Elastic scattering of γ-rays from lead for energies from 0.145 to 1.33 MeV

Differential cross sections for elastic scattering of 889 and 1120 keV γ-rays from lead have been measured at angles ranging from 30° to 150°. These results and previously measured differential cross sections at 145, 279, 412, 662 and 1332 keV are compared with theoretical predictions taking into account Rayleigh scattering, nuclear Thomson scattering, and Delbrück scattering. The Rayleigh amplitudes of the K-shell were obtained from the theory of Brown et al., the amplitudes of the other shells from form factors calculated from relativistic HFS wave functions. Discrepancies are found at 145, 889, 1120 and 1332 keV while the experimental data at 279, 412 and 662 keV are in good agreement with the theory. A discussion of possible explanations and consequences is presented.     

Elastic scattering of 2.754 MeV photons by Ta and interference between Rayleigh,Thomson and Delbrück scattering

Differential cross sections for the elastic scattering of 2.754 MeV photons by Ta have been measured for angles ranging from 30° to 150°. A comparison with lowest-order Delbrück theory reveals discrepancies of the same size as previously observed for Pb and Bi. Consideration is given to interference phenomena between Delbrück, Rayleigh and nuclear Thomson scattering.     

Delbrück scattering of 9 MeV photons from tantalum

The differential elastic scattering cross section of 9.0 MeV photons by ¹⁸¹Ta has been measured at angles between 25° and 140° and a good agreement was obtained between the measured and predicted values at θ = 35–90°. In calculating the theoretical cross sections the coherent scattering contributions of nuclear Thomson (NT), nuclear resonance (NR) and Delbrück (D) amplitudes were included while that of Rayleigh (R) scattering was excluded. The D-amplitudes were taken from a recent calculation by Mork and Papatzacos. Evidence for the contribution of the real D-amplitude is obtained.     

The energy dependence of Delbrück scattering investigated at Z = 73, 82 and 92

Using neutron capture γ-rays from a ¹⁴⁰CeO₂ source installed in the Grenoble high-flux reactor, differential cross sections for the elastic scattering of photons by Ta, Pb and U through θ = 120° have been measured for E = 4.291 and 4.767 MeV. These data have been supplemented by measuring elastic differential cross sections for U, θ = 120° and energies ranging from 0.279 to 1.332 MeV, using radioactive sources. The experimental differential cross sections below 1 MeV confirm the predicted Rayleigh amplitudes based on the second-order S-matrix within 3%. An excellent agreement between experiment and lowest-order Delbrück theory is observed between 1.0 and 1.4 MeV, showing that Coulomb corrections are small close to the threshold for pair production. At 4.291 and 4.767 MeV experiment and lowest-order Delbrück theory agree within ~12%     

Coulomb correction to Delbrück scattering investigated atZ=94

Differential cross sections for the elastic scattering of 2.754 MeV photons by Pu were measured for angles ranging from 45 to 120° and interpreted in terms of Delbrück, nuclear Thomson, Rayleigh and nuclear resonance scattering. It is shown that the largest part of the discrepancy between experiment and the lowest-order Delbrück theory can be removed by introducing a (Zα)⁴-dependent Coulomb correction term. Evidence is obtained for additional Coulomb correction terms of higher order in (Z α).     

Delbrück scattering of 2.754 MeV photons by Bi and Th

Differential cross sections for the elastic scattering of 2.754 MeV photons by Bi and Th have been measured for angles ranging from 60° to 120°. The results deviate from the predictions of lowest-order Delbrück theory by factors between 1.1 and 1.4. The strong increase of these deviations with charge number, previously reported for Pb and U, has been confirmed. An interpretation in terms of the effect of the Coulomb correction is given.     

