Internal construct validity of the Warwick-Edinburgh Mental Well-being Scale (WEMWBS): a Rasch analysis using data from the Scottish Health Education Population Survey

Background: The Warwick-Edinburgh Mental Well-Being Scale (WEMWBS) was developed to meet demand for instruments to measure mental well-being. It comprises 14 positively phrased Likert-style items and fulfils classic criteria for scale development. We report here the internal construct validity of WEMWBS from the perspective of the Rasch measurement model. Methods: The model was applied to data collected from 779 respondents in Wave 12 (Autumn 2006) of the Scottish Health Education Population Survey. Respondents were aged 16–74 (average 41.9) yrs. Results: Initial fit to model expectations was poor. The items 'I've been feeling good about myself', 'I've been interested in new things' and 'I've been feeling cheerful' all showed significant misfit to model expectations, and were deleted. This led to a marginal improvement in fit to the model. After further analysis, more items were deleted and a strict unidimensional seven item scale (the Short Warwick Edinburgh Mental Well-Being Scale (SWEMWBS)) was resolved. Many items deleted because of misfit with model expectations showed considerable bias for gender. Two retained items also demonstrated bias for gender but, at the scale level, cancelled out. One further retained item 'I've been feeling optimistic about the future' showed bias for age. The correlation between the 14 item and 7 item versions was 0.954. Given fit to the Rasch model, and strict unidimensionality, SWEMWBS provides an interval scale estimate of mental well-being. Conclusion: A short 7 item version of WEMWBS was found to satisfy the strict unidimensionality expectations of the Rasch model, and be largely free of bias. This scale, SWEMWBS, provides a raw score-interval scale transformation for use in parametric procedures. In terms of face validity, SWEMWBS presents a more restricted view of mental well-being than the 14 item WEMWBS, with most items representing aspects of psychological and eudemonic well-being, and few covering hedonic well-being or affect. However, robust measurement properties combined with brevity make SWEMWBS preferable to WEMWBS at present for monitoring mental well-being in populations. Where face validity is an issue there remain arguments for continuing to collect data on the full 14 item WEMWBS

A Novel Longitudinal Mode in the Coupled Quantum Chain Compound KCuF3

Inelastic neutron scattering measurements are reported that show a new longitudinal mode in the antiferromagnetically ordered phase of the spin-1/2 quasi-one-dimensional antiferromagnet KCuF3. This mode signals the cross-over from one-dimensional to three-dimensional behavior and indicates a reduction in the ordered spin moment of a spin-1/2 antiferromagnet. The measurements are compared with recent quantum field theory results and are found to be in excellent agreement. A feature of the data not predicted by theory is a damping of the mode by decay processes to the transverse spin-wave branches.Comment: 9 pages of text plus 4 postscript figures (1 color

Exact two-spinon dynamical correlation function of the Heisenberg model

We derive the exact contribution of two spinons to the dynamical correlation function of the spin-1/2 Heisenberg model. For this, we use the isotropic limits of the exact form factors that have been recently computed through the quantum affine symmetry of the anisotropic Heisenberg model $XXZ$Comment: 9 pages, Latex, 2 corrections of coefficient

On the Nature of the Bright Short-Period X-ray Source in the Circinus Galaxy Field

The spectrum and light curve of the bright X-ray source CG X-1 in the field of the Circinus galaxy are re-examined. Previous analyses have concluded that the source is an accreting black hole of about 50 solar masses although it was noted that the light curve resembles that of an AM Her system. Here we show that the short period and an assumed main sequence companion constrain the mass of the companion to less than one solar mass. Further a possible eclipse seen during one of the Chandra observations and a subsequent XMM-Newton observation constrains the mass of the compact object to less than about 60 solar masses. If such a system lies in the Circinus galaxy, then the accreting object must either radiate anisotropically or strongly violate the Eddington limit. Even if the emission is beamed, then the companion star which intercepts this flux during eclipse will be driven out of thermal equilibrium and evaporate within about 1000 years. We find that the observations cannot rule out an AM Her system in the Milky Way and that such a system can account for the variations seen in the light curve.Comment: 25 pages, 8 figures, accepted for publication in the Astrophysical Journa

