The ground state of the helium 4 dimer is considered using the Monte Carlo technique. In a cylinder with a hard core wall, binding depends on its radius. For a small radius binding occurs as in the one-dimensional case. With an increase of the radius, the binding becomes stronger, reaches its maximum value, and then slowly diminishes. In conical geometry, that may be realized as a generalization of a cylindrical one, this dependence of the binding energy on the radius might lead to an effective force which tends to move the molecule toward the region of minimal energy. Thus, in channels, with nonhomogeneous cross-sections, the particles move easier in dimer form. In addition, the square of the momentum and of the particle separation along the cylinder axis and in the plane perpendicular to it are calculated as well.
Helium atoms or hydrogen molecules are believed to be strongly bound within the interstitial channels (between three carbon nanotubes) within a bundle of many nanotubes. The effects on adsorption of a nonuniform distribution of tubes are evaluated. The energy of a single-particle state is the sum of a discrete transverse energy
Et (that depends on the radii of neighboring tubes) and a quasicontinuous energy
Ez of relatively free motion parallel to the axis of the tubes. At low temperature, the particles occupy the lowest-energy states, the focus of this study. The transverse energy attains a global minimum value
(Et=Emin) for radii near
Rmin=9.95A˚ for
H2 and
8.48A˚ for
4He. The density of states
N(E) near the lowest energy is found to vary linearly above this threshold value, i.e.,
N(E) is proportional to $(E\ensuremath{-}{E}_{\mathit{min}})$. As a result, there occurs a Bose-Einstein condensation of the molecules into the channel with the lowest transverse energy. The transition is characterized approximately as that of a four-dimensional gas, neglecting the interactions between the adsorbed particles. The phenomenon is observable, in principle, from a singular heat capacity. The existence of this transition depends on the sample having a relatively broad distribution of radii values that include some near
Rmin.
We consider dimerization of
3He in a dilute solution of
3He in superfluid
4He 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
(3He)2 arises in place of the
3He Fermi component. At high temperatures, when the
3He 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
3He component, which we calculate at arbitrary degrees of dimerization, show a marked deviation from behavior expected of an undimerized
3He component. We show that the binding energy---which depends on the channel width---is expected to be sufficiently high to make experimental observation feasible. The presence of
(3He)2 dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid
4He, 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
3He polymer will form over the entire length of the channel.
We consider dimerization of 3 He in a dilute solution of 3 He in superfluid 4 He 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 (3 He )2 arises in place of the 3 He Fermi component. At sufficiently high temperatures, for which the 3 He 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 3 He component show a marked deviation from behaviour expected if dimers were absent. Solution of the Schrödinger 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 (3 He )2 dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid 4 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 He polymer will form over the entire length of the channel.