Mechanism and Rate of Long-Range α -Particle Emission in Fission

The statistical theory of fission has been used in previous works to calculate the energy and angular distributions of the long-range $\ensuremath{\alpha}$ particle emitted in fission. It is now applied to calculate the probability of long-range $\ensuremath{\alpha}$-particle-accompanied fission relative to binary fission. For thermal-neutron fission of ${\mathrm{U}}^{235}$ the calculated rate is 1 $\ensuremath{\alpha}$-particle-accompanied fission in 461 binary fissions, which agrees well with the experimental value of 1 in 449. Concerning the mechanism, the large amount of energy required (more than 24 MeV) to emit an $\ensuremath{\alpha}$ particle at the scission point comes mainly from the reduction of the Coulomb energy between the main fragments through an over-stretched form of deformation. The balance of energy shows that the total excitation energy in $\ensuremath{\alpha}$-particle-accompanied fission is reduced by about 4.5 MeV compared with binary fission. According to the statistical theory this reduces the relative probability by several hundred fold.