71 research outputs found
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 , provided that the dimensionless constant characterizing the
strength of the repulsive potential is large enough, . 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 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
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