Photon Angle Research Articles

Surface photoelectric effect and surface orbital geometry on silicon (111)

Photoelectron energy distributions have been measured as a function of photon angle of incidence, ϑi, in the range 28°?ϑi?80°. A resonance lamp with photon energies of 11.7, 16.8, and 21.2 eV was used with a double−pass cylindrical mirror analyzer. Three different surface orbitals were studied: intrinsic surface states, chemisorption orbitals of Cl, and nonbonding orbitals of implanted Ar. All three types of orbitals exhibited a similar dependence of intensity with ϑi which was approximately the same as the net electric field intensity 〈E2z〉z = 0. This implies that the surface photoeffect for silicon (111) is probably not closely related to the detailed surface bond geometry, but is determined by the optical properties of the silicon.

Photo-compton currents at material interfaces: Theory and experiment

Analytical formulae are presented for the electron number current, energy current and energy deposition at the photon irradiated interface between different materials. Representative results are shown and compared with previous experimental data. Experimental results are given for the electron number current as a function of interface materials, photon spectrum and photon angle of incidence. The experimental results are compared to the predictions of the analytical formulae and the Monte Carlo code SANDYL.

Proton-proton bremsstrahlung: Coulomb effect

A nonrelativistic potential model calculation of proton-proton bremsstrahlung is carried out in which the Coulomb potential as well as double scattering are treated exactly. The conventional electromagnetic current operator for point protons with charge and magnetic moment is used. Cross sections differential with respect to the photon angle are calculated in the symmetric, coplanar Harvard geometry for proton angles of 10, 20, and 30\ifmmode^\circ\else\textdegree\fi{}, at laboratory energies of 5, 20, 42, 62, 99, and 158 MeV, using the Hamada-Johnston potential. Cross sections integrated over the photon angle are presented over a wider range of angles. Including the Coulomb potential lowers the cross section by amounts which are comparable with the errors of the most accurate experiments, and at proton angles smaller than any of the existing experiments the Coulomb effect becomes quite large. Cross sections for the asymmetric Orsay experiment are also computed, including the effect of noncoplanarity, and there is a large discrepancy at some of the experimental points.NUCLEAR REACTIONS $p(p,p\ensuremath{\gamma})$; calculated $\ensuremath{\sigma}({\ensuremath{\theta}}_{\ensuremath{\gamma}})$ for lab proton energies 5 to 158 MeV, including Coulomb effects.

Screening and second Born corrections to bremsstrahlung at intermediate energies

The effect of screening on bremsstrahlung cross-sections at medium energy is studied. A formula is derived which reduces the integration of the Bethe-Heitler formula over electron angles to a single integration, which is done numerically, without approximations as to energy or angle, for arbitrary form factors. Although the calculation is confined to Born approximation, it provides a computationally simple method for calculating the effects of screening in energy regions for which such calculations have not previously been possible. A similar method is used to compute bremsstrahlung cross-sections in second Born approximation. Cross-sections differential in photon energy and angle, as well as total cross-sections are presented for the casesZ=13, 79, using the Moliere form factor to describe the screening, and a comparison is made with other recent calculations.

Effect of electron and ? polarization on two-photon bremsstrahlung of electrons in a nuclear field

The cross section for two-photon bremsstrahlung is integrated over the electron scattering angle and the (common) emission angle of the bremsstrahlung photons. Equations are found for the energetic, angular, and polarization distributions of the cross section. The cross section for two-photon bremsstrahlung for the case in which the momenta of the bremsstrahlung photons are parallel can be larger than the corresponding Bethe-Heitler cross section. The probabilities for certain polarization states of the electrons are also analyzed.

Radiative corrections in ee′N coincidence experiments

The cross-section differential in the energies and angles of all final particles for bremsstrahlung accompanying nucléon emission is derived in first Born approximation, in terms of the four form factors introduced by de Forest. This cross section is integrated over photon angles, using the peaking approximation, to give an expression for the radiative tail in nucléon emission processes. A numerical example for the case of ee′p coincidence experiments in 12C is given, using the quasi-elastic model to describe the nuclear excitation.

Absolute cross-section measurement of the elementary process of bremsstrahlung production for gold at 300 keV

The absolute cross section of 300 keV electron bremsstrahlung that is differential with respect to the photon energy and to the photon and electron emission angles was measured by using a coincidence technique. Furthermore, we have measured the disturbance of this elementary process by plural scattering.

