Vector Meson Photoproduction from the BFKL Equation II: Phenomenology

Diffractive vector meson photoproduction accompanied by proton dissociation is studied for large momentum transfer. The process is described by the non-forward BFKL equation which we use to compare to data collected at the HERA collider.Comment: 39 pages, 29 figure

Optical photon transport in powdered-phosphor scintillators. Part II. Calculation of single-scattering transport parameters

Purpose: Monte Carlo methods based on the Boltzmann transport equation (BTE) have previously been used to model light transport in powdered-phosphor scintillator screens. Physically motivated guesses or, alternatively, the complexities of Mie theory have been used by some authors to provide the necessary inputs of transport parameters. The purpose of Part II of this work is to: (i) validate predictions of modulation transform function (MTF) using the BTE and calculated values of transport parameters, against experimental data published for two Gd2O2S:Tb screens; (ii) investigate the impact of size-distribution and emission spectrum on Mie predictions of transport parameters; (iii) suggest simpler and novel geometrical optics-based models for these parameters and compare to the predictions of Mie theory. A computer code package called phsphr is made available that allows the MTF predictions for the screens modeled to be reproduced and novel screens to be simulated.Methods: The transport parameters of interest are the scattering efficiency (Qsct), absorption efficiency (Qabs), and the scatter anisotropy (g). Calculations of these parameters are made using the analytic method of Mie theory, for spherical grains of radii 0.1-5.0 μm. The sensitivity of the transport parameters to emission wavelength is investigated using an emission spectrum representative of that of Gd2O2S:Tb. The impact of a grain-size distribution in the screen on the parameters is investigated using a Gaussian size-distribution (σ = 1%, 5%, or 10% of mean radius). Two simple and novel alternative models to Mie theory are suggested: a geometrical optics and diffraction model (GODM) and an extension of this (GODM+). Comparisons to measured MTF are made for two commercial screens: Lanex Fast Back and Lanex Fast Front (Eastman Kodak Company, Inc.).Results: The Mie theory predictions of transport parameters were shown to be highly sensitive to both grain size and emission wavelength. For a phosphor screen structure with a distribution in grain sizes and a spectrum of emission, only the average trend of Mie theory is likely to be important. This average behavior is well predicted by the more sophisticated of the geometrical optics models (GODM+) and in approximate agreement for the simplest (GODM). The root-mean-square differences obtained between predicted MTF and experimental measurements, using all three models (GODM, GODM+, Mie), were within 0.03 for both Lanex screens in all cases. This is excellent agreement in view of the uncertainties in screen composition and optical properties.Conclusions: If Mie theory is used for calculating transport parameters for light scattering and absorption in powdered-phosphor screens, care should be taken to average out the fine-structure in the parameter predictions. However, for visible emission wavelengths (λ 0.5 μm), geometrical optics models for transport parameters are an alternative to Mie theory. These geometrical optics models are simpler and lead to no substantial loss in accuracy

Optical photon transport in powdered-phosphor scintillators. Part 1. Multiple-scattering and validity of the Boltzmann transport equation

Purpose: In Part 1 of this two-part work, predictions for light transport in powdered-phosphor screens are made, based on three distinct approaches. Predictions of geometrical optics-based ray tracing through an explicit microscopic model (EMM) for screen structure are compared to a Monte Carlo program based on the Boltzmann transport equation (BTE) and Swank's diffusion equation solution. The purpose is to: (I) highlight the additional assumptions of the BTE Monte Carlo method and Swank's model (both previously used in the literature) with respect to the EMM approach; (II) demonstrate the equivalences of the approaches under well-defined conditions and; (III) identify the onset and severity of any discrepancies between the models. A package of computer code (called phsphr) is supplied which can be used to reproduce the BTE Monte Carlo results presented in this work.Methods: The EMM geometrical optics ray-tracing model is implemented for hypothesized microstructures of phosphor grains in a binder. The BTE model is implemented as a Monte Carlo program with transport parameters, derived from geometrical optics, as inputs. The analytical solution of Swank to the diffusion equation is compared to the EMM and BTE predictions. Absorbed fractions and MTFs are calculated for a range of binder-to-phosphor relative refractive indices (n = 1.1-5.0), screen thicknesses (t = 50-200 μm), and packing fill factors (pf = 0.04-0.54).Results: Disagreement between the BTE and EMM approaches increased with n and pf. For the largest relative refractive index (n = 5) and highest packing fill (pf = 0.5), the BTE model underestimated the absorbed fraction and MTF50, by up to 40% and 20%, respectively. However, for relative refractive indices typical of real phosphor screens (n ≤ 2), such as Gd2O2S:Tb, the BTE and EMM predictions agreed well at all simulated packing densities. In addition, Swank's model agreed closely with the BTE predictions when the screen was thick enough to be considered turbid.Conclusions: Although some assumptions of the BTE are violated in realistic powdered-phosphor screens, these appear to lead to negligible effects in the modeling of optical transport for typical phosphor and binder refractive indices. Therefore it is reasonable to use Monte Carlo codes based on the BTE to treat this problem. Furthermore, Swank's diffusion equation solution is an adequate approximation if a turbidity condition, presented here, is satisfied

Calculation of x-ray spectra emerging from an x-ray tube. Part II. X-ray production and filtration in x-ray targets

A new approach to the calculation of the x-ray spectrum emerging from an x-ray tube is proposed. Theoretical results for the bremsstrahlung cross section appearing in the literature are summarized. Four different treatments of electron penetration, based on the work presented in Part I, are then used to generate bremsstrahlung spectra. These spectra are compared to experimental data at 50, 80 and 100 kVp tube potentials. The most sophisticated treatment of electron penetration was required to obtain good agreement. With this treatment both the National Institute of Standards and Technology bremsstrahlung cross sections, based on accurate partial wave calculations, and the Bethe-Heitler cross section [H. A. Bethe and W. Heitler, Proc R. Soc. London, Ser. A. 146, 83-112 (1934)] corrected by a modified Elwert factor [G. Elwert, Ann. Phys. (Leipzig) 426,, 178-208 (1939)], provided good agreement to measured data. An approximate treatment of the characteristic spectrum is suggested. The dependencies of the bremsstrahlung and characteristic outputs of an x-ray tube on tube potential are compared to experimentally derived data for 70-140 kVp potentials. Agreement is to within a few percent of the total output over the entire range. The spectral predictions of the semiempirical models of Birch and Marshall [R. Birch and M. Marshall, Phys. Med. Biol. 24, 505-513 (1979)] (IPEM Report 78) and of Tucker et al. [D. M. Tucker, G. T. Barnes, and D. P. Chakraborty, Med. Phys. 18, 211-218 (1991).] are also assessed. The predictions of Tucker et al. are very close to the model developed here. The predictions of IPEM Report 78 are similar, but consistently harder for the range of tube potentials examined (50 - 100 kV). Unlike the semiempirical models, the model proposed here requires the introduction of no empirical and unphysical parameters in the differential bremsstrahlung cross section, bar an overall normalization factor which is close to unity. (c) 2007 American Association of Physicists in Medicine