Pairing in Fermi fluids in restricted geometries

We consider dimerization of He-3 in a dilute solution of He-3 in superfluid He-4 filling narrow channels of a kind typically found in nanoscale porous media. Dimer formation is facilitated by the one dimensional geometry and occurs despite the fact that the interparticle interaction is too weak to lead to a bound state in bulk fluid. At sufficiently low temperatures, dimerization results in the effective "bosonization" of the system: a Bose quantum fluid of (He-3)(2) arises in place of the He-3 Fermi component. At sufficiently high temperatures, for which the He-3 impurity quasiparticles form a Maxwell-Boltzmann gas, the thermodynamics is significantly affected by the presence of dimers. In particular, the specific heat and magnetic susceptibility of the He-3 component show a marked deviation from behaviour expected if dimers were absent. Solution of the Schrodinger equation for a smooth cylindrical pore indicates that the binding energy in straight nanoscale channels ought to be of sufficiently high magnitude to make experimental observation feasible. The presence of (He-3)(2) dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid He-4, due to resonant absorption and decay of dimers in the acoustic field. We have calculated the absorption coefficient. Several experiments suggest themselves, utilizing, perhaps, K-L zeolites or carbon nanotubes. If the dimers themselves turn out to be attractive, then quadrumers may appear: it may even be the case that a single He-3 polymer will form over the entire length of the channel.