1112.1122 (Xiaoling Cui)

Mixed partial-wave scattering with spin-orbit coupling and validity of
pseudo-potentials    [PDF]

Xiaoling Cui

We present exact solutions of two-body problem for spin-1/2 fermions with
isotropic spin-orbit(SO) coupling and interacting with an arbitrary short-range
potential. We find that in each partial-wave scattering channel, the
parametrization of two-body wavefunction at short inter-particle distance
depends on the scattering amplitudes of all channels. This reveals the mixed
partial-wave scattering induced by SO couplings. By comparing with results from
a square-well potential, we investigate the validity of original
pseudo-potential models in the presence of SO coupling. We find the s-wave
pseudo-potential provides a good approximation for low-energy solutions near
s-wave resonances, given the length scale of SO coupling much longer than the
potential range. However, near p-wave resonance the p-wave pseudo-potential
gives low-energy solutions that are qualitatively different from exact ones,
based on which we conclude that the p-wave model can not be applied to the
fermion system if the SO coupling strength is larger or comparable to the Fermi
momentum.

View original: http://arxiv.org/abs/1112.1122