Positronium state

The most accurate theoretical results for positronium formation in positron-helium collisions in the energy range 20-150 eV are probably those of Campbell et al. (1998a), who used the coupled-state method with the lowest three positronium states and 24 helium states, each of which was represented by an uncorrelated frozen orbital wave function... 

Walters (1996) and Kernoghan et al. (1996) both employed 11 states (five atomic and six positronium). A common feature of all the calculations is that, although they differ in the details of the magnitudes, they do show that the formation of positronium into excited states is a very important process for these targets and is responsible for the peak-shaped cross sections measured by Zhou et al. (1994b). A detailed study by McAlinden, Kernoghan and Walters (1996) shows how the breakdown into the various positronium states occurs. These authors obtained cross sections which, at least for positronium formed in the 2s and 2p states, were a factor 2-3 smaller than those calculated by Hewitt, Noble and Bransden (1993) using the seven-state approximation. 

The measurement of daPs/dQ is not an easy task and, as we shall see, there is little experimental information presently available. We note here that many experimental arrangements which could be used to measure differential positronium formation cross sections sum over all the possible quantum states (nPs, lPs) of the positronium, whereas calculations usually refer to one particular state. Some differentiation between positronium states with different values of nPs can be achieved if the time of flight of the positronium, and hence its kinetic energy, is measured, and such a technique has been used to investigate beams of positronium atoms produced in positron-gas collisions (see section 7.6). 

Fig. 5.1. Cross sections for the excitation of atomic hydrogen obtained using the coupled-state approximation with 30 hydrogen states and pseudostates plus three positronium states (a) 1S-2S (b) 1S-2P (Kernoghan et al., 1996).

The experiments were performed at two values of the magnetic field, 0.375 T and 0.425 T, and at various densities of N2 gas with small admixtures of isobutane to quench the free-positron component (see subsection 6.3.2). Al-Ramadhan and Gidley (1994) derived a quantity A(p) from their measured values of A Ps and Ao-ps, for the mixed and unmixed ortho-positronium states respectively, at a gas density p given by... 

Table 4.3 Positronium states in condensed matter contact density parameters. When more than one site is present, the amount of the first site is also indicated (%).

Now let us estimate the low boundary, Wiow, of the Ore gap in molecular liquids. Because the Ore process is just an electron-transfer reaction, we assume that no rearrangement of molecules occurs and, therefore, the final positronium state will be quasi-free (formation of the bubble requires much longer time). The corresponding Born-Haber cycle is the following ... 

---