Classical Monopoles: Newton, NUT-space, gravomagnetic lensing and atomic spectra

Stimulated by a scholium in Newton's Principia we find some beautiful results in classical mechanics which can be interpreted in terms of the orbits in the field of a mass endowed with a gravomagnetic monopole. All the orbits lie on cones! When the cones are slit open and flattened the orbits are exactly the ellipses and hyperbolae that one would have obtained without the gravomagnetic monopole. The beauty and simplicity of these results has led us to explore the similar problems in Atomic Physics when the nuclei have an added Dirac magnetic monopole. These problems have been explored by others and we sketch the derivations and give details of the predicted spectrum of monopolar hydrogen. Finally we return to gravomagnetic monopoles in general relativity. We explain why NUT space has a non-spherical metric although NUT space itself is the spherical space-time of a mass with a gravomagnetic monopole. We demonstrate that all geodesics in NUT space lie on cones and use this result to study the gravitational lensing by bodies with gravomagnetic monopoles. We remark that just as electromagnetism would have to be extended beyond Maxwell's equations to allow for magnetic monopoles and their currents so general relativity would have to be extended to allow torsion for general distributions of gravomagnetic monopoles and their currents. Of course if monopoles were never discovered then it would be a triumph for both Maxwellian Electromagnetism and General Relativity as they stand!Comment: 39 pages, 9 figures and 2 tables available on request from the author

Quantum singular oscillator as a model of two-ion trap: an amplification of transition probabilities due to small time variations of the binding potential

Following the paper by M. Combescure [Ann. Phys. (NY) 204, 113 (1990)], we apply the quantum singular time dependent oscillator model to describe the relative one dimensional motion of two ions in a trap. We argue that the model can be justified for low energy excited states with the quantum numbers $n\ll n_{max}\sim 100$, provided that the dimensionless constant characterizing the strength of the repulsive potential is large enough, $g_*\sim 10^5$. Time dependent Gaussian-like wave packets generalizing odd coherent states of the harmonic oscillator, and excitation number eigenstates are constructed. We show that the relative motion of the ions, in contradistinction to its center of mass counterpart, is extremely sensitive to the time dependence of the binding harmonic potential, since the large value of $g_*$ results in a significant amplification of the transition probabilities between energy eigenstate even for slow time variations of the frequency.Comment: 19 pages, LaTeX, 5 eps-figures, to appear on Phys. Rev. A, one reference correcte

Physical and Chemical Characterization of Therapeutic Iron Containing Materials: A Study of Several Superparamagnetic Drug Formulations with the Β-FeOOH Or Ferrihydrite Structure

The effectiveness of therapeutically used iron compounds is related to their physical and chemical properties. Four different iron compounds used in oral, intravenous, and intramuscular therapy have been examined by X-ray powder diffraction, iron-57 M6ssbauer spectroscopy, transmission electron microscopy, BET surface area measurement, potentiometric titration and studied through dissolution kinetics determinations using acid, reducing and chelating agents. All compounds are nanosized with particle diameters, as determined by X-ray diffraction, ranging from 1 to 4.1 nm. The superparamagnetic blocking temperatures, as determined by Mössbauer spectroscopy, indicate that the relative diameters of the aggregates range from 2.5 to 4.1 nm. Three of the iron compounds have an akaganeite-like structure, whereas one has a ferrihydrite-like structure. As powders the particles form large and dense aggregates which have a very low surface area on the order of 1 m2 g-1. There is evidence, however, that in a colloidal solution the surface area is increased by two to three orders of magnitude, presumably as a result of the break up of the aggregates. Iron release kinetics by acid, chelating and reducing agents reflect the high surface area, the size and crystallinity of the particles, and the presence of the protective carbohydrate layer coating the iron compound. Within a physiologically relevant time period, the iron release produced by acid or large chelating ligands is small. In contrast, iron is rapidly mobilized by small organic chelating agents, such as oxalate, or by chelate-forming reductants, such as thioglycolate

Structural Modification and Self-Assembly of Nanoscale Magnetite Synthesised in the Presence of an Anionic Surfactant

The earliest reported medical use of magnetite powder for internal applications was in the 10th century A.D. by the Persian physician and philosopher Avicenna of Bokhara [1,2]. Today magnetic nanoparticles are used for magnetic resonance imaging (MRI) and are potential colloidal mediators for cancer magnetic hyperthermia [3]. Twenty years ago magnetite (Fe3O4) was found to be present in the human brain [4] and more recently it has been reported that nanoscale biogenic magnetite (origin and formation uncertain) is associated with neurodegenerative diseases such as Parkinson’s, Huntington’s and Alzheimer’s [5]. Here we show that the synthesis of magnetite in the presence of the surfactant sodium dodecyl sulphate (SDS) gives rise to a variety of nanoscale morphologies, some of which look remarkably similar to magnetite found in organisms, suggesting that similar processes may be involved. Furthermore, these 1D materials with diameters of quantum confined size are of interest in the areas of biosensors [6] and biomedical imaging [7]