R. H. Pratt

Shape functions for atomic-field bremsstrahlung from electrons of kinetic energy 1–500 keV on selected neutral atoms 1 ≤ Z ≤ 92

Abstract A tabulation is presented of theoretical predictions for the shape functions for atomic-field bremsstrahlung for 24 atoms with atomic number Z ranging from 1 to 92 for six incident electron energies T1 from 1 to 500 keV. The shape function is defined as the ratio of the bremsstrahlung cross section differential in photon energy and angle to the photon energy spectrum. Shape functions have been tabulated for photon angles from 0° to 180° in 5° intervals for 12 values of the fraction of energy radiated /T1 from 0 to 1.0. The tables for2 ≤ Z ≤ 92 result from interpolations in atomic number and fraction of energy radiated from a set of benchmark data calculated by treating the bremsstrahlung process as a single-electron transition in a relativistic self-consistent screened potential. The table for Z = 1 is calculated using a screened Born approximation.

Bremsstrahlung energy spectra from electrons of kinetic energy 1 keV ≤ T1 ≤ 2000 keV incident on neutral atoms 2 ≤ Z ≤ 92

Abstract A tabulation is presented of theoretical predictions for the electron bremsstrahlung energy spectrum from neutral atoms as a function of atomic number Z, incident electron kinetic energy T1, and fraction of energy radiated k T 1 . Tabulated values were obtained by interpolation from a smaller set of calculated data points. These calculated points were obtained by describing bremsstrahlung as a single-electron transition in a relativistic self-consistent screened potential and, after expansions in partial waves, by performing a numerical evaluation for radial wavefunctions and matrix elements.

Elastic scattering of γ-rays and X-rays by atoms

Abstract A survey is given of the current status of theoretical and experimental studies of elastic photon-atom scattering, with particular emphasis on the soft γ-ray energy regime 59.5 keV–1.33 MeV. Basic assumptions of theory, simple approximations, and best available calculations are described. The focus is on the Rayleigh scattering amplitudes for elastic scattering off the bound atomic electrons, but it is also necessary to discuss Delbruck and nuclear amplitudes. The numerical code of Kissel is central to the results which are obtained. A new reference data set of theoretical predictions is presented for a grid of 10 elements (Z = 13–103) and 7 energies (59.5 keV–1.33 MeV) at 55 scattering angles (0–180°). Basic considerations of the experiment are described, including sources and detectors and experimental arrangements. All modern experiments (using Ge detectors) are summarized, and older experiments are listed for reference. Finally, the status of comparison between theory and experiment is examined. All experiments available on the reference grid of theoretical calculation are compared with the predictions; agreement appears generally satisfactory. The situations at higher energies (focusing on Delbruck scattering) and lower energy X-ray scattering (anomalous scattering) are also discussed.

The validity of form-factor, modified-form-factor and anomalous-scattering-factor approximations in elastic scattering calculations

The validity of form-factor, modified-form-factor and anomalous-scattering-factor approximations in predictions of elastic photon-atom scattering is assessed with the aid of the state-of-the-art numerical calculation of Rayleigh scattering obtained using the second-order S-matrix theory, in the photon energy range from 100 eV to 1 MeV. A comparison is made with predictions from S-matrix theory in the same atomic model for representative low-Z (carbon, Z = 6) and high-Z (lead, Z = 82) elements to get a general idea of the validity of these simpler more approximate methods. The importance of bound–bound contributions and the angle dependence of the anomalous scattering factors is discussed. A prescription is suggested, with the assumption of angle independence, that uses simpler approaches to obtain the elastic scattering cross sections in the soft-X-ray regime at the level of accuracy of the S-matrix calculation, failing at large momentum transfers for high-Z elements. Predictions from this prescription are compared with experiment. With starting point the many-body elastic scattering amplitude, a detailed discussion is presented of the partition of the elastic scattering amplitude into Rayleigh and Delbruck scattering components. This partition of the optical theorem reveals contributions from bound–bound atomic transitions, bound pair annihilation and bound pair production that are not usually associated with elastic scattering. In the partitioned optical theorem for Rayleigh scattering, as in the many-body optical theorem for scattering from excited states, subtracted cross sections naturally appear. These terms are needed, in addition to the familiar terms for photoionization, to relate the real and imaginary parts of the scattering amplitude.

Genetic Markers: Progress and Potential for Cardiovascular Disease

The recent completion of the Human Genome Project has provided an unprecedented opportunity for researchers to identify high-risk patients and improve human health through the use of technologies that integrate the entire genome. In the past, disorders that yielded their secrets to genetic investigations tended to be rare, single-gene conditions (eg, Brugada syndrome, Liddle syndrome). Today, attention is increasingly focused on elucidating genetic susceptibility to the common multifactorial diseases that clinicians encounter on a daily basis.1 A significant portion of current medical research is devoted to the pursuit of genetic variants that can be used to identify disease. These variants are not necessarily the cause of the illness, but markers that will help improve diagnosis and risk assessment. The level of expression of certain genes (ie, the amount of corresponding RNA or proteins produced) may signify a disease state. If these genes are consistently overexpressed or suppressed in a certain clinical context, they also may be considered biomarkers. Two approaches are used when pursuing genetic markers: researchers can conduct candidate gene studies (which focus on single genes) or genomic studies (which examine the entire genome.) Some diseases are monogenic (ie, caused by defects in only one gene). In such cases, genetic studies make clinical diagnosis straightforward. Mutations can be assessed by patient genotyping, and the expression of single genes can be assessed using techniques such as real-time reverse-transcription polymerized chain reaction (RT-PCR) or Northern blot. However, for more common diseases, it has been more difficult to identify genetic markers, because most common diseases are polygenic. This genetic “web” of multiple genes may be very large and act in complex ways to induce a disease state. In addition, these conditions are often triggered by an interaction of genetic, environmental, and physiological factors, making it difficult for researchers to narrow their …

