Deuteron is p-n, so naively should have zero electric quadrupole moment. However, experimentally it turns out quite large: $0.2859\ e\cdot fm^2$ from https://en.wikipedia.org/wiki/Deuterium#Magnetic_and_electric_multipoles
This Wikipedia article explains it by adding $l=2$ angular momentum states - should we imagine it as a hidden dynamics? Oscillations between 'pn' and 'np' by some $\pi^+$ exchange? (but shouldn't it make it a linear antenna producing EM waves?)
To describe e.g. deuteron-proton scatterings they neglect quark structure, but require three-body force - would including quarks into considerations allow to focus only on two-body forces?
But what happens with quarks when biding proton and neutron into deuteron? I am working on soliton particle model (slides) suggesting that there is a shift of charge from proton to neutron for binding of deuteron, like uud-udd slightly shifting quark u toward right, d toward left - is such explanation of quadrupole moment allowed (e.g. by QCD)?
Could we distinguish experimentally dynamic (angular momentum) from static (e.g. shift of quarks) explanation of deuteron's quadrupole moment?
Update: The $l=2$, $m=0$ spherical harmonic used for the explanation:
Update 2: To avoid bilocation claim for proton, quadrupoles are naturally obtained by shift of charges (like quarks). Here is suggestion from soliton particle model: structure of baryon requires some positive charge (e.g. +2/3), which needs to be compensated in neutron (explaining higher mass than proton), in deuteron this requirement is obtained by partial shift of charge from proton to neutron: