We have studied the annihilation of galactic positrons in order to evaluate the probabilities of various channels of annihilation and to calculate the spectrum of the resulting radiations The narrow width (FWW < 3 " 2 keV) of the 0.511 MeV line observed from the Galactic Center ( Leventhal et al. 1978) implies that a large fraction of positrons should annihilate in a medium of temperature less than 10 5K and ionization fraction greater than 0905, HIl regions at the Galactic Center could be possible sites of annihilation. I I. INTRODUCTION Leventhal, NcCallum and Stang (1978) have recently reported observation of positron annihilation radiation from the Galactic Center using a balloon borne germanium detector. The observed line is at 510.7 ±0.5 keV, and its full width at half maximum (FWHM) is less than 3.2 keV. There is also some evidence for the three--photon continuum from triplet positronium annihilation. The 0.511 MeV line was previously seen from the solar flares of 1972, August 4 and 7 (Chupp, Forrest and Suri 1975), but because the lower energy resolution of the Nal detector used, only an upper limit of about 40 keV could be set on the line width from this observation. Depending on the temperature and density of the ambient medium, positrons and electrons can either annihilate directly or form positronium. The importance of positronium formation in the interstellar medium was pointed out by Steigman (1968), by Stecker (1969), and by Leventhal (1973), and positron annihilation in solar flares, both direct and via positronium, has been treated by Crannell et al. (1976). Positronium can form either in the singlet state which annihilates into two 0.511 MeV photons, or in the triplet state which decays by 3 photon annihilation. Positronium is formed by both radiative recombination with free electrons and charge exchange with neutral hydrogen (atomic or molecular). Charge exchange with heavier ions is much less important than these processes (Crannell et al. 1976). Once formed in a particular spin state, positronium in the interstellar medium annihilates from the same state, because the lifetimes of both singlet and triplet positronium (10 -10 sec and 10 -7 sec, respectively) are much shorter than typical collision times with interstellar gas.
Recent interest in the properties of the negative ion of positronium has encouraged us to compute its cross section for photodetachment.To simplify the calculation, we have used the asymptotic form of the bound-state wave function and a plane wave for the final-state wave function, following the work of Ohmura and Ohmura in the case of photodetachment of H . We have obtained the needed normalization constant from a very precise and extensive Hylleraas wave function for the three-particle bound state.The positronium negative ion (Ps ) has for years' been known to be particle stable and has been the subject of many theoretical investigations, 2 4 but only recently has it been produced in the laboratory. Further investigations have resulted in good measurements of its annihilation lifetime, which agree ' within experimental uncertainty with theory.It has also been suggested' that Ps could be used to generate positronium (Ps) beams of controlled energy; this~ould involve acceleration of Ps ions and photodetachment of one electron. For this application, as well as on general principles, it would be interesting to know the photodetachment cross section of Ps The formulation of the problem is straightforward:The dipole transition matrix element is calculated with use of a sufficiently accurate initial wave function of the bound ionic state as well as a p-wave continuum function describing the e -Ps final state. In this report we will describe a calculation which simplifies the description of the initial bound state by representing it by an asymptotic form whose normalization comes from the most accurate Hylleraas wave function of the ion. ' [This is justified by the very small binding energy (0.326 eV) of the Ps ion]. We make a further simplifying assumption by taking the final state to be a plane wave. (Note that some work designed to take into account the scattering has already been done. ')In Rydberg atomic units, the Hamiltonian of the system consisting of two electrons (pt, pz) and one positron (x) is2 2 2 2 + 2 Ipt -xl Ipz -«I Ipi -pzl For the initial bound state of Ps, it is convenient to transform to the following center-of-mass coordinate system: Omitting R, which describes uniform motion of the center of mass, we previously wrote a wave function for the Ps ground state in the Hylleraas form as follows: I +1 "2 "p;(rq, rz, r~z) = g C(l, m, n ) [rtrz e I, m, n I m "2 "j ] n and obtained an extremely accurate variationa1 energy. " For the final state of the photodetachment, on the other hand, itis more appropriate to describe the Ps+e system in an asymmetric form, since the correct kinematic description involves the motion of an electron relative to the center-ofmass of the Ps atom. That is, we use the coordinate Rz= rz -rt /2 in place of rz, while retaining the other coordinates as before. The Hamiltonian in these unsymmetric coordinates is 0"= -2 V, , +4VR + -+ 1 IRz+ -,r) I The final state, involving the relative motion of a free electron and Ps in the ground state, must be a p state. In this paper, we will as...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.