  The effects of entanglement and spin-spin collision on the gauge field in
ultracold atoms are presented in this paper. Two gauge fields are calculated
and discussed. One of the fields comes from space dependent spin-spin
collisions in ultra-cold atoms, while another results from the usual
Born-Oppenheimer method, which separates the center-of-mass motion from the
relative motion in the two-body problem. Adiabatic conditions that lead to the
key results of this paper are also presented and discussed. Entanglement shared
between the two atoms is shown to affect the atomic motion. In the presence of
entanglement, the additional scalar potential disappears, this is different
from the case of atoms in separable states.
