  We explore the two-body spectra of spin-$1/2$ fermions in isotropic harmonic
traps with external spin-orbit potentials and short range two-body
interactions. Using a truncated basis of total angular momentum eigenstates,
non-perturbative results are presented for experimentally realistic forms of
the spin-orbit coupling: a pure Rashba coupling, Rashba and Dresselhaus
couplings in equal parts, and a Weyl-type coupling. The technique is easily
adapted to bosonic systems and other forms of spin-orbit coupling.
