Electron-positron System Research Articles

Rotating fields and particle-like states of electron-positron systems

It is argued that the field of a charge in a stationary orbit co-rotates with the charge about the centre of mass. Such a field has no radiation term. It is obtained by transformation from the co-rotating frame of reference; direct calculation would require that the constitutional properties of the medium be known, these being such as to curve light rays. For rotating reference system Corum's tetrad field is employed, the object of anholonomity affecting the derivation of fields from potentials. The force between the charge *e of positronium is found to be (1 -p2)'/' e2/ri2 when the charges follow with velocity o x r (= pc) a stationary circular orbit of diameter r12 (= 2r). Stationary orbits are selected by Bohr quantisation of canonical angular momentum. A quadratic equation is obtained for yp and for r12, where y = (1 -p2)-1/2. One solution gives the well-known 'atom-like' states. The other gives 'particle-like' states for which orbital motion is ultrarelativistic (yp = n/a, where a = 1/137), orbital diameters are small compared with eZ/mc2 (zd), m being the electron mass, and energies are 2amc2/n, small compared with mc2. In such a state positronium is termed a 'positronium unit'. The unit has a very long lifetime for radiative transitions, and should possess a weak magnetic moment (p = cued/2n). If it is assigned half-integral orbital angular momentum (hence imaginary parity) it might be identified with the neutrino. A system in which two units orbit around a stationary charge has the properties of the muon, and a system with one orbiting unit has the properties of the charged pion. Spin, charge, rest energy and decay mode are explained in each case. The very different reactivities also can be explained. A system, 'trionium', in which two charges of one sign orbit about a central stationary charge of the opposite sign is explored. Again ultrarela- tivistic states emerge, but the energies differ inappreciably from the rest energy mc2 of the central charge. However, if one adds further pairs of charges in orbits of increasing radius, the magnetic coupling between orbital currents provides energies of order mc2/a. It is speculated that such a system may afford a model for the proton. 1. Introduction and general philosophy In the early years of this century physicists were confronted with an empirical classification of atoms based on their chemical reactivity -the periodic table of the elements. In addition, there was some spectroscopic evidence to be explained, chiefly the spectrum of the hydrogen atom and Moseley's law for x-ray lines. The key for the unravelling of this situation was provided by Rutherford when he proposed his electrodynamical model of the atom, and further crucial steps were taken by Bohr when he introduced the concept of stable orbits and thereby found at least a first-order explanation for the hydrogen atom spectrum. One wonders how long progress might have been delayed had not these steps been taken. Today one has an empirical

Temperature-dependent Coulomb interactions in hydrogenic systems

In a hydrogenic plasma, the effective potentials V/sub i/j(r) of electron-proton, electron-positron, and electron-electron systems are considered. The inclusion of quantum-mechanical effects leads to a finite value of V/sub i/j(0) at the origin. For each system simple and analytical expressions are obtained at high temperature and small interparticle distance. Barker's numerical computations are extended to the high-temperature domain, small-r region, and electron-positron system. The symmetry effects are included for the electron-electron system. Various simple approximate formulas are obtained which describe V/sub i/j(r) at all distances. Some of them are in excellent agreement with the numerical results.

Form-factor corrections to superpositronium and short-distance behavior of the magnetic moment of the electron

We present a nonperturbative theory of superpositronium, the highly massive very narrow resonance states in the electron-positron system due to anomalous-magnetic-moment interactions. From basic coupled equations of quantum electrodynamics we show that the form-factor corrections play a role only at distances smaller than the superpositronium size, $\frac{{\ensuremath{\alpha}}^{2}}{m}$, in such a way as to precisely induce the formation of the superpositronium.

Einstein-Podolsky-Rosen non-separability and Feynman non-locality

It is argued, using the Feynman transition amplitude for the annihilation of an electron-positron pair into two photons, that the Einstein-Podolsky-Rosen non-separability (especially when discussed in polarization terms) and the Feynman non-locality (as exemplified in the case of the electron-positron system) are indeed the same concept. This gives strong support to the view that the EPR correlation occurs through the pair of timelike vectors joining the measurements to the point of severance of the subsystems. An interesting byproduct of the argument is that, given the four energy-momenta and polarization states which are involved, the overall system is in general neither P- nor C-, but is PC-invariant, so that the generalized Landau symmetry concept could have been suggested by quantum electrodynamics.

Resolution in experiments of angular correlation of annihilation photons

The overall resolution function for angular correlation devices is evaluated, removing the point source approximations. The non-uniform intensity distribution in the source is taken into account. The impact of the resolution on the features of the recorded angular correlation curves is discussed, with reference to the electron-positron system annihilation.

