Spectral structure of 245–445 keV electrons and positrons in positron-thorium scattering

Predicted intensity of gamma rays from photonium

“…We emphasize that (6) is a reasonable parametrization of the cross section which depends on the parameter D. D absorbs our overall ignorance of the interaction properties of photonium and can be thought of as the "effective diameter" of photonium. In our paper on production of photonium in the early universe we used the same cross section (6) and found that a D of 80 fermi would make photonium 90% of the mass of the universe. In this paper we will write most of our results for general D but will later choose D to be 80 fermi and will thus predict the flux of gammas if the photonium does indeed comprise 90% of the mass of the galaxy.…”

“…The numerical factor in (11) is proportional to mpr~176 m.~ We now need the integrated number of cosmic-ray protons per cm 3 with energy above the threshold in (11). From Pomerantz [18] we have a power law spectrum for cosmic rays in the solar neighborhood E )-t. 6 Np( > E)= 8.38• 10 -12 10~e V particles (cm) -3 (12) for 101~ eW < E < 1016 eV. We are interested in energies slightly below 101~ eV from (11).…”

“…~}-is given by (6) and is a function of R, the radial distance measured from the galactic center, since both N o and Np are functions of R. We have R 2 = r 2 + (Rs, n) 2 _ 2 rRs~ cos 0 (15) and rm, x = Rsu . cos 0 +/(Rmax) 2 --(Rsun) 2 sin 2 0 (16) where Rs~ is the distance of the sun from the galactic center nominally taken to be 10 kpc.…”

“…Thus the intensity for 0 = 0 ~ from the galactic center has more uncertainty associated with it than the intensity for 0 > 11.5 ~ If we choose the second model where the photonium is uniformly distributed in a halo of radius Rma x = 120 kpc instead of (3), (4), and (5) we use N o = 1.96 photonium cm -3 everywhere in the halo. Putting (13) into (6) and then (6) into (15) where distances in J' are again understood to be in kpc. J" is given in Table 1 also.…”

“…Since photonium has zero elastic width in vacuum it has been argued that the ultra-strong electromagnetic fields of the interacting heavy ion system generate an effective width which is large enough to explain the measured yield [1]. Support for this effective width model is derived through electron-positron (Bhabha) scattering from a high Z atom where a resonance at t.66 MeV was obtained [6]. The peculiar kinematic signature of this resonance was interpreted in terms of a multiple scattering mechanism at short distances which gave rise to a large induced elastic width [ 1,7].…”