Spectral properties and lifetimes of neutral spin-12fermions in a magnetic guide

Abstract

We investigate the resonant motion of neutral spin-$\frac{1}{2}$-fermions in a magnetic guide. A wealth of unitary and antiunitary symmetries is revealed in particular giving rise to a twofold degeneracy of the energy levels. To compute the energies and decay widths of a large number of resonances the complex scaling method is employed. We discuss the dependence of the lifetimes on the angular momentum of the resonance states. In this context the existence of so-called quasibound states is shown. In order to approximately calculate the resonance energies of such states a radial Schr\odinger equation is derived which improves the well-known adiabatic approximation. The effects of an additionally applied homogeneous Ioffe field on the resonance energies and decay widths are also considered. The results are applied to the case of the $^{6}\mathrm{Li}$ atom in the $F=\frac{1}{2}$ hyperfine ground state.