Spectra generated by a confined softcore Coulomb potential

Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator potential terms, and also through `hard confinement' by means of an impenetrable spherical box. A byproduct of this work is the construction of polynomial solutions for a number of linear differential equations with polynomial coefficients, along with the necessary and sufficient conditions for the existence of such solutions. Very accurate approximate solutions for the general problem with arbitrary potential parameters are found by use of the asymptotic iteration method.Comment: 17 pages, 2 figure

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

Safety Implications of High-Field MRI: Actuation of Endogenous Magnetic Iron Oxides in the Human Body

Background: Magnetic Resonance Imaging scanners have become ubiquitous in hospitals and high-field systems (greater than 3 Tesla) are becoming increasingly common. In light of recent European Union moves to limit high-field exposure for those working with MRI scanners, we have evaluated the potential for detrimental cellular effects via nanomagnetic actuation of endogenous iron oxides in the body.Methodology: Theoretical models and experimental data on the composition and magnetic properties of endogenous iron oxides in human tissue were used to analyze the forces on iron oxide particles.Principal Finding and Conclusions: Results show that, even at 9.4 Tesla, forces on these particles are unlikely to disrupt normal cellular function via nanomagnetic actuation

A comparative Mossbauer spectral study of the electronic and magnetic properties of Nd6Fe13Ag and Nd6Fe13AgH13

The Mössbauer spectra of Nd6Fe13Ag and Nd6Fe13AgH13 have been measured between 85 and 295 K and analyzed with a model that takes into account the basal magnetic anisotropy, the iron and hydrogen near-neighbor environments of the five crystallographically and magnetically inequivalent 4d, 16k, 16k\u27, 16l1, and 16l2 iron sites in the former and the six crystallographically and magnetically inequivalent 4d, 16k, 16k\u27, 16l1, 16l2-1 and 16l2-2 iron sites in the latter, where the additional site results from a predominance of hydrogen as near-neighbors on the iron 16l2 site. The increases in hyperfine field and isomer shift observed upon hydrogenation are in agreement with the increase in Wigner-Seitz cell volumes of each site and the changes in the near-neighbor environments