Two-fermion emission from spin-singlet and triplet resonances in one dimension

Abstract

The emission of two correlated fermions from a nuclear, or, in general, quantum meta-stable system is a poorly known, but fundamental problem: the interaction between the fermions can significantly affect the tunneling process. The behaviour of spin-singlet or spin-triplet emission has not been fully studied. In this article, the one-dimensional tunneling process of two fermions of the same kind is investigated. We solve the time-dependent Schrödinger equation for the two-fermion (2F) state, which is initially confined inside the square-well-plus-barrier potential. The interaction between the two fermions is schematically described by a short-range square-well attractive potential. A noticeable difference between the spin-singlet and triplet emissions is shown. Their tunneling probability, which is evaluated from the time-dependent survival probability, depends on the total spin, even if the effective-barrier height is fixed to be equivalent. Also, a spatial correlation of two fermions appears (vanishes) in the spin-singlet (triplet) case. The total-spin dependence of 2F emission can be attributed to the anti-symmetrization condition: it allows (prohibits) degenerate pairing, where two fermions can occupy the same spatial orbit, in the spin-singlet (triplet) case. This degenerate pairing makes the spin-singlet 2F state more long-lived than the spin-triplet one, even under the equivalent conditions. Only in the spin-singlet channel, the short-range 2F attraction enhances the degenerate-pair component, providing the difference between correlated and uncorrelated emissions. On the other hand, the spin-triplet emission cannot profit from the 2F interaction, due to the Pauli principle. These conclusions are independent of the physical scales.