An improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi beta decay

We report new shell-model calculations of the isospin-symmetry-breaking correction to superallowed nuclear beta decay. The most important improvement is the inclusion of core orbitals, which are demonstrated to have a significant impact on the mismatch in the radial wave functions of the parent and daughter states. We determine which core orbitals are important to include from an examination of measured spectroscopic factors in single-nucleon pick-up reactions. We also examine the new radiative-correction calculation by Marciano and Sirlin and, by a simple reorganization, show that it is possible to preserve the conventional separation into a nucleus-independent inner radiative term and a nucleus-dependent outer term. We tabulate new values for the three theoretical corrections for twenty superallowed transitions, including the thirteen well-studied cases. With these new correction terms the corrected Ft values for the thirteen cases are statistically consistent with one another and the anomalousness of the 46V result disappears. These new calculations lead to a lower average Ft value and a higher value of Vud. The sum of squares of the top-row elements of the CKM matrix now agrees exactly with unitarity.Comment: 15 pages, 2 postscript figures, revtex

Langmuir Wave Generation Through A Neutrino Beam Instability

A standard version of a kinetic instability for the generation of Langmuir waves by a beam of electrons is adapted to describe the analogous instability due to a beam of neutrinos. The interaction between a Langmuir wave and a neutrino is treated in the one-loop approximation to lowest order in an expansion in $1/M_W^2$ in the standard electroweak model. It is shown that this kinetic instability is far too weak to occur in a suggested application to the reheating of the plasma behind a stalled shock in a type II supernova (SN). This theory is also used to test the validity of a previous analysis of a reactive neutrino beam instability and various shortcomings of this theory are noted. In particular, it is noted that relativistic plasma effects have a significant effect on the calculated growth rates, and that any theoretical description of neutrino-plasma interactions must be based directly on the electroweak theory. The basic scalings discussed in this paper suggest that a more complete investigation of neutrino-plasma processes should be undertaken to look for an efficient process capable of driving the stalled shock of a type II SN.Comment: 23 pages, incl. 5 postscript figure

A new analysis of 14O beta decay: branching ratios and CVC consistency

The ground-state Gamow-Teller transition in the decay of 14O is strongly hindered and the electron spectrum deviates markedly from the allowed shape. A reanalysis of the only available data on this spectrum changes the branching ratio assigned to this transition by seven standard deviations: our new result is (0.54 \pm 0.02)%. The Kurie plot data from two earlier publications are also examined and a revision to their published branching ratios is recommended. The required nuclear matrix elements are calculated with the shell model and, for the first time, consistency is obtained between the M1 matrix element deduced from the analog gamma transition in 14N and that deduced from the slope of the shape-correction function in the beta transition, a requirement of the conserved vector current hypothesis. This consistency is only obtained, however, if renormalized rather than free-nucleon operators are used in the shell-model calculations. In the mirror decay of 14C a similar situation occurs. Consistency between the 14C lifetime, the slope of the shape-correction function and the M1 matrix element from gamma decay can only be achieved with renormalized operators in the shell-model calculation.Comment: 9 pages; revtex4; one figur

On the theory of composition in physics

We develop a theory for describing composite objects in physics. These can be static objects, such as tables, or things that happen in spacetime (such as a region of spacetime with fields on it regarded as being composed of smaller such regions joined together). We propose certain fundamental axioms which, it seems, should be satisfied in any theory of composition. A key axiom is the order independence axiom which says we can describe the composition of a composite object in any order. Then we provide a notation for describing composite objects that naturally leads to these axioms being satisfied. In any given physical context we are interested in the value of certain properties for the objects (such as whether the object is possible, what probability it has, how wide it is, and so on). We associate a generalized state with an object. This can be used to calculate the value of those properties we are interested in for for this object. We then propose a certain principle, the composition principle, which says that we can determine the generalized state of a composite object from the generalized states for the components by means of a calculation having the same structure as the description of the generalized state. The composition principle provides a link between description and prediction.Comment: 23 pages. To appear in a festschrift for Samson Abramsky edited by Bob Coecke, Luke Ong, and Prakash Panangade

Gravitational Microlensing Near Caustics I: Folds

We study the local behavior of gravitational lensing near fold catastrophes. Using a generic form for the lensing map near a fold, we determine the observable properties of the lensed images, focusing on the case when the individual images are unresolved, i.e., microlensing. Allowing for images not associated with the fold, we derive analytic expressions for the photometric and astrometric behavior near a generic fold caustic. We show how this form reduces to the more familiar linear caustic, which lenses a nearby source into two images which have equal magnification, opposite parity, and are equidistant from the critical curve. In this case, the simplicity and high degree of symmetry allows for the derivation of semi-analytic expressions for the photometric and astrometric deviations in the presence of finite sources with arbitrary surface brightness profiles. We use our results to derive some basic properties of astrometric microlensing near folds, in particular we predict for finite sources with uniform and limb darkening profiles, the detailed shape of the astrometric curve as the source crosses a fold. We find that the astrometric effects of limb darkening will be difficult to detect with the currently planned accuracy of the Space Interferometry Mission. We verify our results by numerically calculating the expected astrometric shift for the photometrically well-covered Galactic binary lensing event OGLE-1999-BUL-23, finding excellent agreement with our analytic expressions. Our results can be applied to any lensing system with fold caustics, including Galactic binary lenses and quasar microlensing.Comment: 37 pages, 7 figures. Revised version includes an expanded discussion of applications. Accepted to ApJ, to appear in the August 1, 2002 issue (v574

Anthropometric discriminators of type 2 diabetes among White and Black American adults

BACKGROUND: The aim of the present study was to determine the best anthropometric discriminators of type 2 diabetes mellitus (T2DM) among White and Black males and females in a large US sample. METHODS: We used Atherosclerosis Risk in Communities study baseline data (1987–89) from 15 242 participants (1827 with T2DM) aged 45–65 years. Anthropometric measures included a body shape index (ABSI), body adiposity index (BAI), body mass index, waist circumference (WC), waist:height ratio (WHtR), and waist:hip ratio (WHR). All anthropometric measures were standardized to Z-scores. Using logistic regression, odds ratios for T2DM were adjusted for age, physical activity, and family history of T2DM. The Akaike information criterion and receiver operating characteristic C-statistic were used to select the best-fit models. RESULTS: Body mass index, WC, WHtR, and WHR were comparable discriminators of T2DM among White and Black males, and were superior to ABSI and BAI in predicting T2DM (P < 0.0001). Waist circumference, WHtR, and WHR were the best discriminators among White females, whereas WHR was the best discriminator among Black females. The ABSI was the poorest discriminator of T2DM for all race–gender groups except Black females. Anthropometric values distinguishing T2DM cases from non-cases were lower for Black than White adults. CONCLUSIONS: Anthropometric measures that included WC, either alone or relative to height (WHtR) or hip circumference (WHR), were the strongest discriminators of T2DM across race–gender groups. Body mass index was a comparable discriminator to WC, WHtR, and WHR among males, but not females

Survival Probability for Open Spherical Billiards

We study the survival probability for long times in an open spherical billiard, extending previous work on the circular billiard. We provide details of calculations regarding two billiard configurations, specifically a sphere with a circular hole and a sphere with a square hole. The constant terms of the long-term survival probability expansions have been derived analytically. Terms that vanish in the long time limit are investigated analytically and numerically, leading to connections with the Riemann hypothesis