Pb208-daughter cluster radioactivity and the deformations and orientations of nuclei

Abstract

The role of deformations and orientations of nuclei is studied for the first time in cluster decays of various radioactive nuclei, particularly those decaying to doubly closed shell, spherical $^{208}\mathrm{Pb}$ daughter nucleus. Also, the significance of using the correct $Q$-value of the decay process is pointed out. The model used is the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta et al., Proc. Int. Conf. on Nuclear Reactions Mechanisms, Varenna, 1988, p. 416; Phys. Rev. C 39, 1992 (1989); 55, 218 (1997); Heavy Elements and Related New Phenomena, edited by W. Greiner and R. K. Gupta, World Sc. 1999, Vol. II, p. 731]. In this model, cluster emission is treated as a tunneling of the confining interaction barrier by a cluster considered already preformed with a relative probability ${P}_{0}$. Since both the scattering potential and potential energy surface due to the fragmentation process in the ground state of the parent nucleus change significantly with the inclusion of deformation and orientation effects, both the penetrability $P$ and preformation probability ${P}_{0}$ of clusters change accordingly. The calculated decay half-lives for all the cluster decays investigated here are generally in good agreement with measured values for the calculation performed with quadrupole deformations ${\ensuremath{\beta}}_{2}$ alone and ``optimum'' orientations of cold elongated configurations. In some cases, particularly for $^{14}\mathrm{C}$ decay of Ra nuclei, the inclusion of multipole deformations up to hexadecapole ${\ensuremath{\beta}}_{4}$ is found to be essential for a comparison with data. However, the available ${\ensuremath{\beta}}_{4}$-values, particularly for nuclei in the mass region $16\ensuremath{\leqslant}A\ensuremath{\leqslant}26$, need be used with caution.