ИСТИНА

When experimental data on positron annihilation data are interpreted, the positronium atom (Ps) is usually considered as a structureless point particle, although it is well-known that Ps is a finite-sized electron-positron pair bound by the Coulombic force. The reason of a tremendous abundance of the “point-Ps” approximation is its mathematical simplicity and practical convenience in treatment of annihilation spectra. However, ignorance of an internal structure of e+e- pair and variation of its energy during a Ps formation process are rather questionable (remind, that in vacuum Coulombic energy in Ps is rather large -Ry=-13.6 eV). This quantity (together with the other terms) enters an energy balance of the final Ps bubble state, determines its radius (and, therefore, its mobility, chemical reaction rate constants), pick-off lifetime, contact density [1]. We have attempted to develop a model of the Ps bubble state, considering Ps atom not as a structureless particle, but as a finite-sized e+e- pair in which both particles interact with surrounding medium. We have suggested a reasonable expression for the wave function of the e+e- pair in its ground state and minimized the total energy <Ψ|H|Ψ> of the pair with respect to variational parameters entering the wave function Ψ. However, when e+ and e- reside inside a nanobubble, the dielectric permittivity ε(r+, r-) has to be taken into account. It diminishes of e+e- Coulombic interaction by the medium even when the pair is localized in the bubble. In this case ε depends on the positions of both species (r+, r-) with respect to the bubble. We have used the simplest approximation for ε, which correctly links two limiting cases of large and small Ps bubbles. We have tried two different types of localization potentials of the e+e- pair: 1) both particles interact with the medium via same spherically symmetric square-well potentials, U(r+)=U(r-); 2) only electron entering the Ps atom interacts with the medium, but e+ does not. Obtaining optimized wave function of the pair and its total energy, one may calculate pick-off annihilation rate and Ps contact density. Including into minimization a rearrangement (surface) energy of the medium during the bubble formation, one may estimate equilibrium radius of the Ps bubble and kinetics of its growth. Finally we reconsider interpretation of the LT spectra in water basing on the suggested Ps bubble model. [1] S.V. Stepanov, D.S. Zvezhinski, G. Duplatre, V.M. Byakov, Yu.Yu. Batskikh, P.S. Stepanov, Materials Science Forum Vol. 666, 109-114 (2011)