Ambiguous threshold energy

Close to the threshold for the formation of positronium, however, the effects of —iVabs are significant since it introduces ambiguity Tn into the energy of positronium, and hence, into the threshold energy. Thus, the threshold effects are described incorrectly by the unperturbed wavefunction . Indeed, the absorption cross section diverges unphysically toward the threshold according to the standard perturbation theory [15, 16, 18, 19] see Section 4.3.3 for further details. 

This experiment may be regarded as the forerunner of mass spectro-metric appearance-potential determination in that both are threshold techniques, that is they depend on slow variation in the energy supplied by the impacting electron until a change in the electron-molecule interaction is observed. Thus, just as the Hertz experiment did not distinguish between excitation and ionization potentials, mass spectrometric appearance potential measurements are subject to similar ambiguities in interpretation as between ionization and autoionization. 

We should also briefly discuss the reliability of PC threshold measurements for determining ,. The problem here is that for each temperature the spectroscopic data (Atheoretical expression, such as that found in Eq. (45). Above T = 0, when phonons are involved, there is no well-accepted theory of the photon capture cross section to use for data fitting. In fact, even at T = 0, the theoretical situation is ambiguous because the exact form of the impurity potential is not known. Thus, unless the PC threshold data are very steep, the energies derived from them may be hard to determine with great accuracy. 

The ambiguity due to the occurrence of multiple peaks in Nal (Tl) spectrometry for energies above the pair threshold can be removed, at the expense of sensitivity, by the use of a three-crystal spectrometer. In this instrument pulses from the centre crystal are only accepted when there is simultaneously a pulse due to an annihilation quantum in each of two side crystals. The difference between single- and three-crystal spectra is shown in Fig. 12. For energies below the pair threshold improved resolution can be obtained by using a two-crystal coincidence spectrometer to measure the pulse height due to Compton recoil electrons (Hofstadter and McIntyre ). 

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