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We derive an expression for the correction to the spin-system Hamiltonian that arises due to the system-bath interaction, starting both from the standard master equation for the spin density matrix and a perturbative diagonalization of the system-bath Hamiltonian to the second order in the interaction. We show that the dynamic frequency shifts observed in the evolution of the nuclear spin coherences are a result of these Hamiltonian corrections. We present a systematic decomposition of thedoi:10.1063/1.1313526 fatcat:mrcvwpehujczxkpxbjzoeikuw4