  We report that the Bloch-Siegert shift which appears in Nuclear Magnetic
Resonance (NMR) spectroscopy can also be shown to originate as a part of a
complex drive-induced second-order susceptibility term. The shift terms thus
obtained are shown to have an absorptive Kramers-Kronig pair. The theoretical
treatment involves a finite time-propagation of a nuclear spin-$1/2$ system and
the spin-bearing molecule under the action of thermal fluctuations acting on
the latter. The finite propagator is constructed to account for many instances
of thermal fluctuations occurring in a time-scale during which the spin density
matrix changes infinitesimally. Following an ensemble average, the resulting
quantum master equation directly yields a finite time-nonlocal complex
susceptibility term from the external drive, which is extremely small but
measurable in solution-state NMR spectroscopy. The dispersive part of this
susceptibility term originating from the non-resonant component of the external
drive results in the Bloch-Siegert shift. We have verified experimentally the
existence of the absorptive Kramers-Kronig pair of the second-order shift term,
by using a novel refocussed nutation experiment. Our method provides a single
approach to explain both relaxation phenomena as well as Bloch-Siegert effect,
which have been treated using non-concurrent techniques in the past.
