Extension of the λ curve of 4He into the region of the metastable state of liquid helium

A possible extension (λ^') of the λ curve of liquid helium beyond the T, p boiling line, i.e., into the region of a metastable liquid state, is examined. The relation between the slope of the λ curve dp/dT_λ and the sign of the thermal expansion coefficient of liquid helium a_p is discussed. Experimental data for a_p are analyzed using thermodynamic equations to reveal that the derivative dp/dT_λ changes sign in the metastable region. As a result, the shape of the λ^' extension becomes similar to that of the pressure-shifted Bose-condensation line of an ideal ⁴He gas. The position of the λ^' curve is not entirely arbitrary due to the spinodal nature of stretched liquid helium.