As I understand, particles such as the neutron, whilst having no external charge still possess a magnetic moment due to the underlying charges of its components.
By that logic why does the alpha particle have a magnetic moment of zero?
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2 Answers
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The answer by dmckee doesn't really work. The wavefunction he describes is an approximation, so then it would only be approximately true that the magnetic dipole moment would vanish.
Actually, the dipole moment of any spin-zero state must vanish exactly. A spin-zero state is invariant under rotation, so its dipole moment must also be invariant under rotation. The only vector that is invariant under rotation is a zero vector.
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$\begingroup$ Agreed, and welcome to Physics.SE! $\endgroup$– knzhouCommented Aug 31, 2022 at 1:35
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$\begingroup$ Correct! For a generalization of this argument to higher spins, see this answer. $\endgroup$– rob ♦Commented Aug 31, 2022 at 4:11
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This is actually the least hypothesis for this configuration.
Four nucleons comprising all four allowed $\text{spin} \times \text{isospin}$ states can all be expected to be in the s1 state so that they have no orbital contribution and for each pair the intrinsic magnetic moments cancel as the spins are opposed. Boom. Zero and done.
answered Jan 25, 2013 at 19:55
dmckee --- ex-moderator kittendmckee --- ex-moderator kitten
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2$\begingroup$ a more interesting question is how the spherical symmetry in the ground state of the $He_4$ nucleus is determinant for the degeneracy observed in the Bose-Einstein condensate, and why similarly symmetric nuclei do not show the condensate transition $\endgroup$– lurscherCommented Jan 25, 2013 at 19:59
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2$\begingroup$ @lurscher Can bosons that are composed of several fermions occupy the same state? has some discussion on that issue, but it is mostly beyond my poor, weak, experimentalist brain. $\endgroup$ Commented Jan 25, 2013 at 20:04