Phase-space consideration on barrier transmission in a time-dependent variational approach with superposed wave packets

Abstract

A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a superposition of Gaussian wave packets, to describe the relative motion between two colliding nuclei, which may be simplified to a problem for one particle in one dimension. In this article, how the model describes the potential-barrier transmission is investigated by paying attention to the time evolution of the phase space distribution, which in particular reveals that the behavior of the free propagation of the incoming state is not trivial, depending on the number of superposed wave packets. Passage over the barrier can occur due to the high-momentum components in the incoming state corresponding to energies above the barrier height, which is, however, of classical nature and needs to be distinguished from the true quantum tunneling. Although a transmitted wave packet in some case may end up with an energy lower than the barrier, a difficulty is noticed in guaranteeing the energy conservation when the energies of different exit channels, e.g. of transmission and reflection, are individually measured. To overcome these issues for a description of quantum tunneling is still a challenging problem. This article mainly treats the same system with the same model as in the paper Phys. Lett. B 808 (2020) 135693, arXiv:2006.06944v1 by N. Hasegawa, K. Hagino and Y. Tanimura. However, the conclusion of the present work disagrees with their quick conclusion that quantum tunneling was simulated by the model. Comments are made on this.

Comment on "Phase-space consideration on barrier transmission in a time-dependent variational approach with superposed wave packets (arXiv:2201.02966)"

“…We agree with Ref. [2] that each Gaussian function in Eq. (1) has a broad momentum distribution if ν r is taken to be 1.0 fm −2 as in Ref.…”

“…As is pointed out in Ref. [2], the relative wave function between two nuclei with such s.p. wave functions reads,…”

“…In a recent publication, we employed the timedependent generator coordinate method (TDGCM) and discussed a many-particle tunneling in the context of nuclear reaction [1]. In his preprint, Ono claims that our interpretation of the calculated results are unphysical and erroneous [2]. The claim is based on the fact that the initial wave function employed in Ref.…”