The electron-nucleon cross section in (e,e′p)(e,e'p) reactions

We examine commonly used approaches to deal with the scattering of electrons from a bound nucleon. Several prescriptions are shown to be related by gauge transformations. Nevertheless, due to current non-conservation, they yield different results. These differences reflect the size of the uncertainty that persists in the interpretation of $(e,e'p)$ experiments.Comment: 6 pp (10 in preprint form), ReVTeX, (+ 4 figures, uuencoded

Local gauge invariance implies Siegert's hypothesis

The nonrelativistic Ward-Takahashi identity, a consequence of local gauge invariance in quantum mechanics, shows the necessity of exchange current contributions in case of nonlocal and/or isospin-dependent potentials. It also implies Siegert's hypothesis: in the nonrelativistic limit, two-body charge densities identically vanish. Neither current conservation, which follows from global gauge invariance, nor the constraints of (lowest order) relativity are sufficient to arrive at this result. Furthermore, a low-energy theorem for exchange contributions is established.Comment: 5 pages, REVTE

Nuclear currents based on the integral form of the continuity equation

We present an approach to obtain new forms of the nuclear electromagnetic current, which is based on an integral form of the continuity equation. The procedure can be used to restore current conservation in model calculations in which the continuity equation is not verified. Besides, it provides, as a particular result, the so-called Siegert's form of the nuclear current, first obtained by Friar and Fallieros by extending Siegert's theorem to arbitrary values of the momentum transfer. The new currents are explicitly conserved and permit a straightforward analysis of their behavior at both low and high momentum transfers. The results are illustrated with a simple nuclear model which includes a harmonic oscillator mean potential.Comment: 19 pages, revtex, plus 2 PS figure

Rayleigh scattering in the transit spectrum of HD 189733b

The transit spectrum of the exoplanet HD 189733b has recently been obtained between 0.55 and 1.05 microns. Here we present an analysis of this spectrum. We develop first-order equations to interpret absorption spectra. In the case of HD 189733b, we show that the observed slope of the absorption as a function of wavelength is characteristic of extinction proportional to the inverse of the fourth power of the wavelength (lambda^-4). Assuming an extinction dominated by Rayleigh scattering, we derive an atmospheric temperature of 1340+/-150 K. If molecular hydrogen is responsible for the Rayleigh scattering, the atmospheric pressure at the planetary characteristic radius of 0.1564 stellar radius must be 410+/-30 mbar. However the preferred scenario is scattering by condensate particles. Using the Mie approximation, we find that the particles must have a low value for the imaginary part of the refraction index. We identify MgSiO3 as a possible abundant condensate whose particle size must be between 0.01 and 0.1 microns. For this condensate, assuming solar abundance, the pressure at 0.1564 stellar radius is found to be between a few microbars and few millibars, and the temperature is found to be in the range 1340-1540 K, and both depend on the particle size.Comment: Accepted for publication in A&A Lette

Nuclear effects in positive pion electroproduction on the deuteron near threshold

Positive pion electroproduction from the deuteron near threshold has been considered within an approach based on the unitary transformation method. The gauge independence of the treatment is provided by using an explicitly gauge independent expression for the reaction amplitude. The results of calculations for kinematics of the experiments on forward-angle $\pi^+$ meson electroproduction accomplished at Saclay and Jefferson Laboratory are discussed and compared with those given by the impulse approximation. It is shown that the observed behaviour of the cross sections is in accordance with the calculations based on the pion-nucleon dynamics. In particular, the pion production rate suppression in the $^2H(e,e'\pi^+)nn$ reaction compared to that for the $^1H(e,e'\pi^+)n$ one can be due to such ``nuclear medium'' effects as nucleon motion and binding along with Pauli blocking in the final $nn$ state.Comment: 15 pages, 8 figure

Final State Charge Exchange Interactions in the 12C(e,e′p)^{12}C(e,e'p) Reaction

The $^{12}C(e,e'p)$ reaction is analyzed in a model which explicitly includes final state interactions due to the coupling of the proton and neutron emission channels. We find that the effects of the final state interactions due to charge exchange reactions are important to get a good description of the symmetry properties of the recently measured Mainz spectral functions. We discuss the possible role the off-shell effects may play for the correct interpretation of spectral functions at large positive missing momenta.Comment: 9 pages Revtex, 4 figure

Measuring portfolio performance using a modified measure of risk

This paper reports the results of an investigation into the properties of a theoretical modification of beta proposed by Leland (1999) and based on earlier work of Rubinstein (1976). It is shown that when returns are elliptically symmetric, beta is the appropriate measure of risk and that there are other situations in which the modified beta will be similar to the traditional measure based on the capital asset pricing model. For the case where returns have a normal distribution, it is shown that the criterion either does not exist or reduces exactly to the conventional beta. It is therefore conjectured that the modified measure will only be useful for portfolios that have nonstandard return distributions which incorporate skewness. For such situations, it is shown how to estimate the measure using regression and how to compare the resulting statistic with a traditional estimated beta using Hotelling's test. An empirical study based on stocks from the FTSE350 does not find evidence to support the use of the new measure even in the presence of skewness.Journal of Asset Management (2007) 7, 388-403. doi:10.1057/palgrave.jam.225005

Relativistic Effects in the Electromagnetic Current at GeV Energies

We employ a recent approach to the non-relativistic reduction of the electromagnetic current operator in calculations of electronuclear reactions. In contrast to the traditional scheme, where approximations are made for the transferred momentum, transferred energy and initial momentum of the struck nucleon in obtaining an on-shell inspired form for the current, we treat the problem exactly for the transferred energy and transferred momentum. We calculate response functions for the reaction $^2H(e,e'p)n$ at CEBAF (TJNAF) energies and find large relativistic corrections. We also show that in Plane Wave Impulse Approximation, it is always possible to use the full operator, and we present a comparison of such a limiting case with the results incorporating relativistic effects to the first order in the initial momentum of the struck nucleon.Comment: 31 pages, 8 figures, Revte