Pion–Pion Interaction in a Soluble Two-Level Nambu–Jona-Lasinio Model

We explore the interplay between the few-body aspects of few-pion states and the many-body aspects of their quark structure. We show for a schematic quasispin model similar to the Nambu–Jona-Lasinio model how one can derive rather accurately the pion–pion scattering length from the excitation spectrum in a box.     

Gas-phase reactivity of lactones: structure and stability of their Cu+ complexes

The structure and relative stability of different lactone-Cu⁺ complexes, including cycles changing from four to six-membered rings, have been investigated through the use of density functional theory methods. The geometries and vibrational frequencies were calculated at the B3LYP/6-311G(d,p) level. Final energies were obtained in single point calculations carried out at the B3LYP/6-311+G(2df,2p) level of theory. Upon interaction with Cu⁺ in the gas phase, lactones behave in a rather similar way as they do in protonation processes. Systematically the global minimum of the potential energy surface corresponds to the attachment of the metal cation to the carbonyl oxygen cis with respect to the ether-like oxygen. Also, similarly to proton affinities, the calculated Cu⁺ binding energies increase with the size of the system. The unsaturated compounds are found to be only slightly more basic than the saturated counterparts. Cu⁺ attachment leads to significant bond activation and bond reinforcement effects, reflected in redshiftings and blueshiftings of the stretching frequencies, respectively. Cu⁺ is able to form agostic bonds with some of the CH² groups of the lactone moiety. These agostic complexes can be good precursors for the unimolecular loss of H², which very likely should be observed in the mass spectra.     

The reactions of Cl+ (3P) and Cl+ (1D) with hydrogen sulphide. A G2 molecular orbital study

G2 ab initio molecular orbital calculations have been performed to study the potential energy surfaces (PESs) associated with the reactions of Cl⁺ in its ³P ground state and in its ¹D first excited state with hydrogen sulphide. [H₂, Cl, S]⁺ singlet and triplet state cations present very different bonding characteristics. The latter are systematically ion-dipole or hydrogen-bonded weakly bound species, while the former are covalent molecular ions. As a consequence, although the Cl⁺(³P) is 34.5 kcal mol^?1 more stable than Cl⁺(¹D), the global minimum of the singlet PES lies 37.3 kcal mol^?1 below the global minimum of the triplet PES. Both singlet and triplet potential energy surfaces show significant differences with respect to those associated with Cl⁺ + H₂O reactions as well as with SH₂ reactions with F⁺. In both cases, the major product should be SH⁺ ₂; SH⁺ and HCl⁺ being the minor products, in agreement with the experimental evidence. The estimated heat of formation for the most stable H₂SCl⁺ singlet state species is 198 ± 1 kcal mol^?1.     

Photon echoes generated by reversing magnetic field gradients in a rubidium vapor

We propose a photon echo quantum memory scheme using detuned Raman coupling to long-lived ground states. In contrast to previous three-level schemes based on controlled reversible inhomogeneous broadening that use sequences of pi pulses, the scheme does not require accurate control of the coupling dynamics to the ground states. We present a proof-of-principle experimental realization of our proposal using rubidium atoms in a warm vapor cell. The Raman resonance line is broadened using a magnetic field that varies linearly along the direction of light propagation. Inverting the magnetic field gradient rephases the atomic dipoles and re-emits the light pulse in the forward direction.