Hyperfine splitting in Hydrogen atom

DMESONS
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We know this tiny splitting in degenerate levels in Hydrogen spectrum due to magnetic interactions between spins of electron and proton. but is that true the proton spin is independent of energy in this (hyperfine) splitting? I want to understand the physics of this splitting and how the spin orientation of massive proton, in comparison to electron, become independent of the energy of splitting.
 
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The proton spin is the cause of hyperfine splitting, so what is the meaning of saying the former (cause) is independent from the latter (result)?
 

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