ZhETF, Vol. 125,
No. 2,
p. 233 (February 2004)
(English translation  JETP,
Vol. 98, No. 2,
p. 207,
February 2004
available online at www.springer.com
)
NONERGODIC NUCLEAR DEPOLARIZATION IN NANOCAVITIES
Fel'dman E.B., Rudavets M.G.
Received: June 17, 2003
PACS: 05.30.d, 76.20.+q
Recently, it has been observed that the effective dipolar interactions between nuclear spins of spincarrying molecules of gas in a closed nanocavities are independent of the spacing between all the spins. We derive exact timedependent polarization for all spins in the spin1/2 ensemble with spatially independent effective dipolar interactions. If the initial polarization is on a single (first) spin, P_{1}(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) Nspin clusters, with g standing for the spin coupling, the polarization of spin 1 switches quickly from unity to the timeindependent value 1/3 over the time interval about . Thus, spin 1 spends almost all the time in the timeindependent condition P_{1}(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 timevarying nanofluctuations of the volume V(t) of cavitation nanobubbles. If the coupling g(V(t)) is varied by the Gaussianintime 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 nanovolume 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 Nspin gaseous aggregate.

