Alpha Decay of Spheroidal Nuclei

The consequences of spheroidal deformation of nuclei on the barrier transmission in alpha decay are considered. A set of coupled differential equations is derived relating the amplitudes of the various groups of alpha particles emitted from a nucleus described by the Bohr-Mottelson model. The cases of the decay of ${\mathrm{Th}}^{228}$ and ${\mathrm{Cm}}^{242}$ were studied numerically and from them information regarding the probability distribution of alpha particles on the nuclear spheroidal surface is obtained. It is found that the one-body model of an alpha particle in a well does not yield these distributions, and it is thus concluded that "alpha-particle clusters" have a short mean free path in nuclear matter. The shift in the surface distributions of ${\mathrm{Th}}^{228}$ and ${\mathrm{Cm}}^{242}$ may be explained qualitatively in terms of the order of nucleon orbital filling.