Wannier exponent

In all cases the same Wannier exponent occurs, and for a selected photon energy the excess energies differ due to the state-dependent ionization energies Ef+. However, of importance in the present context are the state-dependent values for the constants of proportionality a0. Within the LS-coupling scheme the complete final state built from the ion core and the electron-pair wavefunction must have Sf = 0 and L = 1. Therefore one gets the following possibilities ... 

The collinear models are also useful close to the two-electron break-up threshold. In 1994 Rost was able to obtain the correct Wannier exponent by a semiclassical treatment of electron impact ionization of hydrogen, another important quantum problem which involves nonintegrable three-body dynamics (see also Rost (1995)). 

Ashley, Moxom and Laricchia (1996) measured the positron impact-ionization cross section in helium and found that its energy dependence up to 10 eV beyond the threshold was quite accurately represented by a power law, as in equation (5.8), but with the exponent having the value 2.27 rather than Klar s value of 2.651. This discrepancy prompted Ihra et al. (1997) to extend the Wannier theory to energies slightly above the ionization threshold using hidden crossing theory. They derived a modified threshold law of the form... 

The first hints that the energy dependence of a + near E was different for positrons and electrons came from the results of Fromme et al. (1986, 1988) for helium and molecular hydrogen, which revealed that energy dependence than <7+(e ) and that the former falls below the latter very close to E. This type of behaviour is consistent with the expected Wannier laws for the two projectiles, though the energy width of the positron beam and other instrumental effects (see section 4.3 for a discussion of the operation of the ion extractor in this experiment) meant that the measurements were insufficiently precise for a value of the exponent to be extracted. 

The latter workers found that their data for both helium and molecular hydrogen could be fitted by power laws of the Wannier type, but in each case the exponent ( was substantially lower than the value 2.651 predicted by Klar (1981). Fitting over the full energy range of their investigations, up to approximately E = 10 eV, they found ( = 2.27T0.08 for helium and 1.71 0.03 for molecular hydrogen. 

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