Superfluidity in 3He films

Superfluid 3He films in the thickness regime k/sub F//sup /minus/-1/ << d < /zeta/ are considered. The authors find that for smooth boundaries the transition temperature decreases with thickness and, contrary to what is found for s-wave pairing, exhibits only weak oscillatory behavior. Other quantities, such as Nuclear Magnetic Resonance frequency shifts, however, show discontinuous jumps. Diffusive boundary scattering has a qualitative influence in the phase diagram: for a specified degree of surface roughness there is a critical thickness d/sub c/ below which superfluidity disappears. As the thickness decreases towards d/sub c/ an intermediate region of gapless superfluidity is reached. This region appears to be experimentally accessible. Properties of the gapless state are briefly discussed