Memory effects on descent from the nuclear fission barrier

Abstract

Non-Markovian transport equations for nuclear large amplitude motion are derived from the collisional kinetic equation. The memory effects are caused by Fermi surface distortions and depend on the relaxation time. It is shown that nuclear collective motion and nuclear fission are influenced strongly by memory effects at the relaxation time у5ϫ10 Ϫ23 s. In particular, the descent of the nucleus from the fission barrier is accompanied by characteristic shape oscillations. The eigenfrequency and the damping of the shape oscillations depend on the contribution of the memory integral in the equations of motion. The shape oscillations disappear at the short relaxation time regime at →0, which corresponds to the usual Markovian motion in the presence of friction forces. We show that the elastic forces produced by the memory integral lead to a significant delay for the descent of the nucleus from the barrier. Numerical calculations for the nucleus 236 U show that due to the memory effect the saddle-to-scission time grows by a factor of about 3 with respect to the corresponding saddle-to-scission time obtained in liquid drop model calculations with friction forces.

A new formula for the saddle-to-scission time

“…But when the friction parameter is derived from a microscopic model [28][29][30], it depends on the relaxation time chosen for the memory kernel. In [29,30] β is proportionnal to this relaxation time.…”

“…When the Langevin equation is derived from a microscopic model, one obtains a memory kernel which is due to the coupling of the collective variable to the deformation of the Fermi surface [28][29][30].…”

Solution of the master equation for Wigner’s quasiprobability distribution in phase space for the Brownian motion of a particle in a double well potential

“…͑1͒ is almost invariably used to model noise driven motion in bistable physical and chemical systems. Examples are diverse subjects such as simple isometrization processes, 27-31 chemical reaction rate theory, [32][33][34][35][36][37][38][39][40] bistable nonlinear oscillators, [41][42][43] second order phase transitions, 44 nuclear fission and fusion, 45,46 stochastic resonance, 47,48 etc. The dissipative barrier crossing process we have mentioned is characterized by the ͑Kramers͒ escape rate ⌫ which may be calculated in closed form using ingenious asymptotic methods devised by Kramers 6 to approximately solve the Fokker-Planck equation governing the Brownian motion in the potential in the limits of very high and low dissipations to the heat bath.…”

Cavitation and bubble collapse in hot asymmetric nuclear matter

“…More complicated bubble dynamics occurs in the case of a Fermi liquid where the dynamic distortion of the Fermi surface produces an additional pressure tensor [13,14]. Moreover, the Fermi surface distortion and the interparticle collisions lead here to the non-Markovian equations of motion for the relevant collective variables [15]. Below the non-Markovian dynamics will be applied to the problem of the collapse of bubbles.…”

“…The (2) is caused by the Fermi surface distortion. In the case of the most important quadrupole distortion of the Fermi surface, the pressure tensor P ′ νµ satisfies the following equation [15] …”