Influence of Pairing Correlations on the Probability and Dynamics of Tunnelling Through the Barrier in Fission and Fusion of Complex Nuclei

Abstract

An analytically solvable model is used to study the barrier penetrability pattern for subbarrier fission and fusion of nuclei in the case when the pairing gap parameter Δ is treated as an additional dynamical variable whose behaviour in tunnelling is governed by the least action principle. It is found that, as compared to the standard (BCS) approach, the dynamical treatment of pairing correlations essentially modifies (considerably weakens) the dependence of the fission barrier penetrability on the intensity of pairing correlations in the initial state (Δ0), on the barrier height, and on the energy of the initial state. On this basis, a more adequate explanation is proposed for typical order-of-magnitude values of the empirical hindrance factors associated with ground-state spontaneous fission of odd nuclei. It is also shown that a large enhancement of superfluidity in tunnelling - the inherent effect of the dynamical treatment of pairing correlations - strongly facilitates deeply subbarrier fusion of complex nuclei and results in increasing fusion cross sections by several orders of magnitude. Finally, an analysis is given for the probability of spontaneous fission decay from K-isomeric quasi-particle (q-p) states in even-even heavy nuclei. It is found that the relative change of the partial spontaneous fission half-life in going from the ground-state to a high-spin q-p isomeric state, Tsf*/Tsf, is strongly dependent on whether or not there takes place the dynamically induced enhancement of superfluidity in the tunnelling process. Measurements of Tsf*/Tsf provide thus a unique possibility of verifying theoretical predictions about the strong, inversesquare Δ dependence of the effective inertia associated with large-scale cold rearrangements of nuclei in fission and fusion.