  The liquid-vapor transition in He-3 and He-4 is investigated by means of
path-integral molecular dynamics and the quantum virial expansion. Both methods
are applied to the critical isobar and the critical isochore. While previous
path-integral simulations have mainly considered the lambda transition and
superfluid regime in He-4, we focus on the vicinity of the critical point and
obtain good agreement with experimental results for the molar volume and the
internal energy down to subcritical temperatures. We find that an effective
classical potential that properly describes the two-particle radial
distribution function exhibits a strong temperature dependence near the
critical temperature. This contrasts with the behavior of essentially classical
systems like xenon, where the effective potential is independent of
temperature. It is conjectured that, owing to this difference in behavior
between classical and quantum-mechanical systems, the crossover behavior
observed for helium in the vicinity of the critical point differs qualitatively
from that of other simple liquids.
