Quasi-free Ps state

Coulombic attraction and increase average e+-e separation in the positronium. Both these factors decrease binding energy between the positron and electron constituting the positronium and therefore reduce the width of the Ore gap. 

Elementary estimation of the Ps confinement effect is the following. The ground-state energy of a point particle with mass 2m in an infinite potential well of radius R is where m is the electron mass and 

Of course, simulation of the Ps repulsion from molecules by an infinitely deep potential well is a crude approximation. A more realistic approach, based on the finite well Ps bubble model [10, 11], gives information about the depth U of the well, which has a meaning of the Ps work function, VoPs, i.e., the energy needed for Ps to enter the liquid without any rearrangement of molecules and stay there in the delocalized quasi-free state, qf-Ps. This state has no preferential location in the bulk. The qf-Ps state corresponds to the bottom of the lower-energy band available to the interacting e+-e pair. Obviously, this state precedes the formation of the Ps bubble. The same state may be obtained from the Ps bubble state if the free-volume radius R of the bubble is tending to zero, Fig. 5.4. 

One should expect that Vq is negative because of the prevalence of the polarization interaction of ej with the medium molecules over repulsion from the nuclei [12]. So we may roughly equate V + to the energy P of polarization interaction, eqf, which can be calculated by decomposition of Vq into the sum of kinetic K- and polarization P terms [13]  

Based on the Ps bubble model, [10, ll] experimental data on o-Ps lifetimes, and the widths of the narrow component of the ACAR spectrum, it was found that in practically all investigated liquids of various chemical nature, values of V0Ps = U are close to +3 eV. Thus, from Eq. (6) we obtain Eb —(0.5 to 1) eV. This means that qf-Ps is a loosely bound structure although the long-range Coulombic attraction between e+ and e always provides for the existence of the bound state. Because e+-e separation, rep, in qf-Ps is expected to be large, we may rewrite E, in the following form  

---