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 Th²²⁸ and Cm²⁴² 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 Th²²⁸ and Cm²⁴² may be explained qualitatively in terms of the order of nucleon orbital filling.The over-all penetration factors for the spheroidal case are compared with those for the spherical case, and it is found that the resultant enhancement due to the deformation is not early as large as that predicted by Hill and Wheeler on the basis of a one-dimensional approximation.