Constraints on intersection forms of spin 4-manifolds bounded by Seifert rational homology 3-spheres in terms of $\bar{\mu }$ and $\kappa$ invariants

We give some constraints on intersection forms of spin 4-manifolds bounded by Seifert rational homology 3-spheres in terms of the $\bar{\mu }$ invariant and compare them with those in terms of the $\kappa$ invariant. We also show that the difference between $\kappa$ and $-\bar{\mu }$ for a Seifert rational homology 3-sphere is at most 2, and under certain extra conditions the difference is 0.