Higher order spin-dependent terms in D0-brane scattering from the Matrix model

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 non-trivial fermionic background ψ. The ν3ψ2/r8 term in the effective action has been computed by Kraus and shown to correspond to a spin-orbit interaction between D0-branes, and the ψ8/r11 term in the static potential has been obtained by Barrio et al. In this paper, the ν2ψ4/r9 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.