Short-range asymptotic behavior of the wave functions of interacting spin-1/2 fermionic atoms with spin-orbit coupling: A model study

We consider spin-1/2 fermionic atoms with isotropic Rashba spin-orbit coupling in three directions. The interatomic potential is modeled by a square-well potential. We derive the analytic form of the asymptotic wave functions at short range for two fermions in the subspace of zero net momentum and zero total angular momentum. We show that the spin-orbit coupling has perturbative effects on the short-range asymptotic behavior of the wave functions away from resonances. We argue that our conclusion should hold generally.

Figure 1

Phase shift ${\delta }_{-}\left(k{r}_0\right)$ vs $k{r}_0$ for $\tilde{\lambda }=0.01$ and $\eta =1$.

Figure 2

Phase shift ${\delta }_{+}\left(k{r}_0\right)$ vs $k{r}_0$ for $\tilde{\lambda }=0.01$ and $\eta =1$.