Compton Cross Section Research Articles

Theoretical Momentum Densities

This review is primarily concerned with theoretical calculations of momentum densities and Compton cross sections for molecular systems. Qualitative properties of a momentum space representation are given. A comparison between experimental and theoretical cross sections within the impulse approximation is made. Ab initio calculations for small molecules, like the nitrogen and water molecules, are studied. Various approaches to treat large molecules are studied and compared for the formamide and p-benzoquinone molecules. Some comments on calculations for solid state systems are given.

Angular variation of Compton cross-sections due to L-shell electrons

The differential cross-sections for the Compton scattering of 279 keV gamma photons by L-shell electrons of thorium have been measured by the coincidence technique. The angular dependence of the cross-section due to L-shell electrons is compared with the Klein-Nishina cross-section for electrons which are initially free and stationary. The experimental bound-to-free electron Compton cross-section ratio converges to zero as the scattering angle decreases to zero and approaches unity at about 150°. The value of the total Compton cross-section ratio is less than unity, indicating the effect of binding due to L-shell electrons.

Multigroup radiation cross sections of high temperature uranium plasmas

Multigroup cross sections for thermal radiation in a uranium plasma at solid state density and temperatures in the KeV range are presented. Bound-free and free-free absorption is taken into account. Compton scattering is approximately described by the Thomson formula and by the Compton cross section for free electrons at rest. The results contain tables of one-group Rosseland means of the mean free path (valid in the optically thick limit) and of six-group Planck absorption and scattering cross sections (valid in the optically thin limit).

Erratum: Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states

Erratum: Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states

Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states. II. Effects of anisotropy and polarization

Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states. II. Effects of anisotropy and polarization

Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states

An approximate relativistic treatment of the differential cross section for Compton scattering against bound electron states is discussed. A simple relationship between the cross section and the Compton profile is found. On contrast to previous work this relationship is valid for all scattering angles.

Photon emission by an electron in a bichromatic field

A general expression for the probability of photon emission by an electron in a unidirectional bichromatic classical field is calculated making use of the exact solution to the Dirac equation for the electron in the field. In the limit that one component of the field is weak, a cross section for scattering a photon out of this component is derived. This has a complicated form but numerical values have been obtained in the particular case of an electron of energy 5 GeV travelling through radiation from a ruby laser (considered weak) and an intense C${\mathrm{O}}_{2}$ laser. It is found that, as a function of the intensity of the C${\mathrm{O}}_{2}$ laser, the cross section first increases, but eventually decreases to values below the Compton cross section. The spectrum of the scattered radiation is also calculated; is shows intensity-dependent shifts attributable to a field-induced drift velocity of the electron.

The influence of multiple scattering on the total and differential Compton cross sections in aluminium

Abstract The ratio of the elastic to the inelastic differential Compton cross section of aluminium has been measured, using 241Am 59·54 keV gamma rays at a scattering angle of 150°. The sample thickness was 7 mm. A Monte Carlo procedure was used to correct the data for the effect of multiple scattering. The resultant cross section ratio of elastic to inelastic scattering was compared with the prediction of the Waller-Hartree theory and good agreement was obtained after the multiple scattering correction had been made. The Compton profile, after applying this correction, was in agreement with a previous measurement on a thin sample, and with a calculation based on an electron-gas model including correlation.

Relationship of the relativistic Compton cross section to the electron's velocity distribution

A relativistic treatment of the Compton cross section for free electrons is given. In addition, conditions are specified when it is correct to within 1% to relate in a simple manner the results of Compton-scattering experiments to a simple Compton profile (velocity distribution of electrons). Many different approaches previously used to achieve this simple relationship have been arbitrary and thus have resulted in the possibility that two investigators with the same experimental data would deduce different Compton profiles. The relationship derived here differs from all the previous ones, and in some cases, would yield a significantly different Compton profile from reported data.

A partial-wave analysis for proton compton scattering in the Δ(1232) energy region

Based on the nowadays available phenomenological multipoles for pion photoproduction, a systematic dispersion theoretic calculation of Compton partial amplitudes has been performed. By comparing with the new experimental data in the Δ(1232) region it is found that the hitherto existing discrepancies between the data and theory remain. Our results allow us to isolate the basis of this problem. It is due to the fact that the imaginary parts of the Compton amplitudes determined already by unitarity, give too large contributions to the cross section thus leaving no space for real parts required by the dispersion integrals. Therefore a simultaneous partial-wave analysis for Compton scattering and pion photoproduction was carried through employing only the unitarity connections between both. The resulting amplitudes give a good fit to the Compton cross section and all photoproduction data; moreover the photoproduction multipoles agree essentially with those of the previous analyses. On the other hand for Compton scattering, phenomenological amplitudes are obtained for the first time and a model independent test of dispersion theoretic amplitudes can be carried out. For the resonating f MM 1+ amplitude which describes the M1 excitation and deexcitation to the Δ-isobar, large discrepancies have been found. Possible consequences especially for the forward scattering amplitude and the validity of the Kramers-Kronig relation are discussed.