Correction to the formula for the radiative tail in elastic electron scattering

The only major drawback in the use of the electron as a probc of nuclear structure m its tendency to radiate during scattering processes. The radiation effects require important corrections in the analysis of electron scattering experiments. Among the most important of these are the effects due to the interaction of the electron with the radiation field during scattering by the nucleus, causing it to emit real and vir tual photons, and thus modifying the scattering cross-section. Two types of such corrections must be considered: the radiative correction, which arises from the emission and re-absorption of virtual photons by the electron, and from the emission of soft, unobserved real photons, and the radiative tail, which consists of electrons which have emitted a hard photon during the scattering process, and whose energy has thus been degraded below the cut-off AE of the elastic peak. A theoretical expression for the radiative tail is obtained by integrating the crosssection for emission of a bremsstrahlung photon during the scattering process over the directions of the unobserved photon. All previous calculations (~) of the radiative tail have been limited by the use of the first Born approximation to describe the interaction of thc electron with the nucleus. A resilt which goes beyond the Born approxiination would be extremely useful, particularly in the analysis of electron scattering by heavy nuclei. However, the Bethe-Heitler cross-section (~) has been the only available useful expression for the bremsstrahlung cross-section, thus making it impossible to extend the calculation of the radiative tail beyond the first Born approximation. Recently, two independent calculations of the lowest-order correction to the BetheHeitler formula for bremsstrahlung by electrons scattered in a point Coulomb field have been made (3.4). In this paper we present an integration of this expression over the angles of the unobserved photon, using the peaking approximation due to SCHIF) (s).

Comments on radiative Ke3 decays

Abstract Calculations of the radiative K e3 branching ratios have been performed with cuts in the photon energy as well as in the electron photon angle as imposed by the experimental set-up. We found good agreement with preliminary experimental results.

Wide-Angle Bremsstrahlung

We have extended our earlier measurements of the cross section for wide-angle electron bremsstrahlung. Besides the data for symmetric final electron and photon angles already published, we report results for asymmetric angles. The circulating electron beam of the Cornell 10-GeV synchrotron struck a carbon target and was monitored by observing the forward bremsstrahlung beam. Wide-angle photons were counted in coincidence with the corresponding scattered electrons. The recoil momentum of the unobserved nucleus was minimized. The experimental cross sections are compared with the predictions of the Bethe-Heitler formula corrected for elastic and inelastic nuclear form factors and for virtual nuclear Compton scattering. The agreement is excellent, confirming the predictions of quantum electrodynamics for timelike electron four-momenta up to 1.2 GeV. If one assumes a deviation in the experiment/theory ratio proportional to the square of the final electron-photon invariant mass, the 95% confidence upper limit on the corresponding distance parameter is ${{\ensuremath{\Lambda}}_{(2)}}^{\ensuremath{-}1}=5.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ cm. The upper limit for a fourth-power deviation is ${{\ensuremath{\Lambda}}_{(4)}}^{\ensuremath{-}1}=6.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ cm.

Comments on the Calculation of Relativistic Bremsstrahlung Cross Sections

Recent attempts to calculate relativistic bremsstrahlung cross sections in the intermediate energy region are discussed, using results from an independent exact numerical calculation. The numerical work of Brysk, Zerby, and Penny gives quite good results for the bremsstrahlung cross section, differential only in photon energy, but significantly underestimates and over-estimates the cross section, differential in photon energy and angle, in small-photon-angle regions and in large-photon-angle regions, respectively. The approximate analytical results of Elwert and Haug are quite good for low atomic number $Z$, but we can already see deviations for $Z=13$. For $Z=79$, their theory underestimates the cross section by large factors.

Analysis of Optical- and Inelastic-Electron-Scattering Data III Reflectance Data for Beryllium, Germanium, Antimony, and Bismuth

A procedure is described for simultaneously fitting reflectance data obtained for various photon energies and angles of incidence using a simple physical model for ε(ω), the complex frequency-dependent dielectric constant. The mutual consistency of the model and of the experimental data is tested, within the accuracy of each measurement. As an example of the technique, reflectance data in the vacuum ultraviolet obtained by Toots, Fowler, and Marton for Be, Ge, Sb, and Bi have been satisfactorily fitted. The model parameters have been used to derive the optical constants n and k (in satisfactory agreement with conventional determinations) and can be readily related to other relevant experimental results or theoretical calculations of ε(ω) if these are available.

Absolute cross section measurement of the elementary process of Bremsstrahlung production

The absolute cross section of electron bremsstrahlung that is differential with respect to the photon energy and to the photon and electron emission angles has been measured by using a coincidence technique. The incident electron energy was 300 keV.

Optical Emission from Surface Plasmons

AbstractA theory of light emission by surface plasmons created on a semi‐infinite plane‐bounded electron gas by grazing incidence fast electrons is presented. Photon‐surface plasmon coupling is assumed to occur through surface roughness and is taken to be weak enough so that it may be treated in low‐order perturbation theory. Formulae are given for the distribution in angle and energy of emitted photons of both polarizations, assuming that the surface roughness may be described by a stochastic model.

Potential model calculation for coplanar and noncoplanar proton-proton bremsstrahlung

The cross section for proton-proton bremsstrahlung is calculated for both coplanar and noncoplanar events using the Hamada-Johnston and Reid (soft-core) potentials. Agreement is obtained with the experimental data for angular distributions and cross sections integrated over the photon directions. We present a detailed analysis of the kinematics, the phase space and the matrix element in the neighborhood of the kinematic limit of noncoplanarity. We find a rapid decrease of the cross section integrated over photon angles as this limit is approached. This is due not to a strong variation of the phase space, which is essentially constant, but to the fact that near the kinematic limit for noncoplanarity of the protons, the photon is restricted to angles for which the probability for emission is small. For low energies (⪅ 30 MeV) of the incident proton, we give analytic expressions for the scattering amplitude, valid for coplanar as well as for noncoplanar events.