Self-Consistent Dispersion-Theoretic Electromagnetic Scattering Amplitudes

A procedure for calculating self-consistent electromagnetic scattering amplitudes when there are bound states, applied in a previous paper to the electron-positron system, is extended to include spin-0-spin-0 and spin-0-spin-$\frac{1}{2}$ elastic scattering. The second-order amplitudes which result have the correct double-spectral functions and are cutoff-independent, analytic, and crossing-symmetric. The Regge trajectory functions which are required by self-consistency imply the usual Coulomb bound-state spectrum with reduced mass and recoil corrections, and the appropriate Regge asymptotic behavior. The correspondence between the amplitudes obtained by this procedure and by other means is discussed briefly.

Self-Consistent Dispersion-Theoretic Electron-Positron Scattering Amplitude

A method is outlined for the construction of dispersion-theoretic electromagnetic scattering amplitudes for processes in which bound states may appear; in particular, the electron-positron system is examined. A Lorentz-covariant spinor amplitude is exhibited which is analytic, cutoff independent, and crossing symmetric, which has the correct double-spectral functions through second order in the fine-structure constant $\ensuremath{\alpha}$, and which reduces to the usual Born approximation in lowest order. Moreover, the amplitude displays Regge asymptotic behavior and the positronium Regge poles. Self-consistency requires that the positronium poles appear at the correct position and with the proper residue, and that the amplitude possesses a well-defined Jacob-Wick expansion. It is found that this second-order amplitude provides a suitable basis for iterative calculation of the higher-order terms using the same procedure.

Note on Positronium

By means of an inequality providing an upper bound for the norm of integral operators, it is shown that the Bethe-Salpeter equation for bound states of the electron-positron system (in the ladder approximation) admits solutions associated with a discrete spectrum of binding energies. It is found that in the weak coupling limit the spectrum B(α) approaches asymptotically the Coulomb spectrum in the sense lim lim α→0(B(α)/mα2)={(1/4n2) | n=1, 2, 3, … ∞},where α is the fine-structure constant and m the electron rest mass.

Reaction,π−+p→e++e−+n, as a Means of Measuring the Electromagnetic Form Factor of the Charged Pion

The success of the single pion exchange approximation in explaining the experimental results for the reaction $\ensuremath{\pi}+n\ensuremath{\rightarrow}\ensuremath{\pi}+\ensuremath{\pi}+n$ in the region of the two-pion resonance suggests that the single pion exchange contribution to the reaction $\ensuremath{\pi}+n\ensuremath{\rightarrow}{e}^{+}+{e}^{\ensuremath{-}}+n$ should be dominant for center-of-mass energies of the electron-positron system in the region of this resonance. A measurement of the rate of this reaction in this region should, therefore, provide direct information about the charged-pion electromagnetic form factor in the neighborhood of the two-pion resonance. We have calculated the differential cross section for the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}{e}^{+}+{e}^{\ensuremath{-}}+n$, assuming a counter experiment. Our estimates indicate that counting rates of the order of ten per hour are attainable by accelerators capable of producing negative-pion beams with an average flux of ${10}^{6}$ pions per second.

On the Positronium in Metals

Experimental results indicate that in metals positrons reach thermal velocity in a short time and subsequently remain free, annihilating with conduction electrons. However, the possibility of the existence of positronium in metals undergoing continuous change of the electron partner may not be excluded. An electron-positron system in metals is considered, and its properties are investigated. The properties are somewhat different from those in free space. The binding energy and lifetimes ware computed and tabulated for several alkali metals. The binding energies of positronium in alkali metals are smaller than that of positronium in free space and the lifetimes are longer, except in lithium. (A.C.)

Electrodynamic Displacement of Atomic Energy Levels. III. The Hyperfine Structure of Positronium

A functional integro-differential equation for the electron-positron Green's function is derived from a consideration of the effect of sources of the Dirac field. This equation contains an electron-positron interaction operator from which functional derivatives may be eliminated by an iteration procedure. The operator is evaluated so as to include the effects of one and two virtual quanta. It contains an interaction resulting from quantum exchange as well as one resulting from virtual annihilation of the pair. The wave functions of the electron-positron system are the solutions of the homogeneous equation related to the Green's function equation. The eigenvalues of the total energy of the system may be found by a four-dimensional perturbation technique. The system bound by the Coulomb interaction is here treated as the unperturbed situation. Numerical values for the spin-dependent change of the energy from the Coulomb value in the ground state are finally obtained accurate to order $\ensuremath{\alpha}$ relative to the hyperfine structure ${\ensuremath{\alpha}}^{2}$ Ry. The result for the singlet-triplet energy difference is $\ensuremath{\Delta}{W}_{\mathrm{ts}}=\frac{1}{2}{\ensuremath{\alpha}}^{2}{\mathrm{Ry}}_{\ensuremath{\infty}}[\frac{7}{3}\ensuremath{-}(\frac{32}{9}+2\mathrm{ln}2)\frac{\ensuremath{\alpha}}{\ensuremath{\pi}}]=2.0337\ifmmode\times\else\texttimes\fi{}{10}^{5}\frac{\mathrm{Mc}}{sec}.$ Theory and experiment are in agreement.