Approximate treatment of electron Coulomb distortion in quasielastic (e,e') reactions

In this paper we address the adequacy of various approximate methods of including Coulomb distortion effects in (e,e') reactions by comparing to an exact treatment using Dirac-Coulomb distorted waves. In particular, we examine approximate methods and analyses of (e,e') reactions developed by Traini et al. using a high energy approximation of the distorted waves and phase shifts due to Lenz and Rosenfelder. This approximation has been used in the separation of longitudinal and transverse structure functions in a number of (e,e') experiments including the newly published 208Pb(e,e') data from Saclay. We find that the assumptions used by Traini and others are not valid for typical (e,e') experiments on medium and heavy nuclei, and hence the extracted structure functions based on this formalism are not reliable. We describe an improved approximation which is also based on the high energy approximation of Lenz and Rosenfelder and the analyses of Knoll and compare our results to the Saclay data. At each step of our analyses we compare our approximate results to the exact distorted wave results and can therefore quantify the errors made by our approximations. We find that for light nuclei, we can get an excellent treatment of Coulomb distortion effects on (e,e') reactions just by using a good approximation to the distorted waves, but for medium and heavy nuclei simple additional ad hoc factors need to be included. We describe an explicit procedure for using our approximate analyses to extract so-called longitudinal and transverse structure functions from (e,e') reactions in the quasielastic region.Comment: 30 pages, 8 figures, 16 reference

Extended Superscaling of Electron Scattering from Nuclei

An extended study of scaling of the first and second kinds for inclusive electron scattering from nuclei is presented. Emphasis is placed on the transverse response in the kinematic region lying above the quasielastic peak. In particular, for the region in which electroproduction of resonances is expected to be important, approximate scaling of the second kind is observed and the modest breaking of it is shown probably to be due to the role played by an inelastic version of the usual scaling variable.Comment: LaTeX, 36 pages including 5 color postscript figures and 4 postscript figure

Time crawls when you’re not having fun: Feeling entitled makes dull tasks drag on

All people have to complete dull tasks, but individuals who feel entitled may be more inclined to perceive them as a waste of their "precious" time, resulting in the perception that time drags.This hypothesis was confirmed in three studies.In Study 1, participants with higher trait entitlement (controlling for related variables) thought dull tasks took longer to complete; no link was found for fun tasks.In Study 2, participants exposed to entitled messages thought taking a dull survey was a greater waste of time and took longer to complete.In Study 3, participants subliminally exposed to entitled words thought dull tasks were less interesting, thought they took longer to complete, and walked away faster when leaving the laboratory.Like most resources, time is a resource valued more by entitled individuals.A time-entitlement link provides novel insight into mechanisms underlying self-focus and prosocial dynamics. © 2011 by the Society for Personality and Social Psychology, Inc

Analysis of exchange terms in a projected ERPA Theory applied to the quasi-elastic (e,e') reaction

A systematic study of the influence of exchange terms in the longitudinal and transverse nuclear response to quasi-elastic (e,e') reactions is presented. The study is performed within the framework of the extended random phase approximation (ERPA), which in conjuction with a projection method permits a separation of various contributions tied to different physical processes. The calculations are performed in nuclear matter up to second order in the residual interaction for which we take a (pi+rho)-model with the addition of the Landau-Migdal g'-parameter. Exchange terms are found to be important only for the RPA-type contributions around the quasielastic peak.Comment: 29 pages, 6 figs (3 in postscript, 3 faxed on request), epsf.st

Functional approach to the electromagnetic response function: the Longitudinal Channel

In this paper we address the (charge) longitudinal electromagnetic response for a homogeneous system of nucleons interacting via meson exchanges in the functional framework. This approach warrants consistency if the calculation is carried on order-by-order in the mesonic loop expansion with RPA-dressed mesonic propagators. At the 1-loop order and considering pion, rho and omega exchanges we obtain a quenching of the response, in line with the experimental results.Comment: RevTeX, 18 figures available upon request - to be published in Physical Review

Superscaling of Inclusive Electron Scattering from Nuclei

We investigate the degree to which the concept of superscaling, initially developed within the framework of the relativistic Fermi gas model, applies to inclusive electron scattering from nuclei. We find that data obtained from the low energy loss side of the quasielastic peak exhibit the superscaling property, i.e., the scaling functions f(\psi') are not only independent of momentum transfer (the usual type of scaling: scaling of the first kind), but coincide for A \geq 4 when plotted versus a dimensionless scaling variable \psi' (scaling of the second kind). We use this behavior to study as yet poorly understood properties of the inclusive response at large electron energy loss.Comment: 33 pages, 12 color EPS figures, LaTeX2e using BoxedEPSF macros; email to [email protected]

Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order $1/k^2$, where $k$ is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.Comment: 12 pages, 6 Postscript figure

Superscaling in inclusive electron-nucleus scattering

We investigate the degree to which the scaling functions $F(\psi')$ derived from cross sections for inclusive electron-nucleus quasi-elastic scattering define the same function for different nuclei. In the region where the scaling variable $\psi'< 0$, we find that this superscaling is experimentally realized to a high degree.Comment: Corrected previously mislabeled figures and cross references; 9 pages, 4 color figures, using BoxedEPS and REVTeX; email correspondence to [email protected]

Quasielastic 12C(e,e'p) Reaction at High Momentum Transfer

We measured the 12C(e,e'p) cross section as a function of missing energy in parallel kinematics for (q,w) = (970 MeV/c, 330 MeV) and (990 MeV/c, 475 MeV). At w=475 MeV, at the maximum of the quasielastic peak, there is a large continuum (E_m > 50 MeV) cross section extending out to the deepest missing energy measured, amounting to almost 50% of the measured cross section. The ratio of data to DWIA calculation is 0.4 for both the p- and s-shells. At w=330 MeV, well below the maximum of the quasielastic peak, the continuum cross section is much smaller and the ratio of data to DWIA calculation is 0.85 for the p-shell and 1.0 for the s-shell. We infer that one or more mechanisms that increase with $\omega$ transform some of the single-nucleon-knockout into multinucleon knockout, decreasing the valence knockout cross section and increasing the continuum cross section.Comment: 14 pages, 7 figures, Revtex (multicol, prc and aps styles), to appear in Phys Rev

Comparative Life Cycle Assessment of Direct and Indirect Solar Water Disinfection Processes in Developing Countries

In July 2010, the UN General Assembly recognized the universal human right to sufficient water for health and sanitation (UN…, 2010). The reliable disinfection of this water plays a critical role in public health (Carter and Miller, 2005), and this study investigates the use of four ultraviolet (UV) disinfection methods for use in international development and disaster relief. The study focuses on the life cycle impacts of four direct and indirect solar ultraviolet disinfection systems. Direct solar disinfection refers to exposure of water to solar radiation, while indirect solar disinfection collects solar energy and uses this to power a UV lamp disinfection reactor. These four systems were compared to chlorine disinfection and automobile distribution as baseline methods. Existing literature was used to define a life cycle functional unit for each system, which quantified the material use, infrastructure required, and life cycle of the components of each system. The impact of each system was then defined in the Life Cycle Analysis software SimaPro. Analyses compared the use of each technology at “community, school, small group, and family” scales. Due to the significant impact that end-of-use of a system can have on rural communities, an end-of-life analysis was conducted in addition to the quantitative life cycle analysis. Life cycle analysis shows that both direct and indirect UV disinfection methods vary dramatically over several categories of impact assessment. End of life analysis and this variation highlight the extremely complicated process of designing the appropriate disinfection system for use in developing countries