In order to find theoretically the deuterium magnetic dipole moment μ, one uses the formula for a nuclear magnetic moment
with
g and g are g-factors of the nucleons.
Since the proton and neutron have different values for g and g, one must separate their contributions. Each gets half of the deuterium orbital angular momentum  and spin . One arrives at
where subscripts p and n stand for the proton and neutron, and .
By using the same identities as here and using the value , we arrive at the following result, in units of the nuclear magneton μ
For the ,  state (), we obtain
For the ,  state (), we obtain
The measured value of the deuterium magnetic dipole moment, is , which is 97.5% of the  value obtained by simply adding moments of the proton and neutron. This suggests that the state of the deuterium is indeed to a good approximation ,  state, which occurs with both nucleons spinning in the same direction, but their magnetic moments subtracting because of the neutron's negative moment.
But the slightly lower experimental number than that which results from simple addition of proton and (negative) neutron moments shows that deuterium is actually a linear combination of mostly ,  state with a slight admixture of ,  state.
The electric dipole is zero as usual.
The measured electric quadrupole of the deuterium is . While the order of magnitude is reasonable, since the deuterium radius is of order of 1 femtometer (see below) and its electric charge is e, the above model does not suffice for its computation. More specifically, the electric quadrupole does not get a contribution from the l =0 state (which is the dominant one) and does get a contribution from a term mixing the l =0 and the l =2 states, because the electric quadrupole operator does not commute with angular momentum.
The latter contribution is dominant in the absence of a pure  contribution, but cannot be calculated without knowing the exact spatial form of the nucleons wavefunction inside the deuterium.
Higher magnetic and electric multipole moments cannot be calculated by the above model, for similar reasons.