How can a potential be non-central? I'm studying nucleon-nucleon interactions and I'm reading that the potential for said interaction has a non-central (or tensor) component. 
Now, I understand that, when describing a 2-bodies problem, with relative distance, momentum etc, the potential energy depends on their relative direction in relation to the spin axis. But with the gravitational/electric potential it was possible to describe the interaction with a "test mass/charge", and therefore draw a graph $V(r)$ centered on the non-test mass/charge: anything entering such potential, if small enough, would just undergo the potential without interfering with it.
Is such a description possible for the nucleon tensor potential (or any other non-central potential)?
 A: I'm not sure about your question exactly, but the way I think about it is that the graph of the potential you draw itself is just different based on the spin. For example, depending on which spin you choose for your test nucleon, you will have one potential if the other particle is spin-aligned, and another (shifted) potential if it is not.
A bit of history: for nucleon-nucleon interaction, the tensorial nature of the force was discovered because of the orbital angular momentum of the deuteron. It was shown in 1939 that the deuteron ground state is a mixture of $L=0, L=2$ states. This is unexpected as both the proton and neutron has a zero electric quadrupole moment. The best explanation for this process is that the nuclear force applies a torque and is thus a function of relative orientation (or spin). In fact, we normally write the tensorial component as:
$$ V_T(r) = 3 (\vec{\mu}_1\cdot\hat{r}) \cdot (\vec{\mu}_2\cdot\hat{r}) - \vec{\mu}_1 \cdot \vec{\mu}_2$$
where $\vec{\mu}$ is the spin operator for each nucleon, respectively. So this component itself switches based on the alignment of the two spins.
For further references, please see:


*

*This paper due to Reid, 1968 shows an early observation of this tensorial character.

*and this note due to Comay which provides a more rigorous version of the argument I'm briefly outlining here.


I hope this answers your question!
