Although the pion has spin zero, one-pion exchange depends on nucleon spin and isospin and includes a nuclear tensor force. Shorter-range and multiple-nucleon interactions also matter. The scalar Yukawa potential isolates a range mechanism rather than specifying the complete nuclear force.[ref]
Modern Theory of Nuclear Forces by Evgeny Epelbaum and others. Modern Theory of Nuclear Forces, inspected preprint sections I.B and II.B, especially equation (2.11) and Fig. 12
The linear operator couples nucleon spin orientations to their separation direction . Here are Pauli matrices. A scalar radial potential energy alone omits this directional dependence.
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