Two-dimensional nuclear inertia: Analytical relationships.

Abstract

The components of the nuclear inertia tensor, functions of the separation distance {ital R} and of the radius of the light fragment {ital R}{sub 2}, {ital B}{sub {ital RR}}({ital R},{ital R}{sub 2}), {ital B}{sub {ital RR}{sub 2}}({ital R},{ital R}{sub 2}), and {ital B}{sub {ital R}{sub 2}{ital R}{sub 2}}({ital R},{ital R}{sub 2}) are calculated within the Werner-Wheeler approximation, by using the parametrization of two intersected symmetric or asymmetric spheres. Analytical relationships are derived. When projected to a path {ital R}{sub 2}={ital R}{sub 2}({ital R}), the reduced mass is obtained at the touching point. The two one-dimensional parametrizations with {ital R}{sub 2}=const, and the volume {ital V}{sub 2}=const previously studied, are found to be particular cases of the present more general approach. Illustrations for the cold fission, cluster radioactivity, and {alpha} decay of {sup 252}Cf are given.