About Conditions of Spatial Collapse in an Infinite System of Bose Particles

Using the variational principle, we show that the condition of spatial collapse in a Bose gas is not determined by the value of the scattering length of the interaction potential between particles contrary to the result following from the Gross–Pitaevskii equation, where the collapse should take place at a negative scattering length.

The BCS energy gap at low density

We show that the energy gap for the BCS gap equation is $$\begin{aligned} \varXi = \mu \left( 8 {\mathrm{e}}^{-2} + o(1)\right) \exp \left( \frac{\pi }{2\sqrt{\mu } a}\right) \end{aligned}$$ Ξ = μ 8 e - 2 + o ( 1 ) exp π 2 μ a in the low density limit $$\mu \rightarrow 0$$ μ → 0 . Together with the similar result for the critical temperature by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in the low density limit, the ratio of the energy gap and critical temperature is a universal constant independent of the interaction potential V. The results hold for a class of potentials with negative scattering length a and no bound states.

Bose-Einstein Condensation of Confined Atomic Gases at Ultra Low Temperatures

In this work I solve the Gross-Pitaevskii equation describing an atomic gas confined in an isotropic harmonic trap by introducing a variational wavefunction of Gaussian type. The chemical potential of the system is calculated and the solutions are discussed in the weakly and strongly interacting regimes. For the attractive system with negative scattering length the maximum number of atoms that can be put in the condensate without collapse begins is calculated.

Structural studies of CaAl12O19, SrAl12O19, La2/3+δ Al12–δO19, and CaAl10NiTiO19 with the hibonite structure; indications of an unusual type of ferroelectricity

Various oxides with the hibonite structure were synthesized and structurally analyzed using powder neutron diffraction. The structure of CaAl12O19 at 298 and 11 K shows dipoles that are apparently too dilute to order unless subjected to a suitable electric field. Magnetoplumbites, such as BaFe12O19, are isostructural with hibonite. These compounds possess ferromagnetic properties, which combined with the electric dipoles may influence multiferroic behavior. Our SrAl12O19 sample showed two distinct hexagonal phases, a major phase with the normal hibonite structure and a minor phase having a closely related structure. Our sample of the defect hibonite phase La2/3+δAl12–δO19 shows a distinctly higher δ value (0.25) vs. that reported (~0.15) for samples made from the melt. Finally, we used to advantage the negative scattering length of Ti to determine the site occupancies of Ni and Ti in CaAl10NiTiO19.

Finite-range model potentials for resonant interactions

We show that it is possible to model two-body resonant interactions at low energy with a class of finite-range potentials based on the methods of Jost and Kohn. These potentials are expressed in terms of the effective range [Formula: see text] and the [Formula: see text]-wave scattering length [Formula: see text]. We derive continuum solutions of these potentials. By writing [Formula: see text], where the sign [Formula: see text] refers to positive(negative) scattering length, [Formula: see text] is of the form of Pöschl–Teller potential and [Formula: see text] is expressed as a power series of the small parameter [Formula: see text] when [Formula: see text] is large, we derive Green’s function of [Formula: see text]. Using the Green’s function, solutions of [Formula: see text] for [Formula: see text] can be obtained numerically by treating [Formula: see text] as a perturbation. We describe the threshold behavior of scattering phase shift for [Formula: see text]. This study may be important for developing a better understanding of physics of strongly interacting ultracold atomic gases with tunable interactions.

A systematic neutron reflectometry study on hydrogen absorption in thin Mg1-xAlx alloy films Special issue on Neutron Scattering in Canada.

In this article, we show how neutron reflectometry (NR) can provide deep insight into the absorption and desorption properties of commercially promising hydrogen storage materials. NR benefits from the large negative scattering length of hydrogen atoms, which changes the reflectivity curve substantially, so that NR can determine not only the total amount of stored hydrogen but also the hydrogen distribution along the film normal, with nanometer resolution. To use NR, the samples must have smooth surfaces, and the film thickness should range between 10 and 200 nm. We performed a systematic study on thin Mg1–xAlx alloy films (x = 0.2, 0.3, 0.4, 0.67) capped with a Pd catalyst layer. Our NR experiments showed that Mg0.7Al0.3 is the optimum alloy composition with the highest amount of stored hydrogen and the lowest desorption temperature. All the thin films expand by about 20% because of hydrogen absorption, and the hydrogen is stored only in the MgAl layer with no hydrogen content in the Pd layer.