= Hyperfine structure
{wiki}
Hyperfine structure is the small splitting of atomic or molecular <energy levels> caused by interactions involving the <atomic nucleus>'s <magnetic dipole moment> or <electric quadrupole moment>. It is finer than the electronic <fine structure>. A leading <magnetic-dipole hyperfine interaction> couples the <nuclear spin> $I$ to the electronic <angular momentum> $J$; their total <angular momentum> $F$ labels the resulting <hyperfine levels>.
With dimensionless <angular momentum operators>, the model $H_{\rm hf}=A\mathbf I\cdot\mathbf J$ gives shifts $A[F(F+1)-I(I+1)-J(J+1)]/2$. A <hydrogen atom> in its electronic <ground state> has $I=J=1/2$, giving $F=0,1$. Resolved <microwave> transitions between <hyperfine levels> permit precise <spectroscopy> and provide the working transitions in many <atomic clocks>. Applied <magnetic fields> can split each <hyperfine level> further into <magnetic sublevels>.
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