Chandra Phase-Resolved Spectroscopy of the Crab Pulsar

We present the first phase-resolved study of the X-ray spectral properties of the Crab Pulsar that covers all pulse phases. The superb angular resolution of the Chandra X-ray Observatory enables distinguishing the pulsar from the surrounding nebulosity, even at pulse minimum. Analysis of the pulse-averaged spectrum measures interstellar X-ray extinction due primarily to photoelectric absorption and secondarily to scattering by dust grains in the direction of the Crab Nebula. We confirm previous findings that the line-of-sight to the Crab is underabundant in oxygen, although more-so than recently measured. Using the abundances and cross sections from Wilms, Allen & McCray (2000) we find [O/H] = (3.33 +/-0.25) x 10**-4. Analysis of the spectrum as a function of pulse phase measures the low-energy X-ray spectral index even at pulse minimum -- albeit with large statistical uncertainty -- and we find marginal evidence for variations of the spectral index. The data are also used to set a new (3-sigma) upper limit to the temperature of the neutron star of log T(infinity) < 6.30.Comment: 20 Pages including 7 figures. Accepted for publication in the Astrophysical Journa

Measured Radiation and Background Levels During Transmission of Megawatt Electron Beams Through Millimeter Apertures

We report measurements of photon and neutron radiation levels observed while transmitting a 0.43 MW electron beam through millimeter-sized apertures and during beam-off, but accelerating gradient RF-on, operation. These measurements were conducted at the Free-Electron Laser (FEL) facility of the Jefferson National Accelerator Laboratory (JLab) using a 100 MeV electron beam from an energy-recovery linear accelerator. The beam was directed successively through 6 mm, 4 mm, and 2 mm diameter apertures of length 127 mm in aluminum at a maximum current of 4.3 mA (430 kW beam power). This study was conducted to characterize radiation levels for experiments that need to operate in this environment, such as the proposed DarkLight Experiment. We find that sustained transmission of a 430 kW continuous-wave (CW) beam through a 2 mm aperture is feasible with manageable beam-related backgrounds. We also find that during beam-off, RF-on operation, multipactoring inside the niobium cavities of the accelerator cryomodules is the primary source of ambient radiation when the machine is tuned for 130 MeV operation.Comment: 9 pages, 11 figures, submitted to Nuclear Instruments and Methods in Physics Research Section

Chandra Phase-Resolved X-ray Spectroscopy of the Crab Pulsar II

We present a new study of the X-ray spectral properties of the Crab Pulsar. The superb angular resolution of the Chandra X-ray Observatory enables distinguishing the pulsar from the surrounding nebulosity. Analysis of the spectrum as a function of pulse phase allows the least-biased measure of interstellar X-ray extinction due primarily to photoelectric absorption and secondarily to scattering by dust grains in the direction of the Crab Nebula. We modify previous findings that the line-of-sight to the Crab is under-abundant in oxygen and provide measurements with improved accuracy and less bias. Using the abundances and cross sections from Wilms, Allen & McCray (2000) we find [O/H] = $(5.28 \pm 0.28)\times10^{-4}$ ($4.9 \times10^{-4}$ is solar abundance). We also measure for the first time the impact of scattering of flux out of the image by interstellar grains. We find $\tau_{\rm scat} = 0.147 \pm 0.043$. Analysis of the spectrum as a function of pulse phase also measures the X-ray spectral index even at pulse minimum --- albeit with increasing statistical uncertainty. The spectral variations are, by and large, consistent with a sinusoidal variation. The only significant variation from the sinusoid occurs over the same phase range as some rather abrupt behavior in the optical polarization magnitude and position angle. We compare these spectral variations to those observed in Gamma-rays and conclude that our measurements are both a challenge and a guide to future modeling and will thus eventually help us understand pair cascade processes in pulsar magnetospheres. The data were also used to set new, and less biased, upper limits to the surface temperature of the neutron star for different models of the neutron star atmosphere.Comment: 32 pages, 6 figures submitted to the Astrophysical journa