Eq. (4): nucleon axial matrix elements in the quark model

Fix a spin component and write $u_p = \langle p|\bar u\gamma\gamma_5u|p\rangle$, $d_p = \langle p|\bar d\gamma\gamma_5d|p\rangle$, $S_p = \langle p|S|p\rangle$ for the proton and $u_n, d_n, S_n$ for the neutron (real numbers). Assume the isovector relation and the quark-model isosinglet relation for the proton, and their isospin mirrors ($u\leftrightarrow d$, $p\leftrightarrow n$) for the neutron:

Then

These are the single-nucleon matrix elements from which the nuclear spin-dependent couplings are built.

Formalization Note The paper's "analogous results for neutrons" are encoded as the isospin-mirrored relations for the neutron.