the daughter products of these new radioactive decay modes.