Microscopic description of the coldαand10Beternary fission yields of252Cfin spheroidal coordinates

Abstract

The dynamics of light charged particle emission in the cold fission of ${}^{252}\mathrm{Cf}$ is studied in terms of spheroidal coordinates. This system of coordinates provides a more adequate description for a hyperdeformed fissioning nucleus than the standard spherical variables. We derive the system of coupled differential equations describing the motion of the emitted light cluster and we give a generalization of the Fr\"oman matrix. The phase-shift analysis predicts long half-lives with respect to the characteristic particle nuclear time, but shorter than the cold fission transient time for those fissioning configurations that are emitting $\ensuremath{\alpha}$ particles and ${}^{10}\mathrm{Be}.$ Consequently, such configurations could be interpreted as ternary nuclear molecules.