# What is the dominant interaction between two neighboring neutrons?

Suppose they are held 10 nm apart.

What is the dominant interaction between them?

The magnetic dipole interaction or something else?

It's a sort of an angular momentum selection rule. The matrix element $$\langle s_1| T | s_2\rangle$$ between two $j=1/2$ spinors of a $j=2$ operator has to vanish because two $j=1/2$ cannot be combined to yield a (much larger) $j=2$ result.
Quadrupole moments only arise for ellipsoid-shape nuclei that are stretched in one (or two) directions and shrunk in the remaining two (or one) direction. But a neutron cannot have such privileged axes because its spin is just 1/2 and both spin-up and spin-down state correspond to the same "preferred axis". The value $j=1/2$ is just too small and qualitatively similar to $j=0$: when it comes to the quadrupole moments (electric or magnetic), the neutron is exactly spherical.