Abstract
It has been known that the time-dependent Hartree-Fock (TDHF) method, or the time-dependent density functional theory (TDDFT), fails to describe many-body quantum tunneling. We overcome this problem by superposing a few time-dependent Slater determinants with the time-dependent generator coordinate method (TDGCM). We apply this method to scattering of two α particles in one dimension, and demonstrate that the TDGCM method yields a finite tunneling probability even at energies below the Coulomb barrier, at which the tunneling probability is exactly zero in the TDHF. This is the first case in which a many-particle tunneling is simulated with a microscopic real-time approach.
Highlights
One of the primary goals of nuclear reaction theory is to develop a microscopic framework for nuclear reactions, starting from the nucleonic degrees of freedom
We have applied the time-dependent generator coordinate method (TDGCM) to the 4 He+4 He scattering in one dimension at energies below the Coulomb barrier
By superposing Slater determinants, a many-body tunneling can be simulated with this method, whereas the time-dependent HartreeFock (TDHF) method yields the tunneling probability of either 0 or
Summary
One of the primary goals of nuclear reaction theory is to develop a microscopic framework for nuclear reactions, starting from the nucleonic degrees of freedom. Since a TDHF trajectory shows a classical behavior, to describe quantum tunneling based on the TDHF and its extension has a common feature to a problem of how to simulate quantum tunneling using classical trajectories This problem has been discussed in the field of quantum chemistry, in which the entangled trajectory molecular dynamics (ETMD) has been developed [29,30,31,32]. In this method, the Winger function of a one particle wave function is represented as an ensemble of classical test particles. We shall investigate in this paper whether such entanglement of Slater determinants improves the failure of the TDHF method
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