NONERGODIC NUCLEAR DEPOLARIZATION IN NANO-CAVITIES
Fel'dman E.B., Rudavets M.G.

Received: June 17, 2003

PACS: 05.30.-d, 76.20.+q

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Recently, it has been observed that the effective dipolar interactions between nuclear spins of spin-carrying molecules of gas in a closed nano-cavities are independent of the spacing between all the spins. We derive exact time-dependent polarization for all spins in the spin-1/2 ensemble with spatially independent effective dipolar interactions. If the initial polarization is on a single (first) spin, P₁(0)= 1, then the exact spin dynamics of the model is shown to exhibit periodic short pulses of the polarization of the first spin, the effect being typical of systems having a large number N of spins. If , then within the period 4π/g (2π/g) for odd (even) N-spin clusters, with g standing for the spin coupling, the polarization of spin 1 switches quickly from unity to the time-independent value 1/3 over the time interval about . Thus, spin 1 spends almost all the time in the time-independent condition P₁(t)= 1/3. The period and the width of the pulses determine the volume and the form factor of the ellipsoidal cavity. The formalism is adapted to the case of time-varying nano-fluctuations of the volume V(t) of cavitation nano-bubbles. If the coupling g(V(t)) is varied by the Gaussian-in-time random noise due to the variation of the volume V(t), then the envelope of the polarization peaks goes irreversibly to 1/3. The polarization dynamics of a single spin exhibits the Gaussian (exponential) time dependence when the correlation time of fluctuations of the nano-volume is larger (smaller) than , where is the variance of the g(V(t)) coupling. Finally, we report exact calculations of the NMR line shape for the N-spin gaseous aggregate.