Axially Symmetric Deformations of Fibre-reinforced Cylinders

General solutions are obtained for boundary-value problems givingaxially symmetric deformations of "ideal" fibre-reinforced cylinders.The cylinders are hollow, thick-walled and elastic, and arecontinuously reinforced throughout by two families of helicalfibres making an angle ±ø with the axis of symmetry.We consider traction boundary-value problems and in particularobtain two fundamental solutions corresponding to axial andradial concentrated loadings. The theory is applied to the problemof inflation of the cylinder under uniform internal pressure.     

The dipole polarizability of the hydrogen molecular cation HD+ and other isotopomers

Fully non-adiabatic calculations are reported of the electric dipole polarizabilities for the N = 0 and N = 1 levels of the ground electronic states of H⁺ ₂ (ν ≤ 16), D⁺ ₂ (ν ≤ 24) and HD⁺ (ν ≤ 20). For H⁺ ₂ (ν = 0, N = 0) the calculated value still differs from the experimental value; this difference cannot be explained by the inclusion of higher order contributions.     

Energy shifts and forbidden transitions in H+ 2 due to electronic g/u symmetry breaking

A full account is given of calculations and measurements of transition frequencies and intensities of the forbidden pure rotation transition (v = 19, N = 1)-(v = 19, N = 0) in the ground electronic state (1sσ_g) of H⁺ ₂. The transition has measurable intensity because of ortho-paru mixing that arises from electronic g/u symmetry breaking caused by the Fermi contact hyper-fine interaction. Measurements of the transition were made in both single and double resonance using a fast ion beam/microwave spectrometer. The transition frequency was determined to be at 14961.7 ± 1.1 MHz (95% confidence, 5 measurements), in excellent agreement with the theoretical prediction of 14960 ± 3 MHz. The intensity of the transition relative to the allowed 1sσ_g (v = 19, N = 1)-2pσ_u,(v = 0, N = 2) transition was estimated from the available measurements to be 8000, in reasonable agreement with the theoretically predicted value of ?3000.     

Adiabatic and non-adiabatic corrections to properties of the hydrogen molecular cation and its isotopomers: dissociation energies and bond lengths

A study is presented of adiabatic and non-adiabatic corrections to the dissociation energies and bond lengths of H⁺ ₂, D⁺ ₂ and HD⁺ in vibration-rotation levels of their ground electronic states, with particular attention to isotopic scaling. In previous work (MOSS, R. E., 1999, Molec. Phys., 97, 1) on rotationless levels, an anomalous non-adiabatic correction to the bond length was found for v = 20, N = 0 of HD⁺. Other levels close to dissociation are identified that display anomalous non-adiabatic corrections to the dissociation energies and to the bond lengths. The source of these anomalies is discussed.     

Relativistic corrections for the vibration-rotation levels of the ground electronic state of the hydrogen molecular cation H+ 2

Previous work [Moss, R. E., and Valenzano, L., 2002, Molec. Phys., 100, 649 and 1527] on the non-adiabatic properties of the vibration-rotation levels of the ground electronic state of the hydrogen molecular cation is extended to the calculation of relativistic corrections. Unlike the earlier calculations, in which all matrix elements were evaluated analytically, numerical methods are needed for some of the integrals.