The RMS Charge Radius of the Proton and Zemach Moments

On the basis of recent precise measurements of the electric form factor of the proton, the Zemach moments, needed as input parameters for the determination of the proton rms radius from the measurement of the Lamb shift in muonic hydrogen, are calculated. It turns out that the new moments give an uncertainty as large as the presently stated error of the recent Lamb shift measurement of Pohl et al.. De Rujula's idea of a large Zemach moment in order to reconcile the five standard deviation discrepancy between the muonic Lamb shift determination and the result of electronic experiments is shown to be in clear contradiction with experiment. Alternative explanations are touched upon.Comment: 6 pages, 4 figures, final version includes discussion of systematic and numerical error

Effective theories of scattering with an attractive inverse-square potential and the three-body problem

A distorted-wave version of the renormalisation group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wave function satisfies a Schroedinger equation with an attractive inverse-square potential, as shown by Efimov. The resulting oscillatory behaviour controls the renormalisation of the three-body interactions, with the renormalisation-group flow tending to a limit cycle as the cut-off is lowered. The approach used here leads to single-valued potentials with discontinuities as the bound states are cut off. The perturbations around the cycle start with a marginal term whose effect is simply to change the phase of the short-distance oscillations, or the self-adjoint extension of the singular Hamiltonian. The full power counting in terms of the energy and two-body scattering length is constructed for short-range three-body forces.Comment: 19 pages (RevTeX), 2 figure

Self-adjoint extensions and spectral analysis in Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential $\alpha x^{-2}$. Although the problem is quite old and well-studied, we believe that our consideration, based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some "paradoxes" inherent in the "naive" quantum-mechanical treatment. We study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In addition, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.Comment: 39 page

Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length

We study the problem of the attractive inverse square potential in quantum mechanics with a generalized uncertainty relation. Using the momentum representation, we show that this potential is regular in this framework. We solve analytically the s-wave bound states equation in terms of Heun's functions. We discuss in detail the bound states spectrum for a specific form of the generalized uncertainty relation. The minimal length may be interpreted as characterizing the dimension of the system.Comment: 30 pages, 3 figure

Dirac-Foldy term and the electromagnetic polarizability of the neutron

We reconsider the Dirac-Foldy contribution $\mu^2/m$ to the neutron electric polarizability. Using a Dirac equation approach to neutron-nucleus scattering, we review the definitions of Compton continuum ($\bar{\alpha}$), classical static ($\alpha^n_E$), and Schr\"{o}dinger ($\alpha_{Sch}$) polarizabilities and discuss in some detail their relationship. The latter $\alpha_{Sch}$ is the value of the neutron electric polarizability as obtained from an analysis using the Schr\"{o}dinger equation. We find in particular $\alpha_{Sch} = \bar{\alpha} - \mu^2/m$ , where $\mu$ is the magnitude of the magnetic moment of a neutron of mass $m$. However, we argue that the static polarizability $\alpha^n_E$ is correctly defined in the rest frame of the particle, leading to the conclusion that twice the Dirac-Foldy contribution should be added to $\alpha_{Sch}$ to obtain the static polarizability $\alpha^n_E$.Comment: 11 pages, RevTeX, to appear in Physical Review

Meson exchange and nucleon polarizabilities in the quark model

Modifications to the nucleon electric polarizability induced by pion and sigma exchange in the q-q potentials are studied by means of sum rule techniques within a non-relativistic quark model. Contributions from meson exchange interactions are found to be small and in general reduce the quark core polarizability for a number of hybrid and one-boson-exchange q-q models. These results can be explained by the constraints that the baryonic spectrum impose on the short range behavior of the mesonic interactions.Comment: 11 pages, 1 figure added, expanded discussio

Black-hole concept of a point-like nucleus with supercritical charge

The Dirac equation for an electron in the central Coulomb field of a point-like nucleus with the charge greater than 137 is considered. This singular problem, to which the fall-down onto the centre is inherent, is addressed using a new approach, based on a black-hole concept of the singular centre and capable of producing cut-off-free results. To this end the Dirac equation is presented as a generalized eigenvalue boundary problem of a self-adjoint operator. The eigenfunctions make complete sets, orthogonal with a singular measure, and describe particles, asymptotically free and delta-function-normalizable both at infinity and near the singular centre $r=0$. The barrier transmission coefficient for these particles responsible for the effects of electron absorption and spontaneous electron-positron pair production is found analytically as a function of electron energy and charge of the nucleus. The singular threshold behaviour of the corresponding amplitudes substitutes for the resonance behaviour, typical of the conventional theory, which appeals to a finite-size nucleus.Comment: 22 pages, 5 figures, LATEX requires IOPAR

Nucleon Charge and Magnetization Densities from Sachs Form Factors

Relativistic prescriptions relating Sachs form factors to nucleon charge and magnetization densities are used to fit recent data for both the proton and the neutron. The analysis uses expansions in complete radial bases to minimize model dependence and to estimate the uncertainties in radial densities due to limitation of the range of momentum transfer. We find that the charge distribution for the proton is significantly broad than its magnetization density and that the magnetization density is slightly broader for the neutron than the proton. The neutron charge form factor is consistent with the Galster parametrization over the available range of Q^2, but relativistic inversion produces a softer radial density. Discrete ambiguities in the inversion method are analyzed in detail. The method of Mitra and Kumari ensures compatibility with pQCD and is most useful for extrapolating form factors to large Q^2.Comment: To appear in Phys. Rev. C. Two new figures and accompanying text have been added and several discussions have been clarified with no significant changes to the conclusions. Now contains 47 pages including 21 figures and 2 table

Acute Exposure to Terrestrial Trunked Radio (TETRA) has effects on the electroencephalogram and electrocardiogram, consistent with vagal nerve stimulation

BACKGROUND: Terrestrial Trunked Radio (TETRA) is a telecommunications system widely used by police and emergency services around the world. The Stewart Report on mobile telephony and health raised questions about possible health effects associated with TETRA signals. This study investigates possible effects of TETRA signals on the electroencephalogram and electrocardiogram in human volunteers. METHODS: Blinded randomized provocation study with a standardized TETRA signal or sham exposure. In the first of two experiments, police officers had a TETRA set placed first against the left temple and then the upper-left quadrant of the chest and the electroencephalogram was recorded during rest and active cognitive processing. In the second experiment, volunteers were subject to chest exposure of TETRA whilst their electroencephalogram and heart rate variability derived from the electrocardiogram were recorded. RESULTS: In the first experiment, we found that exposure to TETRA had consistent neurophysiological effects on the electroencephalogram, but only during chest exposure, in a pattern suggestive of vagal nerve stimulation. In the second experiment, we observed changes in heart rate variability during exposure to TETRA but the electroencephalogram effects were not replicated. CONCLUSIONS: Observed effects of exposure to TETRA signals on the electroencephalogram (first experiment) and electrocardiogram are consistent with vagal nerve stimulation in the chest by TETRA. However given the small effect on heart rate variability and the lack of consistency on the electroencephalogram, it seems unlikely that this will have a significant impact on health. Long-term monitoring of the health of the police force in relation to TETRA use is on-going

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

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