Theory of the Superfluid Transition in Liquid Helium

A simple method for approximately calculating the effect of Bose statistics on the properties of liquid helium is given. It is shown that as the temperature is lowered, normal helium undergoes a transition to a state in which a finite fraction of the atoms are in a coherent state. Using only the experimental interatomic potential and pair-correlation function, the transition temperature for liquid helium in equilibrium with its vapor is calculated to be 2.15\ifmmode^\circ\else\textdegree\fi{}K. The dependence of the transition temperature on pressure is calculated and found to be in good agreement with experiment. The specific heat is calculated and is found to diverge as the $\ensuremath{\lambda}$ temperature is approached. It is also shown that as the temperature is lowered, a density maximum will occur in liquid helium slightly above the $\ensuremath{\lambda}$ temperature.