Threshold law

Wannier G H 1953 The threshold law for single Ionization of atoms or Ions by eleotrons Phys. Rev. 90 817-25... 

Determination of the total excitation cross section is again done by observing the resonance-line emission. Both the initial relative kinetic energy and the N2 temperature may be varied. First experiments of this type have studied the excitation of Na(3p) by N2, H2, and D2, vibrationally excited at 2000 to 3000°K for initial relative velocities from 1000 to 4000 m/sec l25-126 as well as both potassium and sodium.127 Recent studies with seeded beams 128131 on K + N2 and K + CO involved lower initial vibrational states v. This type of experiment is very difficult to analyze and evaluation invokes a number of assumptions for fitting the experimental data. A special threshold law for the energy dependence of the partial cross sections is adopted ... 

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 experimental helium data are shown in Figure 5.16, along with the theoretical results of Ihra et al. (1997), and good accord between the two is found. Thus, Ihra et al. (1997) deduced that, for most of the energy range investigated, the experiment can be fitted by a threshold law of the form of equation (5.10). This threshold law was derived by... 

Threshold law for positron impact ionization of atoms. Phys. Rev. Lett. 78 4027-4030. 

Sometimes in the literature, a resonance refers to the passage of the phase shift across 7t/2, but that does not necessarily mean steep slope of 5(E), a large time delay, or formation of a QBS. On the other hand, a large time delay is not necessarily associated with the formation of a QBS. For example, Wigner s threshold law for a short-range potential states that the s-wave phase shift 50(E) is proportional to E1/2 at low energies E [33]. This leads to the time delay At a E 1/2, which becomes extremely large at very low E (and is positive if the interaction is attractive), in spite of its irrelevance to any QBS [34], Note... 

Our interest in this section is in the case where the particle D is formed in a QBS and decays subsequently into Da + Db/ for example, in a finite lifetime r. Then, the threshold energy Eth has an uncertainty Y = h/x. The threshold law (103) must be "blurred" in some sense and is considered to break down for E — Eth comparable to or lower than L. 

Physical interpretation of the divergent and smooth threshold laws... 

Double photoionization in the outer shell of rare gases by a single photon is an important manifestation of electron correlations. One specific aspect which has received much attention over the years is double photoionization in the vicinity of the double-ionization threshold. On the theoretical side, this attention is due to the possibility of deriving certain threshold laws without a full solution of the complicated three-body problem of two electrons escaping the field of the remaining ion. On the experimental side, the study of threshold phenomena always provides the challenge for mastering extremely difficult experiments. 

This is known as the Wannier threshold law and for Z = 1, 2, 3, n has the values 1.127, 1.056, and 1.036 respectively. The deviation of n from the expected value of unity arises from the instability in the escape configuration discussed above. 

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