  We report a \^{23}Na and \^{27}Al nuclear magnetic resonance (NMR)
investigation of low-silica X (LSX) zeolite with chemical formula
Na_{12}Al_{12}Si_{12}O_{48} (Na_{12}-LSX) loaded with n additional guest sodium
atoms. Na_{n}/Na_{12}-LSX exhibits an insulator-to-metal transition around
n=11.6, which is accompanied by a significant enhancement of bulk magnetic
susceptibility. Paramagnetic moments are thermally activated in the metallic
Na_{12}/Na_{12}-LSX with an activation energy of around 0.1 eV. At the same
time, a new shifted component (SC) appears in the \^{23}Na NMR, whose large and
positive NMR shift scales with bulk magnetic susceptibility. Its spin-lattice
relaxation rate 1/T_{1} is governed by the fluctuations determined by the same
activation energy as obtained from the bulk magnetic susceptibility data. The
timescale of these fluctuations is typical for atomic motions, which suggest
strong electron-phonon coupling, a hallmark of polaron states. The
insulator-to-metal transition in Na_{n}/Na_{12}-LSX is thus discussed within a
polaron model.
