This looks like a spin-spin problem in a two-body system. As far as bound states are concerned, you may have a look at the Breit equation, where such terms are encountered. You may find a quite detailed discussion on it in Bethe&Salpater book "Quantum Mechanics of one- and two-electron atoms", pg 170. For a non-relativistic treatment, you may have a look at http://people.ccmr.cornell.edu/~clh/p654/MM-Lec0.pdf . If you look at Eq. 4.1.23, it is a spin-spin coupling term very similar to what you propose.
How this hamiltonian is attacked: I believe that what is usually done is reducing these kind of terms to the total spin, which is normally a conserved quantity. You may use $\vec \sigma_1\cdot \vec \sigma_2=(\vec \sigma_1+\vec \sigma_2)^2/2- 1/2(\vec \sigma_1^2 + \vec \sigma_2^2)$. The three operators in the right hand side are conserved operators in a two-body system. So, you can easily act on the two-body wavefunction extracting their eigenvalues.
I hope it helped.