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Dimensional crossover to the one-dimensional (1D) state from higher dimensions has been studied for dilute $$^3$$ 3 He fluid adsorbed in 2.4 nm $$^4$$ 4 He-preplated nanochannels, by susceptibility measurements down to 70 mK using 4.29 MHz nuclear magnetic resonance. In nanochannels, since energy states of $$^3$$ 3 He motion perpendicular to the channel axis are discrete,...