Solving complex-valued differential systems

Linear two-point boundary-value problems defined in complex space arise frequently in physical studies. We examine initial-value procedures based on superposition principles applied to the associated real system of equations. We show how to take advantage of the fact that the underlying problem is complex, thereby cutting the usual number of necessary integrations of the homogeneous system by one-half. We also discuss several aspects of incorporating these ideas into a computer code utilizing an orthonormalization procedure.     

Ultrasonic attenuation near the cholesteric → smectic A transition

Ultrasonic attenuation at 2 MHz has been measured through the cholesteric → smectic A transition in cholestryl nonanoate. Very near the transition, 0.1 < (T ? T_c) < 0.6°C, the excess attenuation varies as (T ? T_c)ⁿ, where n for four separate runs varies between 0.30 and 0.34. These values are very close to the exponent of 0.33 predicted using a scaling laws and observed for the divergence of the twist viscosity in the nematic phase as the smectic A transition is approached.     

Auger emission and colour centres in lithium fluoride

Low energy Auger transitions from lithium fluoride, below 50 eV, have been associated by Gallon and Matthew [Phys. Status Solidi 41 (1970) 343] with transition processes between an ionised lithium ion and neighbouring fluorine ions. Two of these transitions, giving rise to lines at 36 eV and 43 eV were thought to involve de-excitation via colour centre defects. The growth behaviour of these lines has been investigated as a function of temperature, between 200°K and 600°K, and correlations have been established between this behaviour and optical absorption data obtained in situ. The effects of deposited nickel films on the Auger spectrum have also been investigated, and it is concluded that the 43 eV transition arises from lithium metal produced by electron beam dissociation of the lithium fluoride while the 36 eV line does indeed arise from de-excitation via a defect centre.     

High resolution mass spectrometry—III: Loss of water from a nitro compound under electron-impact

Deuterium labelling has been utilised to elucidate the mechanism by which a molecule of water is eliminated from a heterocyclic nitro compound under electron-impact.     

Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.     

The thermodynamics of aqueous borate solutions. II. Mixtures of boric acid with calcium or magnesium borate and chloride

Potentials for the cell without liquid juction

Experimental confirmation of the predicted shallow donor hydrogen state in zinc oxide

We confirm the recent prediction that interstitial protium may act as a shallow donor in zinc oxide, by direct spectroscopic observation of its muonium counterpart. On implantation into ZnO, positive muons--chemically analogous to protons in this context--form paramagnetic centers below about 40 K. The muon-electron contact hyperfine interaction, as well as the temperature and activation energy for ionization, imply a shallow level. Similar results for the cadmium chalcogenides suggest that such shallow donor states are generic to the II-VI compounds. The donor level depths should serve as a guide for the electrical activity of interstitial hydrogen.