  The potential describing long-range interactions between D0-branes contains
spin-dependent terms. In the matrix model, these should be reproduced by the
one-loop effective action computed in the presence of a nontrivial fermionic
background $\psi.$ The $\frac{v^3 \psi^2}{r^8}$ term in the effective action
has been computed by Kraus and shown to correspond to a spin-orbit interaction
between D0-branes, and the $\frac{\psi^8}{r^{11}}$ term in the static potential
has been obtained by Barrio et al. In this paper, the $\frac{v^2 \psi^4}{r^9}$
term is computing in the matrix model and compared with the corresponding
results of Morales et al obtained using string theoretic methods. The technique
employed is adapted to the underlying supersymmetry of the matrix model, and
should be useful in the calculation of spin-dependent effects in more general
Dp-brane scatterings.
