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I'm a bit confused having heard two different terms in different lecture parts:

  • J-coupling

There is the J-coupling (= indirect dipole dipole coupling = scalar coupling) which arises from a hyperfine interaction between the nuclei and the interaction. The J-coupling is a coupling between the two nuclear spins of two nuclei (e.g. a C-H bond). Because of the Pauli principle the two binding electrons are anti-parallel located so the nuclear spins $I_1$ and $I_2$ also have an anti-parallel nuclear spin.

  • j,j-coupling

There is as well the jj-coupling (= spin orbit coupling) which describes the coupling of the different $j_i$. This coupling scheme is valid for heavier atoms. (For leight atoms the ls-coupling is valid). In atoms with bigger nuclear charges, spin-orbit interactions are frequently as large as or larger than spin-spin interactions or orbit-orbit interactions. $\mathbf J = \sum_i \mathbf j_i = \sum_i (\boldsymbol{\ell}_i + \mathbf{s}_i).$ Wikipedia

I don't see any commonalities. Why is the term "J-coupling" similar to the term "j,j-coupling"?

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I don't believe there are any commonalities, and the terms have been derived independently.

The term J coupling in NMR was first proposed in 1951 by Erwin Hahn in his paper describing the spin echo experiment, in which two frequencies are observed; one at the chemical shift (which they called delta, as was convention, even back then) as expected, and a second frequency which they labelled as frequency J. There is no explanation for why the choice of J is given. Gutowsky and McCall who observed the same phenomenon independently did not give it a label, and the term J splitting stuck. J coupling describes the relationship between nuclear spin, the intrinsic angular momentum of atomic nuclei.

The term jj coupling relates orbital angular momentum of electrons. I'm not going to pretend to know anything about the origins of the term, nor anything about its application in physics and astronomy. However, the term J is sometimes used to represent total angular momentum, which is made up of individual components ji. It is the interaction between these individual j terms that give rise to jj coupling.

Other than being types of interactions between entities of angular momentum, the two couplings are quite unrelated, as are the terms used to describe them.

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