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ZhETF, Vol. 125, No. 2, p. 233 (February 2004)
(English translation - JETP, Vol. 98, No. 2, p. 207, February 2004 available online at )

Fel'dman E.B., Rudavets M.G.

Received: June 17, 2003

PACS: 05.30.-d, 76.20.+q

DJVU (169.3K) PDF (394.7K)

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 N \gg 1, 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 (g\sqrt{N})^{-1}. 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  \langle ( \delta g )^2 \rangle^{-1/2} , where  \langle ( \delta g )^2 \rangle 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.

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