“Recoil”-effect-induced contribution of order mα 6 to the hyperfine splitting of the positronium ground state

The recoil-effect-induced part of the mα ⁶ contribution to the hyperfine splitting of the positronium ground state is calculated. The method employed is based on noncovariant perturbation theory within QED. The result is 0.381(6)mα ⁶, which agrees well with the results of previous studies. This means that it deviates sizably from experimental data.     

Two-Photon Detachment Cross Section of the Positronium Negative Ion

The two-photon detachment cross section of positronium negative ion is calculated within the lowest-order perturbation theory for the final-state energies below the Ps(n = 2) threshold. A coupled-channel method with positronium orbital expansion is used to prepare the wavefunctions. The resonance structure below the threshold is clearly seen.     

Calculations of Coulomb systems with optimization of nonlinear parameters

Precise variational calculations of the energy and diverse physical characteristics are performed for the ground state of a fully nonadiabatic four-particle system—the positronium molecule e⁺e^?e⁺e^?. The nonlinear exponential parameters of correlated Gaussian basis functions dependent on all interparticle separations are systematically optimized. The dependence of the calculated energy values and the expectation values of interparticle separations (as well as their degrees and Dirac delta functions of interparticle separations) on the basis size N is examined. For N=200, the ground-state energy of the positronium molecule is found to be E=?0.5160028 au. For an extended basis set with N=4700 containing 200 basis functions with the optimized parameters and 4500 additional functions with random values of nonlinear parameters, E=?.5160036 au. At present, this result is the most accurate variational energy value of the positronium molecule, and it demonstrates the high efficiency of optimization of the nonlinear parameters in calculations of atomic-molecular systems. The lifetime of the positronium molecule e⁺e^?e⁺e^? with respect to electron-positron annihilation is calculated to be τ=2.26×10^?10 s.     

Induced decay of positronium and grasers

The differential cross section and the total cross section for the stimulated decay of positronium by an incident photon of frequencyΩ is calculated as a function of the dimensionless variableξ=hΩ/mc ². Forξ?1 the total cross section is found to decrease asξ ^?2. We also look at the particular case of positronium in a black-body radiation field. Expressions for the number of induced annihilations per second as functions of the dimensionless ratiomc ²/kT and the number of positronium atoms are obtained. It is found that this rate is proportional to (kT/mc ²)² forkT?mc ² and to (kT/mc ²)ln(kT/mc ²) forkT?mc ². The possibility of utilizing induced two-photon decay of positronium as a γ-ray laser at the wavelength λ _C /2 is examined, where λ _C is the Compton wavelength.     

Screening effect of the coulomb interaction on the energy levels of atomic and molecular systems

The energies of atomic and molecular systems with a screened Coulomb interaction are expressed in terms of properties of the system with a conventional Coulomb interaction to the third order in the screening constant. The energy levels of an H atom, an H^? ion, and nonadiabatic systems, namely, the positronium ion e ⁺ e ^? e ^? and the positronium molecule e ⁺ e ⁺ e ^? e ^?, are calculated for screened Coulomb interactions of charged particles. It is demonstrated that, as the screening constant of the Coulomb interaction increases, the stability of the hydrogen atom, the H^? ion, and the positronium molecule e ⁺ e ⁺ e ^? e ^? decreases, whereas the stability of the positronium ion e ⁺ e ^? e ^? increases after a slight decrease.     

Doubly excited resonances of positronium negative ions

Some lower-lying doubly excited ¹S^e and ³S^e resonances of positronium negative ions associated with N = 2 up to N = 5 positronium thresholds are calculated by a method of complex-coordinate rotation. Hylleraas-type wave functions with N = 203 terms are used to represent the system.     

Simplified Bethe-Salpeter equation for positronium

The Bethe-Salpeter equation for a fermion-antifermion system, coupled by photons, is considered in the Feynman gauge. The kernel is that resulting from exchange of a single photon. The usual reduction of the sixteen B-S spinor amplitudes in terms of tensors leads to 16 coupled integro-differential equations. By straightforward application of charge conjugation-, parity-, and Lorentz-invariance, the system of coupled equations is reduced to ones involving no more than eight and as few as three scalar structure functions for the various parity, charge conjugation, and total angular momentum states. The results hold for arbitrary coupling strength. As a check of the equations obtained, a perturbation theory is carried out for the Coulomb interaction. It leads to effective potentials in agreement with those obtained previously to order mα⁴ for positronium.     

