Breakup of positronium by Compton scattering of high-energy photons

We study the breakup of positronium (Ps) by Compton scattering in the range of photon energies, where the motion of the electron and the positron remains nonrelativistic and the process is dominated by the interaction terms <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>∼</a:mo><a:msup><a:mover accent="true"><a:mi mathvariant="bold-italic">A</a:mi><a:mo>̂</a:mo></a:mover><a:mn>2</a:mn></a:msup></a:mrow></a:math>, where <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mover accent="true"><d:mi mathvariant="bold-italic">A</d:mi><d:mo>̂</d:mo></d:mover></d:math> is the vector potential of the photon field. In this study we first compare the total cross section for this process with the total cross section for the positronium breakup by photoabsorption, showing that they become equal at the incident photon energy <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>ℏ</g:mi><g:msubsup><g:mi>ω</g:mi><g:mi>i</g:mi><g:mtext>Ps</g:mtext></g:msubsup><g:mo>≈</g:mo><g:mn>2.2</g:mn></g:mrow></g:math> keV and that—due to strong (and opposite) dependencies of these cross sections on the photon energy—the Compton scattering rapidly becomes by far the dominant breakup channel when the photon energy exceeds <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>ℏ</h:mi><h:msubsup><h:mi>ω</h:mi><h:mi>i</h:mi><h:mtext>Ps</h:mtext></h:msubsup></h:mrow></h:math>. Then we explore the energy and angular spectra of electrons and positrons, which are emitted from the positronium in collisions with high-energy photons, and of the scattered photons. By analyzing the physical mechanisms, which determine the properties of the spectra, we demonstrate that in such collisions the atomic particles can be clearly subdivided into the “participator,” on which the incident photon scatters, and the “spectator,” which is not directly involved in the scattering process. The results for the positronium breakup are compared with the corresponding results for the ionization of atomic hydrogen and the similarities in these processes as well as the differences between them are discussed.