# J-coupling constants and nuclei with zero total angular momentum

Scalar or J-couplings (also called indirect dipole dipole coupling) are mediated through chemical bonds connecting two spins. It is an indirect interaction between two nuclear spins which arises from hyperfine interactions between the nuclei and local electrons.

My question is: provided that J-couplings are some metric for hyperfine interactions between electron spins and nuclear spins, is there something special we can say regarding J-couplings between two atoms in a lattice with even integer mass numbers, i.e. where the nuclei of both atoms have a spin quantum number of zero? Shouldn't the lack of a nuclear spin on both bonded atoms abrogate any j-coupling term?

Yes. If any of the two nuclei has spin $j=0$, then there will be no J-coupling between them. This is made clear by the J-coupling hamiltonian, $$H\propto\sum_{ik}I^{(1)}_i J_{ik} I_k^{(2)}.$$
If either spin is zero then all the spin components $I_i$ will be zero as operators, and $H$ will be zero.