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We predict the effect of the nuclear spin density fluctuations on NMR spectraof critical solutions of spin-carrying atoms in closed carbon nanotubes (CNTs).The total effective dipolar coupling of nuclear spin-carrying of 129^Xe atomsis the sum of 2 terms i.e. g_0 of non-correlated 129^Xe atoms and g_1 dependingon density fluctuations of Xe atoms. The coupling g_0 falls off to 0 as 1/Vwith increasing the volume V of CNTs, while the g_1 remains finite for longCNTs containing critical solution of Xe atoms. The g_1 is derived within theLandau-Ginzburg framework. When temperature T goes to critical temperature T_c,the g_1 is about 10 Hz for 129^Xe fluid in closed long tubes. To achieve theg_1>> g_0, 3 conditions should be met: (1) the large mobility of 129^Xe atoms,(2) the maximal isothermal compressibility of Xe nanofluid within CNTs thathave to be (3) long and closed. We discuss 3 applications of such a behavior.First, when T goes to T_c, the FID from N magnetically equivalent 129^Xe atomsis broadened so wide that the FID splits into lattice of N equidistantresonances with finite spacing G=3g_1. Second, the absorption line shape of129^Xe atoms in spin state I=N/2, m=N/2 has a single delta peak at frequencywith the large shift N*G/2 from Larmor frequency W for N>>1. The dipolar fieldof nanofluid in the spin state I=N/2, m=-N/2 inverts the total magnetic fieldif N>1+2W/G. Third, we discuss the spontaneous superradiation of the nanofluidin course of depolarization I_x(t) in low-field resonator. At CP of thenanofluid, the I_x(t) causes the bursts of dissipated power ~(g_1)^2*N^3. Inthe opposite limiting case of the strong field resonator, the depolarizationI_x(t) has the Dicke's power ~(W*N)^2. Far from the CP of Xe nanofluid, thedissipated power scales linear with N for fixed density of 129^Xe atoms.

Giant enhancement of the NMR resolution and sensitivity of the critical solutions of hyperpolarized fluids within closed carbon nanotubes