Quasiclassical green function in an external field and small-angle scattering processes

A representation is obtained for the quasiclassical Green functions of the Dirac and Klein-Gordon equations allowing for the first nonvanishing correction in an arbitrary localized potential which generally possesses no spherical symmetry. This is used to obtain a solution of these equations in an approximation similar to the Furry-Sommerfeld-Maue approximation. It is shown that the quasiclassical Green function does not reduce to the Green function obtained in the eikonal approximation and has a wider range of validity. This is illustrated by calculating the amplitude of small-angle scattering of a charged particle and the amplitude of Delbrück forward scattering. A correction proportional to the scattering angle was obtained for the amplitude of charged particle scattering in a potential possessing no spherical symmetry. The real part of the Delbrück forward scattering amplitude was calculated in a screened Coulomb potential.     

Numerical calculations of Delbrück scattering amplitudes

The computation of the imaginary Delbrück amplitudes with the formulae of Constantini et al. gave results whose accuracy is greater by a factor of 10 than that available in the literature. The real amplitudes were computed using the code of Papatzacos and Mork. This computation was extended to all angular and energy regions of interest, and hence may be very useful in the interpretation of scattering experiments.     

Elastic and Raman scattering of 8.5–11.4 MeV photons from 159Tb, 165Ho and 237Np

Differential cross sections for elastic and inelastic Raman scattering from the deformed heavy nuclei ¹⁵⁹Tb, ¹⁶⁵Ho and ²³⁷Np were measured at five energies between 8.5 and 11.4 MeV. Angular distributions at four angles between 90° and 140° for both elastic and inelastic scattering at 9.0 and 11.4 MeV were also measured. The monoenergetic photons were obtained from thermal neutron capture in Ni and Cr. All the angular distributions and the elastic and Raman scattering at the higher energies are in good overall agreement with theoretical predictions. The theory is based on a modified simple rotator model of the giant dipole resonance in which the effect of Delbrück scattering was included. A trend of both the elastic and Raman scattering at lower energies to be stronger than expected are suggested by the data. However, the ratio between the Raman and elastic scattering seem to be in good agreement with theory throughout the whole energy range. This shows that there is no need to introduce a direct nonresonant component to the imaginary part of the elastic scattering amplitude to explain the experimental data.     

Delbrück scattering

The various calculations of the Delbrück scattering amplitude are presented. This is followed by some generalities on the elastic scattering of photons by heavy atoms and finally by a review of the experiments together with a comparison with the calculations.     

Azimuthal asymmetry in processes of nonlinear QED for linearly polarized photon

Cross sections of nonlinear QED processes (photon-photon scattering, photon splitting in a Coulomb field, and Delbrück scattering) are considered for linearly polarized initial photon. The cross sections have sizeable azimuthal asymmetry.     

Delbrück scattering of 2754 keV photons by Nd,Ce, I,Sn, Mo and Zn

The elastic scattering of 2754 keV photons has been investigated for charge numbers Z between 30 and 92. The lowest-order Delbrück theory was found valid for small Z. A Coulomb correction term proportional to (Zα)⁴ fits the experimental data with few exceptions.     

Delbrück scattering of 2.75 MeV photons by uranium

Elastic differential scattering cross sections from U were measured at 2.75 MeV photon energy and compared with the predictions of lowest-order Delbrück theory. Evidence for the effect of multi-photon exchange is obtained.     

Delbrück-Streuung von 17 MeV-Photonen

Differential cross sections have been measured for the small angle scattering ofγ-rays by iron, silver, tantalum, lead and uranium with 17 MeV photons from Li⁷ (p, γ) Be⁸ at mean four momentum transfersq of 0·5mc and 1·3mc and with 7 MeV photons from F¹⁹(p, αγ)O¹⁶ at mean four momentum transfer of 0·5mc. Under these experimental conditions only Compton, Rayleigh and possibly Delbrück scattering are of importance. Extrapolation of known theoretical results to higher energies shows, that Rayleigh and Compton scattering from bound electrons should depend only onq for small angles, smallq and fixedZ. Using this it follows, that at 17 MeV andq≈0·5mc an additional scattering process must be present, which increases with growingZ and which is negligible in the measurements at 17 MeV withq≈1·3mc and at 7 MeV withq≈0·5mc. These results are in qualitative agreement with the approximate theory for Delbrück scattering ofBethe andRohrlich, however experimental cross sections at 17 MeV andq≈0·5mc are about a factor of 1·6 lower than those predicted by this theory. This discrepancy is not unexpected, since exact calculations of Delbrück scattering amplitude fromKessler andZernik at 2·62 MeV and 6·14 MeV show even greater deviations in the same sense.     

