Dimerization of 3He in 3He-4He dilute mixtures filling narrow channels

Abstract

We consider dimerization of ${}^{3}\mathrm{He}$ in a dilute solution of ${}^{3}\mathrm{He}$ in superfluid ${}^{4}\mathrm{He}$ filling straight narrow channels that can be found in nanoscale porous media. Dimer formation is facilitated by the restricted geometry and occurs despite the fact that in bulk fluid the interparticle interaction is too weak to lead to a bound state. Dimerization results in the effective ``bosonization'' of the system: a Bose quantum fluid of ${(}^{3}\mathrm{He}{)}_{2}$ arises in place of the ${}^{3}\mathrm{He}$ Fermi component. At high temperatures, when the ${}^{3}\mathrm{He}$ impurity quasiparticles form a Maxwell-Boltzmann gas, a drastic change in the thermodynamics occurs due to the presence of dimers. The specific heat and magnetic susceptibility of the ${}^{3}\mathrm{He}$ component, which we calculate at arbitrary degrees of dimerization, show a marked deviation from behavior expected of an undimerized ${}^{3}\mathrm{He}$ component. We show that the binding energy\char22{}which depends on the channel width\char22{}is expected to be sufficiently high to make experimental observation feasible. The presence of ${(}^{3}\mathrm{He}{)}_{2}$ dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid ${}^{4}\mathrm{He},$ 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 ${}^{3}\mathrm{He}$ polymer will form over the entire length of the channel.