Positronium quenching reactions and diffusion in solutions

The temperature effect on positronium quenching rates for p-benzoquinone and iodine in several solvents was determined. The quenching rate constantk ₁ follows ak ₁∝1/η relationship better than thek ₁∝T/η one, predicted by ordinary theory. A simple theoretical treatment based on diffusion theory shows that the temperatureT of the solute, positronium, may not be the same as the temperature of the solvent if the positronium is not fully thermalized. This temperature is found to be about twice the room temperature for the solvents investigated. The findings further support the theory that positronium reactions are “diffusion controlled” in liquid solutions. The activation energies of all the positronium reactions studied are either negligible or less than 0.1 eV.     

Positronium interactions with gases in pores of silicagels

Positronium interaction with O₂, NO, Cl₂ molecules in pores of silicagels has been investigated by the methods of lifetime and angular correlation. For silicagel with diameter of pores ≈100 Å it was obtained that the rate constant of positronium conversion on oxygen was (2.4±0.2)10⁷ sec^?1 atm^?1 and on nitrogen oxide (2.6±0.2)10⁷ sec^?1 atm^?1. The rate constant of the positronium chemical reaction with Cl₂ was found to be ≈10^?11 sec^?1 atm^?1. The results of investigation of positronium interactions with oxygen in the gas phase, organic liquids, zeolites, liquid argon, and nitrogen are explained in terms of the formation of an excited complex PsO ₂ ^* . The decay of this complex to Ps and O₂ makes possible positronium conversion, and stabilization of the complex leads to annihilation in the bound state (chemical reaction). Study of positronium interaction with O₂ in silicagels (diameters of pores 100, 30 and 16 Å) confirms the assumption of the complex formation. The rates of chemical reaction and of conversion become equal for pores of diameter of 20 Å. The estimated lifetime of the PsO ₂ ^* complex is τ _k ? 10^?12 sec.     

Three photon virtual annihilation contributions to positronium hyperfine structure

Three photon virtual annihilation contributions to the positronium hyperfine interval are calculated to order α⁶m(α⁴R_∞). The result is obtained in analytic form and leads to the small value of -0.91 MHz for the contribution to the ground state energy difference from this source.     

Complete reduction of fermion-antifermion bethe-salpeter equation with static kernel

The Bethe-Salpeter (BS) equation for a $\text{spin}\text{-}\text{1}\text{2}$ fermion-antifermion bound system is considered for the case in which the kernel is static and is the fourth component (i.e., three-scalar part) of a vector potential. Relative time (or relative energy) dependence can be eliminated easily. The 16 BS bispinor amplitudes are reexpressed in the usual way in terms of corresponding tensor amplitudes which satisfy 16 coupled integrodifferential equations. If Lorentz-, parity-, and charge-conjugation invariance are used, these equations can be reduced through a sequence of transformations to single eigenvalue equations, involving scalar and three-vector wavefunctions for singlet and triplet states, respectively. The effective Hamiltonians obtained in these equations are correct to all orders in the coupling constant and have a simple structure, consisting in general of a scalar, a spin-orbit, and a tensor part, which are explicitly exhibited.Although the equations could well be used for consideration of a general particleantiparticle system (e.g., quark-antiquark), for the present only positronium with a Coulomb interaction kernel is treated as an illustrative example. There exists a singlettriplet splitting in leading order mα⁶ ln α even though no spin-spin forces are directly introduced in the kernel. The splitting is calculated in detail in perturbation theory to order mα⁶ ln α and mα⁶.     

Low-Lying S-States of Two-Electron Systems

The energies of the low-lying bound S-states of some two-electron systems (treating them as three-body systems) like negatively charged hydrogen, neutral helium, positively charged-lithium, beryllium, carbon, oxygen, neon, argon and negatively charged muonium and exotic positronium ions have been calculated employing hyperspherical harmonics expansion method. The matrix elements of two-body interactions involve Raynal–Revai coefficients which are particularly essential for the numerical solution of three-body Schr?dinger equation when the two-body potentials are other from Coulomb or harmonic. The technique has been applied for to two-electron ions ¹H^? (Z = 1) to ⁴⁰Ar¹⁶⁺ (Z = 18), negatively charged-muonium Mu^? and exotic positronium ion Ps^?(e ⁺ e ^? e ^?) considering purely Coulomb interaction. The available computer facility restricted reliable calculations up to 28 partial waves (i.e. K _m  = 28) and energies for higher K _m have been obtained by applying an extrapolation scheme suggested by Schneider.     

