Effect of short-range interaction for collision of ultracold dipoles

We consider the low-energy scattering of two ultracold polarized dipoles with both a short-range interaction (SRI) and a weak dipole-dipole interaction (DDI) which is far away from shape-resonances. In previous analytical studies, the scattering amplitude in this system was often calculated via the first-order Born approximation (FBA). Our results show that significant derivations from this approximation can arise in some cases. In these cases, the SRI can significantly modify the inter-dipole scattering amplitudes even if the scattering amplitudes for the SRI alone are much smaller than the dipolar length of the DDI. We further obtain approximate analytical expressions for these inter-dipole scattering amplitudes.