NMR studies of single crystals of H₂: II. The spectrum of isolated ortho-H₂ pairs

Abstract

The NMR spectrum of isolated ortho-H₂ pairs has been measured on two single crystals of H₂ with ortho concentrations below about 2%. The experiments were carried out over a temperature range between 0.025 and 1 K, and spectra were recorded with the magnetic field applied in a number of directions. Extending the previous analysis of the spectrum for isolated ortho-H₂ to the present data led to the determination of the crystal orientation. The complicated pair spectrum includes the signals from the nine nonequivalent pair orientations in the crystal and is a function of the two lowest rotational states. These states are split by an energy δ, which is different for the pairs with axis respectively in and out of the basal plane of the crystal (denoted IP and OP), namely % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacqqHuoarcaGGOa% Gaam4taiaadcfacaGGPaGaai4laiaadUgadaWgaaWcbaGaamOqaaqa% baGccqWIdjYocaaI2aGaaGinaiaad2gacaWGlbaaaa!3DD4!\[\Delta (OP)/k_B \simeq 64mK\] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacqqHuoarcaGGOa% GaamysaiaadcfacaGGPaGaai4laiaadUgadaWgaaWcbaGaamOqaaqa% baGccqGH8aapcaaI1aGaaeiiaiaad2gacaWGlbaaaa!3D85!\[\Delta (IP)/k_B < 5{\rm{ }}mK\].

A detailed calculation of the NMR spectrum for each pair as a function of the applied field direction and temperature is carried out. The limiting cases are the high-temperature region _BT ≫ δ and the low-temperature regime _BT \2, δ. Therefore at the lowest temperatures attained, the NMR spectrum of the OP and IP pairs should behave differently. There is good agreement between experiment and theory, which is demonstrated in a detailed discussion. While at high temperatures, the transition rate Ω between the rotational states appears to be large in comparision with the NMR splitting constant d = 57.68kHz, there is evidence that Ω becomes smaller than d at temperatures lower than about 60 mK for the OP pairs, but not for the IP pairs. The NMR spectrum intensity for both types of pairs decreases as a function of time at constant temperature, as best seen from experiments below 0.1 K, and the corresponding time constant is appreciably shorter for the IP than for the OP pairs. This phenomenon might possibly be caused by the gradual disappearance of pairs in favor of larger ortho-H₂ cluster formation.