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Title: Compton scattering from positronium and validity of the impulse approximation

Abstract

The cross sections for Compton scattering from positronium are calculated in the range from 1 to 100 keV incident photon energy. The calculations are based on the A{sup 2} term of the photon-electron or photon-positron interaction. Unlike in hydrogen, the scattering occurs from two centers and the interference effect plays an important role for energies below 8 keV. Because of the interference, the criterion for validity of the impulse approximation for positronium is more restrictive compared to that for hydrogen.

Authors:
; ;  [1];  [2];  [3]
  1. Department of Physics, University of Rijeka, Rijeka (Croatia)
  2. (Croatia) and University of Dubrovnik, Dubrovnik (Croatia)
  3. (United States)
Publication Date:
OSTI Identifier:
21546789
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 83; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.83.053406; (c) 2011 American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPTON EFFECT; CROSS SECTIONS; HYDROGEN; IMPULSE APPROXIMATION; INTERFERENCE; KEV RANGE; PHOTON-ELECTRON INTERACTIONS; PHOTON-POSITRON COLLISIONS; POSITRONIUM; APPROXIMATIONS; BASIC INTERACTIONS; CALCULATION METHODS; COLLISIONS; ELASTIC SCATTERING; ELECTROMAGNETIC INTERACTIONS; ELEMENTS; ENERGY RANGE; INTERACTIONS; NONMETALS; PARTICLE INTERACTIONS; PHOTON COLLISIONS; PHOTON-LEPTON INTERACTIONS; POSITRON COLLISIONS; SCATTERING

Citation Formats

Kaliman, Z., Pisk, K., Pratt, R. H., Rudjer Boskovic Institute, P. O. Box 180, Zagreb, and Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260. Compton scattering from positronium and validity of the impulse approximation. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.83.053406.
Kaliman, Z., Pisk, K., Pratt, R. H., Rudjer Boskovic Institute, P. O. Box 180, Zagreb, & Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260. Compton scattering from positronium and validity of the impulse approximation. United States. doi:10.1103/PHYSREVA.83.053406.
Kaliman, Z., Pisk, K., Pratt, R. H., Rudjer Boskovic Institute, P. O. Box 180, Zagreb, and Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260. 2011. "Compton scattering from positronium and validity of the impulse approximation". United States. doi:10.1103/PHYSREVA.83.053406.
@article{osti_21546789,
title = {Compton scattering from positronium and validity of the impulse approximation},
author = {Kaliman, Z. and Pisk, K. and Pratt, R. H. and Rudjer Boskovic Institute, P. O. Box 180, Zagreb and Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260},
abstractNote = {The cross sections for Compton scattering from positronium are calculated in the range from 1 to 100 keV incident photon energy. The calculations are based on the A{sup 2} term of the photon-electron or photon-positron interaction. Unlike in hydrogen, the scattering occurs from two centers and the interference effect plays an important role for energies below 8 keV. Because of the interference, the criterion for validity of the impulse approximation for positronium is more restrictive compared to that for hydrogen.},
doi = {10.1103/PHYSREVA.83.053406},
journal = {Physical Review. A},
number = 5,
volume = 83,
place = {United States},
year = 2011,
month = 5
}
  • We present the first study to examine the validity of the relativistic impulse approximation (RIA) for describing elastic proton-nucleus scattering at incident laboratory kinetic energies lower than 200 MeV. For simplicity we choose a {sup 208}Pb target, which is a spin-saturated spherical nucleus for which reliable nuclear structure models exist. Microscopic scalar and vector optical potentials are generated by folding invariant scalar and vector scattering nucleon-nucleon (NN) amplitudes, based on our recently developed relativistic meson-exchange model, with Lorentz scalar and vector densities resulting from the accurately calibrated PK1 relativistic mean field model of nuclear structure. It is seen that phenomenologicalmore » Pauli blocking (PB) effects and density-dependent corrections to {sigma}N and {omega}N meson-nucleon coupling constants modify the RIA microscopic scalar and vector optical potentials so as to provide a consistent and quantitative description of all elastic scattering observables, namely, total reaction cross sections, differential cross sections, analyzing powers and spin rotation functions. In particular, the effect of PB becomes more significant at energies lower than 200 MeV, whereas phenomenological density-dependent corrections to the NN interaction also play an increasingly important role at energies lower than 100 MeV.« less
  • A series expansion of the Born propagator allows one to represent successive corrections to the impulse approximation and exhibits their relative dependence in momentum transfer k and the Compton (target-structure) parameter q. The proposed treatment provides a physical interpretation of the observed Compton defects. It is shown here to be in close agreement with high-energy-electron-impact spectroscopy measurements obtained for helium atoms.
  • The nonrelativistic (nr) impulse approximation (NRIA) expression for Compton-scattering doubly differential cross sections (DDCS) for inelastic photon scattering is recovered from the corresponding relativistic expression (RIA) of Ribberfors [Phys. Rev. B 12, 2067 (1975)] in the limit of low momentum transfer (q{yields}0), valid even at relativistic incident photon energies {omega}{sub 1}>m provided that the average initial momentum of the ejected electron <p{sub i}> is not too high, that is, <p{sub i}> <m. This corresponds to a binding energy E{sub b}<10 keV. This q{yields}0 nr limit is simultaneous with the approach of the scattering angle {theta} to 0 deg. ({theta}{yields}0 deg.)more » around the Compton peak maximum. This explains the observation that it is possible to obtain an accurate Compton peak (CP) even when {omega}{sub 1}>m using nr expressions when {theta} is small. For example, a 1% accuracy can be obtained when {omega}{sub 1}=1 MeV if {theta}<20 deg. However as {omega}{sub 1} increases into the MeV range, the maximum {theta} at which an accurate Compton peak can be obtained from nr expressions approaches closer to zero, because the {theta} at which the relativistic shift of CP to higher energy is greatest, which starts at 180 deg. when {omega}{sub 1}<300 keV, begins to decrease, approaching zero even though the {theta} at which the relativistic increase in the CP magnitude remains greatest around {theta}=180 deg. The relativistic contribution to the prediction of Compton doubly differential cross sections (DDCS) is characterized in simple terms using Ribberfors further approximation to his full RIA expression. This factorable form is given by DDCS=KJ, where K is the kinematic factor and J the Compton profile. This form makes it possible to account for the relativistic shift of CP to higher energy and the increase in the CP magnitude as being due to the dependence of J(p{sub min},{rho}{sub rel}) (where p{sub min} is the relativistic version of the z component of the momentum of the initial electron and {rho}{sub rel} is the relativistic charge density) and K(p{sub min}) on p{sub min}. This characterization approach was used as a guide for making the nr QED S-matrix expression for the Compton peak kinematically relativistic. Such modified nr expressions can be more readily applied to large systems than the fully relativistic version.« less
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