A recent experiment on the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ fine structure has shown that the branching ratio to ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ ground state is quite different from the one predicted by the various models of cluster emission. Assuming that the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ is preformed in the ${}_{}{}^{223}{}_{}{}^{}\mathrm{Ra}$ nucleus, we have calculated the hindrance factor ${\mathit{F}}^{14}$C of the three ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ branches to ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ states with a barrier penetrability approximated by a square-well Coulomb potential. The ${\mathit{F}}^{14}$C=3.9 and 4.6 values found for the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ transitions to the two excited states at 779 keV (${\mathit{I}}^{\mathrm{\pi }}$=11/$2^{+}$) and 1423 keV (${\mathit{I}}^{\mathrm{\pi }}$=15/$2^{\mathrm{-}}$), respectively, reveal that the cluster formation amplitudes in both transitions are close to those of the ${}_{}{}^{222}{}_{}{}^{}\mathrm{Ra}$ and ${}_{}{}^{224}{}_{}{}^{}\mathrm{Ra}$ ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ decays. Such values could be the result of ‖nlj〉 shell-model components common to both the wave functions of the octupole deformed ${}_{}{}^{223}{}_{}{}^{}\mathrm{Ra}$ nucleus and of the two first excited states of ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ spherical nucleus. The high hindrance factor ${\mathit{F}}^{14}$C=583 of the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ branch to the ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ ground state (${\mathit{I}}^{\mathrm{\pi }}$=9/$2^{+}$) could reveal the absence of ‖1${\mathit{g}}_{9/2}$〉 shell-model component in the ${}_{}{}^{223}{}_{}{}^{}\mathrm{Ra}$ wave function.

• Received 12 February 1990

DOI:https://doi.org/10.1103/PhysRevC.42.R495