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The 21 cm Hydrogen line is from the transition between the hyperfine levels of the ground state of the hydrogen atom.

So, what interaction is coupling the hyperfine levels?

I suspect that it is not the usual EM interaction, which causes the 1s-2p transition.

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The 1s energy level is split into two levels, one where the electron spin and nuclear spin are parallel, and the other where the electron spin and nuclear spin are antiparallel.

The 21 cm line is the transition between these two 1s levels.

The transition is a magnetic dipole transition.

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Then it is simply EM between the electron and the nucleus? –  Peter Horvath Jun 23 at 16:34
    
it is a magnetic dipole transition (M1) as opposed to the more common electric dipole transition (E1). It is still an electro-magnetic transition between two states of the hydrogen atom. The lower energy state is the state with the electron spin and nuclear spin antiparallel, meaning their magnetic dipole moments are parallel. –  DavePhD Jun 23 at 17:00

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