More α61gα terms in positronium ground state splitting

We reconsider the calculation of the contribution to the positronium ground state splitting from the iteration of one-photon direct and exchange diagrams. New α⁶1gα terms are found besides the previously known vacuum polarization contribution. The present situation in the comparison of theory and experiment is summarized.     

Nonadiabatic theory of diamagnetic susceptibility of molecules

A nonadiabatic theory of diamagnetic susceptibility of molecules is presented in which the electrons and nuclei are considered to be a united system of charged particles whose motion is simultaneously per-turbed by a magnetic field. It is found that on separating out the translational motion of the molecule as a whole, there is certain freedom in choosing the phase of the wave function. Its optimum choice corresponds to the gauge of the vector potential with which two contributions opposite in sign to the magnetic susceptibility—the first order diamagnetism and the second order paramagnetism—have minimum magnitudes. Expressions for non-adiabatic calculations of the diamagnetic susceptibility of atoms and molecules are derived. The diamagnetic contributions to the energy of the hydrogen, helium, and lithium atoms, the hydrogen molecule, the π^?μ^?π⁺μ⁺ and p ^? K ^? p ⁺ K ⁺ mesomolecules, and the positronium molecule e ^? e ^? e ⁺ e ⁺ are calculated. The nonadiabatic contribution of the nuclear motion to the diamagnetic susceptibility amounts to 0.01–0.1% for ordinary atoms and molecules, is increased by several hundred times on passing to mesomolecules, and reaches 50% for the positronium molecule.     

Production of ultrarelativistic positronium beams in γe interactions

The possibility of producing ultrarelativistic positronium beams with a Lorentz factor of γ～10⁶ by means of laser-photon conversion on high-energy electron beams (E _e>0.5 GeV) is considered.     

Photodetachment of the positronium negative ion interacting with screened Coulomb (Yukawa) potentials

The effect of screened Coulomb (Yukawa) potentials on the photodetachment cross sections of the positronium negative ion is investigated by using the asymptotic form of the bound-state wave function and a plane wave form for the final-state wave function. The required normalization constant is determined from highly accurate, completely non-adiabatic wave functions for the three-particle systems. Photodetachment cross sections for the Ps^? ion are calculated for different Debye shielding lengths (D) ranging from infinite (pure Coulomb) to D = 1.81.     

Resonances in positron-atom scattering

Theoretical studies of atomic resonances involving positrons will be discussed in this talk. Investigations on resonances in positron-hydrogen scattering below various hydrogen and positronium thresholds are reviewed, as well as resonances in positronalkali and e⁺-He⁺ scattering. Resonance phenomena in other atomic systems involving positrons will also be discussed. These systems include positronium ions Ps⁻, positronium molecules Ps₂, and positronium hydride PsH.     

Process ν → νγ in strong magnetic field with allowance for posironium contribution to photon dispersion

We have studied the radiative decay of neutrinos with relatively high energies E ? m _e in a strong magnetic field taking into account the effect of a bound electron-positron pair (positronium) on photon dispersion. The allowance for the positronium contribution to the polarization operator of the photon substantially modifies the dispersion relation for the photon and the amplitude of the process in the vicinity of the cyclotron resonance. It is shown that the probability of the ?? ?? ??? process considerably increases when the positronium contribution is taken into account.     

A possible spectrum of positron states in porous silicon

A kinetic scheme of transformations and annihilation decays of positron and positronium states is considered in the bulk of a crystal in the crystal skeleton, and on the surface and in the bulk of pores of porous silicon. Formulas relating the intensities of temporal components of annihilation decay to the rates of decays and transformations of positron and positronium states in the pore volume are derived. The rate of interaction with the pore surface, accompanied by the formation of the surface state of a positronium atom, is estimated at 10⁷–10⁸ s^?1, while the estimated value for the pore radius is ≈2 nm.     

Estimates of axion signal from positronium decay

Numerical values for axion decay channel branching ratio in positronium decays are presented. From the ³S₁ state the maximum is of the order of 10^?6. If the axion mass were to be in the vicinity of the positronium mass, the best way of observing the signal would be the decay from the 2¹P₁ state. The feasibility of attaining this by optical pumping is indicated.