Elastic and Raman scattering of 8.5–11.4 MeV photons from 175Lu and 181Ta

Differential cross sections for elastic and inelastic Raman scattering from ¹⁷⁵Lu and ¹⁸¹Ta were measured. Five photon energies between 8.5 and 11.4 MeV were used and were obtained from the (n, γ) reaction on Ni and Cr using thermal neutrons. The results are compared with calculations using a modified simple rotator model (SRM) of the giant dipole resonance (GDR) in which the effect of Delbrück scattering was incorporated. In general, fair agreement between theory and experiment is obtained. A new set of GDR parameters is extracted, based on photon scattering data and, as expected, yield better agreement between experimental and predicted cross sections.     

The Z-dependence of the elastic scattering of γ-rays

The differential cross sections for elastic scattering of 662 keV and 279 keV γ-rays from Pb, Ta, Nd, Sn, Mo, and Zn have been measured at angles ranging from 45° to 135°. The results are compared with theoretical predictions taking into account Rayleigh scattering and nuclear Thomson scattering. The theoretical Rayleigh amplitudes are based on second order perturbation theory according to Brown et al. and on form factors calculated from relativistic HFS wave functions. A semi-empirical method of correcting the form factors is developed, valid for energies between 150 keV and 750 keV and charge numbers up to Z = 82. The average difference between calculated and measured differential cross sections was found to be 6%.     

Elastic scattering of electrons by benzene

Relative differential cross-sections for the elastic scattering of electrons from benzene have been measured at incident energies 300, 500, 700 and 900eV and for scattering angles between 30° and 120°. The results are discussed and compared with the independent atom model (IAM) calculations. Two different sets of scattering amplitudes for the constituent atoms of benzene were used in these calculations, one obtained from first Born approximation and the other from partial wave analysis of the Dirac equation. Only the static interaction was taken into account in the calculations. The higher the incident energy, the better is the observed agreement between experiment and theory. This indicates that at higher energies, absorption, exchange and polarization effects are not significant as compared to the static interaction and that the IAM satisfactorily predicts the interference of scattering from the individual atoms of C₆H₆.     

Symmetric scattering ine ±-H ionization collisions

Triple differential cross-sections for ionization of hydrogen atoms by electrons and positrons have been calculated for symmetric coplanar geometry following a multiple scattering method suggested and used earlier by the authors. Results show single binary peaks exactly at 45° and double binary peaks exactly at 135° for higher energies as are expected from an analysis of Briggs [3]. At lower energies there are certain deviations from these values. An analysis of scattering mechanism at peaks are also given. This supports Briggs’ explanation.     

Determination of the Scattering Amplitudes of Schrödinger Operators from the Cross-Sections,a New Approach

In this Letter we show how the scattering amplitudes of nonrelativistic one-particle Schrödinger operators with a scalar (not necessarily rotation invariant) potential may be obtained from the scattering cross-sections for the system where a scalar potential is added and whose scattering amplitudes are known explicitly.     

Nuclear photoexcitation and delbrück scattering studied in the energy range 2–8 MeV

Elastic scattering by nuclei in the range of mass numbers between 64 and 238 has been studied with monochromatic photons in the energy range between 2 and 8 MeV. These photons were provided either by a Ti(n,γ) source installed in the tangential through channel of the Grenoble high flux reactor, or by²⁴Na and⁵⁶Co sources produced by deuteron bombardment of Al or Fe at the Göttingen cyclotron. The photoexcitation of 23 nuclear levels has been observed and the decay properties and groundstate widths of the majority of these levels have been determined. For the lead scattering target the coherent elastic differential cross section has been studied in detail. There is evidence that below the photo-neutron threshold the elastic scattering via virtual photoexcitation of the nucleus can be approximated by extrapolating the real part of the Giant Dipole Resonance amplitude along a Lorentzian curve. Coulomb corrections to Delbrück scattering seem to play a small role at 6.5 MeV.