Excitation total cross sections

Hayashi s (1989) compilation highly overestimates the total inelastic cross section below 100 eV. These are inconsistent with measured W values. Although the total cross section is reasonably well determined, uncertainties in the elastic cross section might have led Hayashi to overestimate the inelastic cross section. Figure 4.5 shows these cross sections. It is seen, however, that one theoretical calculation is consistent with W value measurement (Pimblott et al., 1990). In any case, Hayashi s values for total inelastic cross section are much greater than all major calculations, and the discrepancy is directly traceable to overestimates of excitation cross sections. 

Figure 15 Calculated total and state-to-state excitation transfer cross sections in the de-excitation of He(2 P)-Ne. (From Ref. 151.) Both electron exchange and dipole-dipole interactions are included in the coupling matrix elements. The threshold energy into each exit channel is shown on the upper axis.

Figure 8 Total cross sections for ionization, excitation, and elastic scattering of electrons in water vapor in the energy range of 10 eV to 10 MeV.

Figure 11 Total cross sections due to proton (left) and alpha particle (right) impact on water vapor. Total ionization cross sections were obtained by fitting polynomial functions to the experimental data [198-200]. The curve for excitation was assumed to be the same between protons and alpha particles. Elastic scattering was evaluated by the classical mechanics trajectory calculations [Eqs. (16) and (17)].

AEAt ft) we have here well-defined excited levels in the quasi-particle picture. There is no contradiction as the superposition of both processes, Eqs. (55) and (56), gives to the total cross section a finite line width which is in agreement with the uncertainty principle. 

In nuclear reactors one has neutrons with energies ranging from thermal (0.025 eV) to several MeV. There are a series of sharp peaks in the total cross section for neutrons with energies between 0.2 and 3000 eV that are called resonances. These resonances correspond to exciting a specific isolated level in the compound nucleus that can decay by fission. The situation is particularly interesting for the neutron irradiation of even-even nuclei, such as 240Pu at subthreshold energies... 

Ion-impact excitation has been widely studied in the rare gases260 270 and for alkali metal ion-atom collisions.271 280 In many cases excitation functions have been measured (i.e., total cross sections as a function of initial relative translational energy), and in some instances the angular dependencies of the differential cross sections for inelastic scattering have been determined. The most striking feature of the results from these experiments is the oscillatory structure that is evident in many of the... 

The oscillatory structure just mentioned has been clearly demonstrated to result from quantum-mechanical phase-interference phenomena. The necessary condition264,265 for the occurrence of oscillatory structure in the total cross section is the existence in the internuclear potentials of an inner pseudocrossing, at short internuclear distance, as well as an outer pseudo-crossing, at long internuclear distance. A schematic illustration of this dual-interaction model, proposed by Rosenthal and Foley,264 is shown in Fig. 37. The interaction can be considered to involve three separate phases, as discussed by Tolk and et al. 279 (1) the primary excitation mechanism, in which, as the collision partners approach, a transition is made from the ground UQ state to at least two inelastic channels U, and U2 (the transition occurs at the internuclear separation 7 , the inner pseudocrossing, in Fig. 37), (2) development of a phase difference between the inelastic channels,... 

Figure 37. Schematic illustration of dual-interaction model for ion-impact excitation resulting in oscillatory structure in total cross section see text.279...

In principle, there is no way to directly measure the exchange process for 4He +4He scattering, as the particles are indistinguishable. But the cross section for metastability exchange can of course be calculated from the determined potentials assuming distinguishable particles.65 The expression for the total excitation transfer cross section is... 

Total Cross Section for Excitation Transfer tialsof Fig. 17 and Table IV. 

If we substitute amplitude (4.32) into formula for the differential excitation cross section (4.9) and integrate it, making the substitution (1/27r) dil = q dqlk0kn, we will get a factor (hk0)6 in the total cross section. Thus, while the direct scattering cross section decreases as 1IE with decrease of the energy, the exchange cross section behaves as 1/E3, meaning that the triplet states can be excited only by the slow electrons. 

Carrying out the sum in formula (4.34) over all the possible states n, we get the total cross section of excitation from the ground state crex. Adding to it the ionization cross section cr(. we obtain the total cross section of inelastic scattering o-tot, which can be presented as... 

In terms of spectroscopic observables, the potential energy function is that function V(r) which, when inserted into the quantum mechanical formulation of the vibration problem, gives the observed vibrational levels. In beam experiments, it is the potential which gives the observed scattering. In chemical excitation processes, it is the surface which predicts the observed total cross section and the observed distribution of products over internal energy states. Potential energy functions may be calculated from first principles14, or they may be constructed... 

As the positron energy is raised above the positronium formation threshold, EPs, the total cross section undergoes a conspicuous increase. Subsequent experimentation (see Chapter 4) has confirmed that much of this increase can be attributed to positronium formation via the reaction (1.12). Significant contributions also arise from target excitation and, more importantly, ionization above the respective thresholds (see Chapter 5). In marked contrast to the structure in aT(e+) associated with the opening of inelastic channels, the electron total cross section has a much smoother energy dependence, which can be attributed to the dominance of the elastic scattering cross section for this projectile. 

Fig. 2.14. Compendium of total cross section data for positron-noble gas and electron-noble gas scattering. The arrows refer to thresholds for (in order of increasing energy) positronium formation (positrons only), excitation and ionization. (From Kauppila and Stein, 1982.)...

The first studies of positron impact ionization were based around the TOF systems originally developed for total cross section measurements see section 2.3 and, for example, Griffith et al. (1979b), Coleman et al. (1982), Mori and Sueoka (1984, 1994), though only the latter workers, as described in section 5.1, claimed to be able to distinguish between ionization and excitation using the TOF technique. 

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