The new mass relation based on the generalised Hugenholtz-Van Hove theorem has been used to obtain a relation for the fission barriers of three nuclei. This relation has been found satisfactory to describe the data. Further a general expression has been given describing satisfactorily the inner barrier height, the second minimum and the second barrier height for all actinides with an rms deviation of 0.32, 0.32 and 0.33 MeV respectively. The estimated shell energies agree reasonably well with those of Brack et al. In addition the barriers for thorium isotopes have been described well.
PACS: 25.85-WRecently one of us and Nayak have proposed a new mass relation [1] for finite nuclei based on a generalization of the Hugenholtz-Van Hove (HVH) theorem [2] in many-body theory. This mass relation takes into account non-perturbatively the two main features of nuclear dynamics, namely the single particle (microscopic) feature and the liquid drop (macroscopic) feature. It has been shown [-1] to be quite successful in describing the masses of nuclei along the valley of stability and also predicting the masses of exotic neutron-rich nuclei far from the valley. In this note we have attempted to apply this relation to the study of strong deformation phenomenon like fission. We recollect below the main steps of the derivation of the mass relation proposed in Ref. 1 to facilitate the discussion.First the usual HVH theorem was extended to asymmetric nuclear matter. Then for the ground state of such a system with N neutrons, Z proton and N-Z asymmetry parameter fl =N + Z' the extended HVH theorem reduces towhere E is the total energy, A =N +Z, e. and ep are the neutron and proton Fermi energies. Equation (i) has been used to arrive at a corresponding equation valid for finite nuclei by taking into account the finite size effects like surface. Coulomb and pairing through the ansatz E~c,,(N, Z)
E(N, Z)= E~(N, Z)--