An overview of the theories used in Compton scattering calculations

This paper discusses theoretical approaches for investigating Compton scattering from bound atomic electrons. It particularly emphasizes the understanding of methods currently used to obtain the scattered photon energy distribution at fixed scattering angle. This distribution is dominated by three features: the Compton line or peak, the resonant-Raman-Compton scattering and the infrared divergence at soft scattered photon energies. No single common approximation accesses all three regions, though they are all exhibited analytically in the nonrelativistic hydrogenic case. S-matrix calculations describe all of these features. The usual approximations utilized for Compton scattering are discussed and assessed in comparison with the more exact, relativistic S-matrix calculations. Finally, some recent developments in the theory of Compton scattering from bound electrons are noted. These include the effort to describe the double ionization of helium by Compton scattering and the theoretical analysis of the more completely differential Compton scattering experiment in which the ejected electron is also observed.

Elastic scattering of photons

Abstract Photon scattering from bound electrons of atoms, a component of the elastic photon-atom scattering amplitude called Rayleigh scattering, is discussed. General features of the many-body scattering amplitude and its partitioning into Rayleigh and Delbruck (and nuclear) single-electron transition scattering amplitudes are examined. The use of the state-of-the-art precise second-order S-matrix calculations of Rayleigh scattering in terms of single-electron transition-amplitudes has led to significant progress in our understanding of the scattering process. The importance of relativistic, higher multipole, and bound-bound contributions in calculating anomalous scattering factor deviations from form factor amplitudes must be emphasized. Accurate interpolation of cross sections in the three-dimensional space of scattering angle, photon energy, and atomic number, utilizing the available published S-matrix data, has permitted extensive tabulation of differential scattering cross sections. S-matrix results may be compared with experiments to assess their validity; they may be compared with simpler but more approximate approaches, to identify the extent of the utility of such approaches and to develop simpler prescription schemes which can give results comparable to the S-matrix results. In spite of their many successes, the present second order S-matrix methods also have limitations and shortcomings, observed in certain recent experiments. We describe the explanation of these experiments in terms of a composite theory which also incorporates non-local exchange and correlation effects. We end with a discussion of other future issues.

Vascular injury augments adrenergic neurotransmission.

BackgroundWe have observed persistent desensitization to exogenous norepinephrine after balloon injury. We postulated that this desensitization may be due to a local increase in the release of neuronal norepinephrine. Methods and ResultsNew Zealand White rabbits underwent left iliac artery angioplasty; 4 weeks later, both iliac arteries were harvested. Maximal response to exogenous norepinephrine was reduced in injured compared with noninjured vessels (12.3±1.0 g versus 10.3±1.5 g; n=7, P = .056). By contrast, response to electrical stimulation (to induce neuronal norepinephrine release) was significantly greater in injured tissues (36±7% versus 14±3%; values expressed as percent of maximal contraction to exogenous norepinephrine; P = .025). Direct measurement of tissue norepinephrine revealed a threefold increase 4 weeks after injury (1236±410 versus 466±97 pg/mg; injured versus noninjured). To determine if desensitization to exogenous norepinephrine was due to a persistent increase in neuronal norepinephrine release, the experiments were repeated after chemical sympatholysis using 6-hydroxydopamine (6-OHDA) (65 mg/kg). To determine if activation of vascular angiotensin II contributed to facilitation of adrenergic neurotransmission, other animals received ramipril (RAM; 1 mg/kg per day). Both treatments were initiated 7 days before angioplasty. In the 6-OHDA group there was no evidence of desensitization, judged by maximal response to exogenous norepinephrine (7.5±0.6 versus 7.5±0.8, noninjured versus injured). Similar results were obtained in RAM animals (9.9±0.8 versus 9.6±1.2, noninjured versus injured). ConclusionsThis is the first study to demonstrate enhanced adrenergic neurotransmission after balloon injury. The facilitation of adrenergic neurotransmission may be due to increased local concentrations of angiotensin II and is associated with desensitization to exogenous norepinephrine.

Bremsstrahlung spectra from atoms and ions at low relativistic energies

Analytic expressions for bremsstrahlung spectra from neutral atoms and ions, including the polarizational bremsstrahlung contribution in a stripped atom approximation, are developed for electron scattering at energies of 10-2000 keV. A modified Elwert factor and a simple higher Born correction are used for the Coulomb spectrum, with ordinary bremsstrahlung screening effects in ions and atoms adequately characterized in the non-relativistic Born approximation. In parallel with the development of this analytic description, new numerical results are obtained for ordinary bremsstrahlung from ions and from bare nuclei, appreciably extending the available data set which can be used to study dependences on element, ionicity, energy and the fraction of incident energy radiated. The accuracy of predictions with the analytic expressions is then determined by comparison with the full numerical relativistic partial-wave results for ordinary bremsstrahlung and with non-relativistic numerical results in the Born approximation or in partial waves for the polarizational amplitude.

RADIATIVE MUON DECAY

Abstract Theoretical predictions for the radiative muon decay process μ a e + ν + ν + γ are given in some detail. The differential transition probability for polarized muons is obtained, and from it are calculated the angular correlations of electron and photon, the photon energy spectrum, and the branching ratio. The probability for internal conversion of the photon is estimated. The consequences of an intermediate vector boson are discussed.