Time-dependent analysis for spontaneous neutron emission

Spontaneous neutron emission has been observed in many neutron-rich nuclei beyond the neutron drip line with the development of experimental nuclear physics. Compared with proton emission, $\ensuremath{\alpha}$ decay, and heavy cluster radioactivity, neutron emission has the same mechanism, namely quantum tunneling, but the research on neutron emission is still at its beginning. Our purpose is to extend the previous theoretical model of charged particle emission to neutron emission, especially the time evolution. In this work, the Woods-Saxon potential and spin-orbit interaction are used to construct the daughter-neutron potential. To calculate the half-life, as a dynamic simulation, TDSE (time-dependent Schr"odinger equation) approach is employed to research the decay process in detail for some neutron emitters, and its results are compared with experiments and the Wentzel-Kramers-Brillouin (WKB) approximation, a conventional method of particle emission, verifying the stability of our model, despite relatively large or small half-lives or the emitters in the island of inversion. Particularly, we also theoretically calculate the extremely fast neutron radioactivity occurring in the recently discovered new nuclide $^{30}\mathrm{F}$ [Phys. Rev. Lett. 133, 082501 (2024)], and obtain results consistent with experiments. We also observe some new phenomena and propose a tentative conjecture to explain them, which is difficult to find using traditional methods. It is expected that this work can be a helpful reference for future studies of neutron-rich nuclei.