STICKY SPHERES IN QUANTUM-MECHANICS

For a 3-dimensional system of hard spheres of diameter D and mass m wi th an added attractive square-well two-body interaction of width a and depth epsilon, let B(D,a) denote the quantum second virial coefficien t. Let B(D) denote the quantum second virial coefficient for hard sphe res of diameter D without the added attractive interaction. We show th at in the limit a --> 0 at constant alpha := epsilona2/(2HBAR2) with a lpha < pi2/8, [GRAPHICS] The result is true equally for Boltzmann, Bos e and Fermi statistics. The method of proof uses the mathematics of Br ownian motion. For a > pi2/8, we argue that th gaseous phase disappear s in the limit a --> 0, so that the second virial coefficient becomes irrelevant.