Investigation of nuclear effects in bremsstrahlung

A generalization of the usual inelastic electron scattering, proposed by Hubbard and Rose, is discussed where, in addition to the scattered electron, the photon is detected in coincidence. This photon is either due to bremsstrahlung or to electroexcitation and subsequent γ-decay of a nuclear level. The interference between both processes is studied in detail. Numerical results are given for the giant resonance region of 16O and two levels in 12C (4.43 and 15.11 MeV). The coincidence experiment seems to be a very useful tool in determining spins and parities of nuclear levels. In contrast to the usual inelastic electron scattering, in this spin analysis, no model concerned with the dependence of the nuclear form factors on momentum transfer enters. The interference phenomena between electron bremsstrahlung and nuclear radiation turn out to be quite noticeable in the differential cross section for coincidence experiments. The interference terms are less important in the cross section integrated over photon angles which corresponds to the usual inelastic electron-scattering experiments.

Relativistic Positron-Electron Bremsstrahlung at Wide Angles: A Numerical Calculation

The bremsstrahlung spectrum for the process ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{+}+{e}^{\ensuremath{-}}+\ensuremath{\gamma}$ has been evaluated at photon-emission angles of roughly 30\ifmmode^\circ\else\textdegree\fi{} to 120\ifmmode^\circ\else\textdegree\fi{} from the incident particles in the c.m. system. The phase-space integrals of the exact, lowest-order differential cross section were evaluated numerically. A computer program was used to reduce the Dirac traces to invariants and to further simplify them until reasonably compact expressions were obtained. Numerical results for selected photon angles and energies are given for 15-BeV positrons incident upon electrons at rest in the laboratory and for 600- and 4000-MeV positrons in the c.m. system (colliding-beam experiments). It was found that certain relativistic approximations to the spectrum, which are valid for forward angles, are still fairly good at wide angles; an empirical modification to such an approximation is given which provides a useful interpolation formula for the wide-angle region.

Elektron-Bremsstrahlungswirkungsquerschnitte von 180- und 380 keV-EIektronen

The bremsstrahlung cross sections, differential in photon energy and angle have been determined by measuring the x-rays emitted from thin targets (Al2O3: 56,5 and 113 μg/ cm2; Au: 9,7 and 24,4 μg/cm2) for incident electron energies of 180 and 380 keV with a 5×5 inch NaI scintillation spectrometer at angles from 0 to 150 degrees. A response matrix is used to convert the measured pulse height distribution into the spectrum of photons incident on the spectrometer. The results show that in this energy region the Bethe-Heitler-Sauter (Born approximation) theory underestimates the cross sectionsd 2 σ/dk · dΩ anddσ/dk. The application of the Elwert factor gives a considerable improvement. For Al2O3 the Elwert corrected Born approximation gives values which are generally within the limits of error of the measurements. The experimental values of theHeitler parameter $$\Phi _{rad} /\bar \Phi $$ are 5,0 (Al2O3) and 6,7 (Au) for 180 keV and 5,6 (A12O3) and 7,3 (Au) for 380 keV. The angular distribution of the radiation has been compared with some characteristic angles predicted by the theory ofSommerfeldKulenkampff. Special consideration has been given to the high frequency limit. The cross sections at this energy have been derived from the correctedSauter-Fano theory and are in good agreement with the measurements.

Coherent Bremsstrahlung from Si Single Crystal I. Experiment

The interference effects in the production of bremsstrahlung in a silicon single crystal have been studied by using 720 MeV electrons. The energy spectrum of the bremsstrahlung has exhibited interference maxima of the first five orders. The intensity variation of the 150 MeV photons with the rotation of the crystal has shown also three interference Maxima on each side of the central minimum. The observed interference conditions for the photon energy and angles of incidence of electrons relative to crystal axes are in good agreement with the theory.

Radiative Tail for Inelastic Electron Scattering

The cross-section differential in the energies and angles of all final particles for the bremsstrahlung which accompanies nuclear excitation is derived, in first Born approximation and neglecting nuclear recoil, in terms of the form factors corresponding to the Coulomb and current interactions, which are left arbitrary through-out the calculation. This cross section is integrated over all photon angles, without approximation, and its limit for large energies ($E\ensuremath{\gg}m{c}^{2}$) of the initial and final electron is discussed. As in the case of elastic electron scattering considered previously, photons emitted in the direction of either the incoming or outgoing electron contribute to this integrated cross section terms of order $\mathrm{ln}(\frac{E}{m{c}^{2}})$, while all other photon directions contribute terms of relative order 1. We give explicit expressions for these terms, as well as a numerical evaluation for some typical cases; the formulas are also valid for electron scattering angles $\ensuremath{\vartheta}$ equal or very close to 180\ifmmode^\circ\else\textdegree\fi{}. It is shown explicitely that the logarithmically divergent terms which appear in the integral of our high-energy cross section over the energy of the final electron are cancelled exactly if to this integral one adds the radiative corrections to the inelastic electron scattering cross section.