<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>melting curve below 15 mK

We have performed new measurements of the $P\ensuremath{-}T$ relation along the $^{3}\mathrm{He}$ melting curve for temperatures between 0.4 and 15 mK in zero magnetic field. The temperature was determined by a Pt-wire nuclear-magnetic-resonance thermometer calibrated against the National Bureau of Standards scale (1983) above 15 mK. Three distinct points on the melting curve (the two superfluid transitions and the nuclear-spin ordering in the solid phase) were observed at temperatures lower than the currently accepted values by about 10%. Our results are in good agreement with the $P\ensuremath{-}T$ relation recently proposed by Greywall using a La-cerium magnesium nitrate thermometer, but differ seriously from the thermodynamic measurements by Halperin et al. From the measured melting curve, we could determine the ground-state energy of a nuclear spin in solid $^{3}\mathrm{He}$ to be -1.24 mK at the melting density. This value can be quantitatively explained by the current four-spin exchange theory.

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