Time-dependent Schrödinger approach to sub-barrier fission

N. Cârjan, O. Sérot, Daniel D Strottman

Vazgen Valerikovich Sargsyan, Yu. V. Palchikov, Z. Kanokov +2 more

The induced nuclear fission is considered a transport process over the fission barrier underlying dissipative forces. Using a quantum master equation for the reduced density matrix, the influence of microscopical diffusion coefficients on the total fission time and transient time is studied. The influence of transient effects on the probability of the first-chance fission is estimated. For different temperatures and friction coefficients, the quasistationary fission rate is compared with the analytical Kramers formula.

N. Takigawa

Shimon Levit, John W. Negele, Zvi Paltiel

A mean-field theory is obtained for the spontaneous decay of unstable nuclei by applying the stationary-phase approximation to a functional integral expression for $\mathrm{Tr}{(H\ensuremath{-}E)}^{\ensuremath{-}1}$. The method is applied first to the lifetime of a metastable state in one-dimensional quantum mechanics and subsequently generalized to many-fermion systems. Solutions to the resulting nonlinear self-consistent field equations are presented for a self-bound, saturating many-body system of fermions in one spatial dimension.NUCLEAR REACTIONS, FISSION Derivation of dynamical mean-field equations for spontaneous fission, using imaginary time stationary-phase approximation to a functional integral expression for $\mathrm{Tr}{(H\ensuremath{-}E)}^{\ensuremath{-}1}$. Application to a many-fermion model in one spatial dimension.

Herbert Massmann, Peter A. Ring, John O Rasmussen

Guillaume Scamps, K. Hagino

We study the dynamics of multidimensional quantum tunneling by introducing a complex absorbing potential into a two-dimensional model for spontaneous fission. We first diagonalize the Hamiltonian with the complex potential to determine a resonance state as well as its lifetime. We then solve the time-dependent Schr\"odinger equation with such basis in order to investigate the tunneling path. We compare this method with the semiclassical method for multidimensional tunneling with imaginary time. A good agreement is found both for the lifetime and for the tunneling path.