State Dependent Δ-pairing and Spontaneous Fission

We examine the fission barriers, mass parameters and spontaneous fission half lives of fermium isotopes within the framework of macroscopic-microscopic model with a δ-pairing interaction. Four different macroscopic models are applied and studied. The results are compared to experimental data and to the corresponding monopole pairing ones. The half lives obtained in the δ-pairing model are comparable with experimental data. The state-dependence of pairing has an important effect on the calculated fission half-lives. The calculations of fission half lives T sf in macroscopic-microscopic methods consist of determining the fission barrier (collective potential energy) and the mass tensor of the nucleus undergoing the fission process. The potential energy V splits into a shell δE shell and a pairing correction δE pair (microscopic part) and the smooth average (macroscopic) energy such as liquid drop 1 , droplet 2 , LSD 3 or Yukawa plus Exponential. 4 The microscopic part of the energy is calculated using the single-particle Woods-Saxon potential with the universal set of parameters. 5 All the former calculations of T sf were done assuming that the pairing matrix elements G ab ≡ ν ¯ ν|ˆV pair |µ¯ µ are constant. Such an approximation leads to the averaging of the superconductive properties of nuclei and weakly reflects the structure of nucleon pairs. In the following we have used the state dependent pairing model where the pairing matrix elements G ab are state dependent and the interactionˆV pair is of the form: 6