Majorana: From Atomic and Molecular, to Nuclear Physics

In the centennial of Ettore Majorana’s birth (1906–1938?), we re-examine some aspects of his fundamental scientific production in atomic and molecular physics, including a not well known short communication. There, Majorana critically discusses Fermi’s solution of the celebrated Thomas–Fermi equation for electron screening in atoms and positive ions. We argue that some of Majorana’s seminal contributions in molecular physics already prelude to the idea of exchange interactions (or Heisenberg–Majorana forces) in his later works on theoretical nuclear physics. In all his papers, he tended to emphasize the symmetries at the basis of a physical problem, as well as the limitations, rather than the advantages, of the approximations of the method employed.     

A new solution to the Anderson-Newns Hamiltonian of chemisorption

A new solution to the Anderson-Newns Hamiltonian of chemisorption is proposed by using the Green-function formalism and an adequate approximation to the adatom self-energy. The method has been checked in simple models. Our results give both the quasi-particle spectrum and the chemisorption energy with a high accuracy better than 99.9%.     

A complete Lagrangian formulation of superconductivity

We present here a complete Lagrangian formulation of superconductivity. Only the boson degrees of freedom are explicitly introduced. The BCS solution is obtained as classical approximation. The physical interpretation of the Goldstone boson comes up naturally from this theory.     

Simultaneous determination of all-trans-retinoic acid, beta-carotene, and vitamin A in galenic preparations by liquid chromatography

The concentrations of vitamin A, beta-carotene, and all-trans-retinoic acid in oral preparations were determined in a single analysis by a method based on isocratic, reversed-phase liquid chromatography (LC). The LC system consisted of a C18 column, a mobile phase of acetonitrile, dichloromethane, methanol, and water and a UV detector set at 330 nm. The linearity ranges were 25-250 ng/mL for trans-retinoic acid and vitamin A, and 100-1,000 ng/mL for beta-carotene. This LC method for the determination of retinoids is simple, precise, and accurate. No extraction procedure is required before the chromatographic analysis; only a suitable dilution is necessary. The method proved to be reliable, fast, and economical. Furthermore, this method is indicative of stability, because it allows for the determination of degradation products such as 13-cis-retinoic acid.     

Relation between molecular and atomic correlation energies via overlap population

A relationship is explored between correlation energies of light diatomic molecules, both hetero and homo, correlation energies of the constituent atoms and the overlap population S. While S is quantitatively sensitive to the choice of basis set, it is demonstrated that the general trends revealed are largely independent of such a choice. A weak residual dependence on molecular chemical potential is also indicated by the present study.     

Continuous glucose monitoring by means of mid-infrared transmission laser spectroscopy in vitro

The continuous surveillance of glucose concentration reduces short-term risks and long-term complications for people with diabetes mellitus, a disorder of glucose metabolism. As a first step towards the continuous monitoring of glucose, reagent-free transmission spectroscopy in the mid-infrared region has been carried out in vitro using a quantum cascade laser and an optical silver halide fiber. A 30 μm gap in the fiber allowed for transmission spectroscopy of aqueous glucose solutions at a wavelength of 9.69 μm, which is specific to a molecular vibration of glucose. A noise-equivalent concentration as low as 4 mg/dL was achieved at an average power of 1.8 mW and an integration time of 50 s. This is among the most precise of glucose measurements using mid-infrared spectroscopy. Even with the very low average laser power of 0.07 mW the sensitivity of previous results (using a fiber optical evanescent field analysis) has been improved upon by almost one order of magnitude. Finally, the impact of potentially interfering substances such as other carbohydrates was analyzed.     

Mutual adaptation of a Faraday instability pattern with its flexible boundaries in floating fluid drops

Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This is implemented by triggering this instability in floating fluid drops. An interaction of Faraday waves with the shape of the drop is observed, the radiation pressure of the waves exerting a force on the surface tension held boundaries. Two regimes are observed. In the first one there is a coadaptation of the wave pattern with the shape of the domain so that a steady configuration is reached. In the second one the radiation pressure dominates and no steady regime is reached. The drop stretches and ultimately breaks into smaller domains that have a complex dynamics including spontaneous propagation.