Compton scattering in external magnetic fields: Spin-zero charged particles

Methods recently developed by Schwinger are applied to derive a general expression for the total spin-0 unpolarized Compton cross section in the presence of an arbitrarily strong homogeneous external magnetic field. This expression is correct to order ${\ensuremath{\alpha}}^{2}$ in radiative effects, but treats the external field exactly. The motion of the incident photon is restricted to lie along the field direction. Special limiting cases corresponding to classical and weakfield limits are discussed.

Gamma ray compton profile of aluminium

Abstract The Compton profile for polycrystalline aluminium is measured using 59·54 keV γ-rays from an 241Am source. To correct the results for relativistic effects an approximation for the energy dependence of the relativistic Compton cross-section has been evaluated. The data are corrected for multiple Compton scattering by extrapolating to zero scattering volume. Final results show deviations at low momenta from free-electron theory of the three valence electrons of Al. On the other hand, at high momenta (p z> 2 a.u.) the results are in good agreement with those calculated from Hartree-Fock free-atom wave functions for the neon core configuration 1δ22δ22p 6. It is suggested that a pseudopotential calculation which gives good agreement with the experimental electron density (atomic scattering factor) of Al would be useful to interpret also the present Compton profile data.

Scaling Limit of Longitudinal Virtual Compton Cross Sections

It is shown that the hypothesis that the quark model gives the correct leading, δ′(x2), light-cone singularity of current commutators requires that R, the ratio of longitudinal to transverse virtual Compton cross sections, go to zero like 1/ν in the Bjorken limit.

Vector-Meson Production by Polarized Photons at 2.8, 4.7, and 9.3 GeV

We present results on vector-meson photoproduction via $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{Vp}$ in the LBL-SLAC 82-in. hydrogen bubble chamber exposed to a linearly polarized photon beam at 2.8, 4.7, and 9.3 GeV. We find ${\ensuremath{\rho}}^{0}$ production to have the characteristics of a diffractive process, i.e., a cross section decreasing slowly with energy and a differential cross section with slope of \ensuremath{\sim} 6.5 ${\mathrm{GeV}}^{\ensuremath{-}2}$. Within errors the ${\ensuremath{\rho}}^{0}$ production amplitudes are entirely due to natural-parity exchange. $s$-channel helicity is conserved to a high degree in the $\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}$ transition. We find evidence for small helicity-flip amplitudes for $\ensuremath{\pi}\ensuremath{\pi}$ pairs in the ${\ensuremath{\rho}}^{0}$ region. Photoproduction of $\ensuremath{\omega}$ mesons is separated into its natural- (${\ensuremath{\sigma}}^{N}$) and unnatural- (${\ensuremath{\sigma}}^{U}$) parity-exchange contributions. The ${E}_{\ensuremath{\gamma}}$ and $t$ dependence and the spin density matrix of the unnatural-parity-exchange contribution are consistent with a one-pion-exchange process. The natural-parity-exchange part has characteristics similar to ${\ensuremath{\rho}}^{0}$ production. At 9.3 GeV the ratio of $\ensuremath{\sigma}({\ensuremath{\rho}}^{0})$ to ${\ensuremath{\sigma}}^{N}(\ensuremath{\omega})$ is \ensuremath{\sim} 7. The slope of the $\ensuremath{\varphi}$ differential cross section is \ensuremath{\sim} 4.5 ${\mathrm{GeV}}^{\ensuremath{-}2}$, smaller than that of ${\ensuremath{\rho}}^{0}$ and $\ensuremath{\omega}$ production. Natural-parity exchange is the main contributor to $\ensuremath{\varphi}$ production. No evidence for higher-mass vector mesons is found in $\ensuremath{\pi}\ensuremath{\pi}$, $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\pi}$, or $K\overline{K}$ final states. The $s$ and $t$ dependences of Compton scattering as calculated from $\ensuremath{\rho}$, $\ensuremath{\omega}$, and $\ensuremath{\varphi}$ photoproduction using vector-meson dominance agree with experiment, but the predicted Compton cross section is too small by a factor of 2.

