Liquid 4He: Contributions to First Principles Theory. II. Quantized Vortices and the λ Transition

Quantized vortices in liquid 4He at finite temperatures are treated by first principles theory that extends results presented in paper I of this two-part set. Then the possible role of thermally excited quantized vortices in accounting for the λ transition is studied. This study indicates that vortices are probably not the dominant mechanism responsible for the λ transition, but that they may account for some minor effects near Tλ. A model that identifies critical fluctuations with quantized isothermal fourth sound waves is developed and used to derive formulas for specific heat in He II and He I. Logarithmic divergence of the constant volume specific heat is found. Numerical calculations using those formulas produce close agreement with experimental data. A formula for the radial distribution function near Tλ in He II and He I is derived and numerically evaluated. A formula for the correlation length is derived and numerically evaluated and physical characteristics of the correlation length are discussed. Numerical calculations based on that formula for correlation length are compared with experimental results. Long-range order in the liquid exhibited in the radial distribution function and correlation length is shown not to involve a Bose-Einstein condensate in this theory. The isothermal compressibility is found by integration of the radial distribution function and the result shows that isothermal compressibility is unchanged by critical fluctuations of isothermal fourth sound.