One‐Photon Annihilation of Lorentzian Positrons in the Interstellar Medium

Abstract

ABSTRACTWe investigate one-photon annihilation of Lorentzian positrons with bound atomic electrons in the interstellarmedium. The K and higher shell contributions, using the effective nuclear charges, are included to evaluate the an-nihilationrateof Lorentzianpositrons.Theresultsshowthattheone-photonpositronannihilationrateincreaseswithincreasing positron temperature T þ ( T þ /ryd), and decreases with increasing spectral index ( ) for both the K andhigher shell electrons. In addition, we find that positron annihilation rates for K-shell electrons are much larger thanfor higher shell electrons. At the intermediate positron temperature T þ ¼1, the K-shell electrons of Si and C atomsproducethelargestannihilationrateswhen ¼ 2and6,respectively.However,atthehightemperatureT þ ¼10,theK-shell electrons of Si and Mg atoms provide the largest annihilation rates for ¼ 2 and 6. Hence, the annihilationrate is quite sensitive to the Lorentzian character of the positron distribution.Subject headinggs: atomic processes — elementary particles — ISM: general1. INTRODUCTIONPositronannihilationhasbeenof greatinterestinastrophysics,since these processes produce gamma-radiation (Gould 1989,2006;Guessoumetal.1991;Fatuzzoetal.2001).Ininteractionswithfreeelectrons,mostpositronsareannihilatedproducingtwoor three photons, depending on the singlet and triplet spin statesof theelectron-positronsystem,i.e.,positronium(Heitler1954;Gould2006).Fordirectpositronannihilationwithboundatomicelectrons, only one photon can be radiated, since the atomic nu-cleus can take up the recoil momentum of the emitting photon.Frommomentumconservation,theone-photonannihilationpro-cess is impossible for the case of positron annihilation with freeelectrons.Thesedirectpositronannihilationswithatomicelectronsproduce 1.02 MeV single photons. This one-photon emissionspectrum is quite different from the 511 keV electron-positronannihilation emission spectrum.Palathingal et al. (1991) performed an experimental investi-gation of one-photonannihilationsof high-energypositronswiththepositronbeamatenergies1MeVandhigher,anddemonstratedthepossibilityof detectingone-photonannihilationspectrafromvarious elements. Theoretical investigations have also been car-ried out for one-photon positron annihilation with atomic electrons(Jung 1994, 1998). It is known that the one-photon annihilationcross section shows a very strong dependence of Z