Estimation of fusion time in heavy-ion collisions

The time for fusion process is estimated by evaluating the time spent by the classical Coulomb trajectory and Coulomb-nuclear trajectory within the fusion formation region r<R/sub F/. The parameter R/sub F/ is taken from the recent works of Udagawa et al. Our estimate of fusion time extends the results of Scalia to a larger number of pairs of nuclei and energies. We find that the fusion time above the barrier obtained by using classical Coulomb-nuclear trajectories which is of the order of 10/sup -22/ to 10/sup -21/ s is about five times larger than the times obtained using Coulomb trajectories. We also see that fusion times for different partial waves are of the same order and do not vary much with angular momentum. We further adopt the quantum-mechanical phase-shift method used by Munzinger and Berkowitz to estimate the fusion time both below and above the barrier. In agreement with their general conclusion, we find that fusion time is oscillatory above the barrier and decreases rapidly with decrease in energy below the barrier up to certain energy. However, at still lower energy it starts increasing rapidly. The order of magnitude of oscillatory time above the barrier falls in between the times obtained using classical Coulomb trajectories and Coulomb-nuclear trajectories. But the trend in the sub-barrier region is physically not well understood. We take an alternative approach to estimate the fusion formation time below the barrier by assuming fusion to be a reverse decay process caused by the incident flux of projectiles on the target. This calculation of fusion time is done within the framework of the WKB method. We find that fusion formation time just below the barrier is of the order of 10/sup -23/ s and starts increasing very rapidly with decrease in energy