Cross section, differential ionization

In this section, the relationship between the measured quantity and the desired center-of-mass differential cross-section will be established and a brief description of the data analysis procedure will then be given. First, consider a Newton sphere with a single value of the product velocity v (see Fig. 4). From the Doppler-shift formula, at a given laser wavelength, the Doppler effect selectively ionizes those ions with vz = vcosO in the... 

It should be noted, however, that gaining a deeper insight into the problem of ionization phenomena is not the only reason for steady interest in the problem. Data on charged particle impact ionization is used both for industrial applications and for fundamental scientific research. For applications it is the collisions rates and total cross sections which are usually the most relevant. But in studies focused on the understanding of collision mechanisms of ionization processes, most of the information is lost in the total cross sections due to the integration over the momenta of the ejected electrons in the exit channel. Therefore it is the singly and doubly differential cross sections which are of... 

More details of the emission of ultralow- and low-energy electrons from fast heavy ion-atom collisions may be seen in the doubly differential cross sections as functions of the longitudinal electron velocity for increasing transverse electron velocity. Examples considered in this chapter include singly ionizing... 

Thirdly we are also interested in the electron spectroscopy method, which allows investigations on the two-center effects that influence electron emission. In particular, the richness of the ionization process lies in the possibility of measuring the doubly differential cross sections as a function of the electron emission angle and energy. This technique of electron emission spectroscopy is... 

Figure 10. Double differential cross sections (ddcs = Avj

Figure 11. Doubly differential cross sections (DDCS — 2m> dufdv ) f°r the electrons emitted after the single ionization of helium by 3.6-MeV/amu Au53+ ions, plotted for the electron s longitudinal momentum distributions for increasing transverse momenta. Here only one very small cut has been made in the electron s transverse momenta (pf < 0.04 a.u.). Experimental data and theoretical results are from Schmitt et at. [50],...

Figure 15. Differential cross sections da/dQp for the ionization of He by protons as a function of the scattering angle of the proton. Experimental data are from Kamber et al. [6]. Theoretical results are present CDW-EIS calculations.

In Fig. 15 we show the theoretical calculation of the singly differential cross section for the single ionization of He by proton impact. There are two impact energies considered here, 3 MeV and 6 MeV, and both are compared to the experimental results of Kamber et al. [6]. For both impact energies there appears a distinctive shoulder effect that takes place at 0.55 mrad in both the experimental data and the theoretical results. This has been attributed to the... 

Figure 17. Doubly differential cross sections for the ionization of He by 1.5-MeV/amu F9+ impact at an observation angle of 0 — 0" as a function of electron energy. Experimental data are from Lee et al. [12]. Theoretical results CDW results [57], CDW-EIS results [58].

To summarize this section on saddle-point ionization, we have calculated doubly differential cross sections for the single ionization of He, H2, and Ne by proton... 

Differential ionization cross sections, differential in ejected electron energy and emission angle, were the subject of intense study during the 1970s and 1980s. Considerable progress was made in both experimental and theoretical methodologies needed to describe differential cross sections these have been reviewed in IAEA TECDOC-799 [19] and ICRU-... 

In the same manner, one can determine the total ionization cross sections ctj by integration of the doubly differential cross sections over both ejected electron energy and emission angle... 

Figure 4 Doubly differential cross sections for the ionization of water vapor by 1-keV electron impact. (From Ref. 38.)...

By careful inspection of the relationships of the semiclassical close collision approximations and Bethe formula, one can obtain simple and accurate information on ionization cross sections. By the method first proposed by Platzman, and used extensively by others, it is instructive to form the ratio of the differential cross sections [measured c(W,T) or calculated da(W,T)ldW)] to the Rutherford cross section. This ratio, called Y, is mathematically defined as... 

Because the semiclassical theories can be used to calculate differential cross sections with relative ease for close collisions between the incident charged particle and the bound electron, and the Bethe theory provides a straightforward method to describe low-energy electrons ejected in distant collisions, it is only natural to combine the best characteristics of the two approaches to derive a comprehensive description of electron impact ionization. 

Figure 12 The ratio of the measured single differential cross section for ionization of helium by protons to the corresponding Rutherford cross sections plotted as a function of the ejected electron energy. The solid line represents the expected high-energy behavior of the ratio it should approach the number of electrons in the atom. The measurements are from Manson et al. [54].

Figure 13 Singly differential cross sections for ionization of several molecular targets by 1-MeV protons are plotted as a function of the ejected electron energy. The cross sections are scaled by the effective number of target electrons in each molecule the effective number of electrons is defined as the total number of molecular electrons minus those of the K-shell. (From Refs. 49, 56, and 58.)...

---