Impulse Approximation in Compton Scattering

Calculations of the core contributions to the Compton profiles for lithium ($1{s}^{2}$), carbon ($1{s}^{2}$), and aluminum ($2{s}^{2}2{p}^{6}$) were made employing excited-state one-electron continuum wave functions evaluated in the ground-state Hartree-Fock-Slater potential of the nucleus and remaining electrons. Good agreement with the impulse approximation is obtained. Measurements of the Compton profiles of lithium metal, graphite, and aluminum metal were made with Mo $K\ensuremath{\alpha}$ radiation and the core contributions were separated from the valence electron contributions. The Compton profiles for the core electrons [$1{s}^{2}$ for lithium and carbon, $2{s}^{2}2{p}^{6}$ for aluminum ($1{s}^{2}$ not excited)] were in fair agreement with the calculations. Total Compton cross sections (integrated over the Compton profile) were calculated in the impulse approximation and compared to the Waller-Hartree theory with and without the Bonham corrections. The agreement can be quite poor, differing at low angles by as much as a factor of 3.

Effects of Daughters on Electromagnetic Mass Differences

A procedure has been suggested for computing $\ensuremath{\Delta}I=1$ electromagnetic mass differences by using a finite-energy sum rule to compute the subtraction function in the dispersion relation for the amplitude ${t}_{1}({q}^{2},\ensuremath{\nu})$ which appears in the Cottingham formula; Regge residues appearing in the subtraction function are found from a superconvergence relation. The present work considers the effect of the inclusion of asymptotic nonleading power behavior on the results of this procedure; we find a surprising sensitivity. In particular, we show that in evaluating the superconvergence relation, the hypothesis of ${A}_{2}$ dominance of high-energy virtual Compton scattering from $K$ mesons is only tenable for an extremely narrow range of the ratio of the longitudinal to transverse total virtual Compton cross sections. (This range does not include zero.) We also discuss the effects of O(4) symmetry, comment on the more complicated nucleon mass-difference problem, and apply the Cottingham formula to nuclear mass differences.

Observation of a New Component in the X-Ray Scattered Spectrum

The results of a spectral analysis of Cu $K{\ensuremath{\alpha}}_{1}$, $K{\ensuremath{\alpha}}_{2}$ x-rays scattered by a single crystal of LiF (lithium fluoride) and by LiF powder (at scattering angles 16\ifmmode^\circ\else\textdegree\fi{}, 25\ifmmode^\circ\else\textdegree\fi{}, 70\ifmmode^\circ\else\textdegree\fi{}, 84\ifmmode^\circ\else\textdegree\fi{}) are evidence of the existence of a new line on the long-wavelength side of the spectrum. This line is 5 eV from the incident beam, and its position and shape are independent of the scattering angle. The peak intensity of the new line is of the same order of magnitude as the Compton intensity. The observed line can be considered to be caused by an "x-ray Raman"-type process from $F$-centers which themselves were produced by the incident x-ray beam. This is not the only possible explanation. However, the position of the line is comparable to the $F$-center absorption energy for LiF as measured by an ultraviolet spectrometer. The relative peak intensity indicates that the differential cross section for the process presently under investigation is higher than the Compton cross section for valence electrons.

Radiation Transport Calculations-``Fore and Aft'' Approximation

An approximate method for describing radiation transport is derived. Photoelectric effect and Compton effect are assumed to be the only mechanisms affecting the transport. Thus the method is restricted to the x-ray and low-energy gamma-ray region of the electromagnetic spectrum. Further, the radiation is assumed to be a collimated beam incident normal to a homogeneous semi-infinite slab. The method described goes one step beyond the classical ``straight-ahead'' approximation used in the theory of gamma-ray attenuation. Because of the assumptions used in obtaining the solution, the expressions derived can most appropriately be applied for the case where Compton scattering is near isotropic (relatively low energies) and where the photoelectric cross section is larger than the Compton cross section.

Compton Scattering and Regge Cuts

Multiple Pomeranchuk-trajectory exchange is studied in nucleon Compton scattering as an alternative means to a wrong-signature fixed pole in order to obtain a constant total asymptotic cross section and avoid paradoxes involving the vector-meson-dominance model. It is argued that the multi-Pomeranchon branch points interfere constructively, and an estimate is made of their contributions. One finds that the inclusion of up to five-Pomeranchon branch points leads to some 40% of the total nucleon Compton cross section. The implications of these results for the Pomeranchuk trajectory are discussed.

Measurement of Photoelectric, Compton, and Pair-Production Cross Sections in Germanium

The lithium-drifted germanium detector's high resolution provides an opportunity to measure the photoelectric, Compton, and pair-production cross sections as a function of photon energy in the range of 100 to 2750 keV. This conceptually simple experiment can be readily performed in an undergraduate laboratory equipped with a small Ge(Li) detector and pulse-height analysis equipment. Results compare very favorably with theoretical calculations.