Electron-positron Pair Annihilation Research Articles

Annihilation of Electron-Positron Pairs into Mesons

We estimate the cross section for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{mesons}$ using (i) $\ensuremath{\rho}$ dominance of the electromagnetic current, (ii) known couplings of resonances to states involving the on-shell $\ensuremath{\rho}$ meson, and (iii) the assumption, for the purpose of obtaining numerical estimates, that the meson couplings vary slowly with virtual $\ensuremath{\rho}$ mass. We conclude that the cross section at 2-GeV total energy could be comparable to the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ cross section. We also attempt to estimate a cross section from the statistical model of Bjorken and Brodsky.

Annihilation into two photons of lepton pairs including anomalous magnetic moment and polarization effects

The high-energy y-ray source from electron-positron pair annihilation has been discussed by several authors (~,2) and looks most attractive for the bubble chamber (3.~). The use of magnetized supermendur foil (~) for polarized electrons will make it possible to obtain polarized high-energy photons from the pair-annihilation process. GATTO (~) analysed the two-quantum annihilation of the electron-positron pair, including a form factor to test qnantum electrodynamics with colliding-beam experiments. The purpose of this note is to report the results of a calculation of matrix elements for annihilation into two photons of lepton pairs with anomalous magnetic moment and polarization effects taken into account. A form factor which can be thought of as a product of a form factor for the vertex and a form factor for the propagator (6) is also included. The mass terms which are usually omitted not without justification for high-energy lepton pairs are included in the present calculation so that the results can be applied to both lowand high-energy experiments. The matrix elements for annihilation into two photons of a lepton pair with anomalous magnetic moments are given by

Neutrino-Electron Interactions and Stellar Evolution

A large part of the energy lost from interiors of evolving stars at temperatures greater than about 5 × 108°K is carried away by neutrinos. Three neutrino-producing reactions which have been incorporated in various evolutionary models are the photoneutrino process: direct annihilation of electron-positron pairs: and the plasma process:

Neutrino Emission from Star-like Sources

IN a previous communication1 we reported some evaluations of the neutrino energy density in the universe taking into account the e+ + e−→ ν + ν process in the pre-supernova stage of the stars. We found that this energy density may be higher than the energy density of the matter. Here we present a similar evaluation on the basis of the Mannino2 hypothesis regarding the star-like objects. It is known that the optical power of these objects is about 1046–1048 ergs/sec (ref. 3). According to Mannino2, this may be due to supernova explosions of as many as 4,000 a year. During the exploding stage the temperature of the stars goes up to 109–1010° K and the star begins to emit neutrino antineutrino pairs through annihilation of electron-positron pairs which at this high temperature are in equilibrium with the photons. The neutrino emission is of the same order and even higher of the photon emission4. Thus we can safely assume that the star-like sources emit 1048 ergs/sec as neutrino power. Because the energies of these neutrinos are of the order of a MeV, we have an emission of ∼1054 ν/sec/star-like source. (We can obtain these figures also supposing that each supernova inside the star-like object emits ∼1045 ergs/sec as neutrino power; since we have 10−4 supernovse/sec, and since the process goes on for about 200 days2, this is the same as saying that at each time we have 10−4.107 = 103 supernova in the whole star-like, which means an emission of 1045.103 = 1048 ergs/sec from the star-like sources.)

Energy spectrum of neutrinos produced in e+, e− pair annihilation

A calculation is made of the energy spectrum of neutrinos and antineutrinos produced in stars by electron-positron pair annihilation, on the basis of Feynman and Gell-Mann’s theory of weak interactions, in the electron density range from 1.6·103 to 1.6·106 g/cm3 and temperature range from 5·108 to 1010 °K. It is seen that the maximum of the neutrino spectrum ranges from 1.5 to 15 MeV.

Momentum Distributions of Photons from Positrons Annihilating in Alkali Halides

The angular correlation of photons from the two-gamma decay of positrons in all sodium halides and all alkali chlorides has been measured. The data yields the momentum distribution of the two gamma rays which is also the momentum distribution of the annihilating electron-positron pairs. It is seen that the positive ion has very little influence on the momentum distribution in comparison with the negative ion. These distributions in momentum are compared with the distributions calculated from various models of electron and positron wave functions in the crystal. For fluorides and chlorides the electron-positron wave-function products which yield fits to the experimental data resemble Hartree-Fock free-ion electron wave functions. Both the wave-function products and the free-ion wave functions yield density distributions which are similar to the electron densities obtained by x-ray measurements. This conclusion makes improbable a model of single-particle wave functions describing both the electrons and the positron tightly bound to the negative ion.

π-Meson-Elektron-Streuung und Struktur des π-Mesons

In this article we propose π-meson-electron scattering as a possibility for investigating the electromagnetic structure of the pion. This experiment requires very high energy, but not necessarily such a high accuracy as the extrapolation procedure of CHEW and Low. After a short discussion of the general properties of the electromagnetic formfactor of the π-meson, we calculate the π—e and the e—π scattering cross sections with form factor. With an energy of 25 GeV and a 10% experimental error we can probe the root mean square radius of the pion down to 0.8 10-13 cm, with 50 GeV down to 0.6·10-13 cm and with 100 GeV to 0.36·10-13 cm. The rms radius of the pion may be larger than previously assumed, because there exists the possibility of a fairly large π — π interaction. A complementary possibility for investigating the electromagnetic structure of the pion consists in electron-positron pair annihilation with the creation of a π± pair. This process will probe the form factor of the π-meson for timelike arguments.

MOMENTUM DISTRIBUTION OF METALLIC ELECTRONS BY POSITRON ANNIHILATION

The angular correlation of photons from the two-photon decay of positrons has been measured for positrons annihilating in some 34 elements, mostly metals. These data give the momentum distribution of photons and hence of the center of mass of the annihilating electron–positron pairs. The momentum distributions are discussed in terms of the velocity dependence of the annihilation probability. It is concluded that the observed momentum distributions are primarily the momentum distributions of the conduction electrons in the metals. A higher momentum component is observed, which is attributed to ion core effects.

The Angular Correlation of Annihilation Radiation

The departure from exact 180° angular correlation of quanta resulting from positrons annihilating in various materials has been measured. This provides data as to the momenta of the centres of mass of the annihilating electron-positron pairs. It does not appear possible to account for the data on the assumption that the positron achieves thermal energy by lattice collisions before annihilating, so that such measurements may not be simply related to the momentum distribution of the more loosely bound electrons in the absorbing substance.