Electron impact ionization cross sections dependence

In summary, preliminary experiments have demonstrated that the efficiency and outcome of electron ionization is influenced by molecular orientation. That is, the magnitude of the electron impact ionization cross section depends on the spatial orientation of the molecule widi respect to the electron projectile. The ionization efficiency is lowest for electron impact on the negative end of the molecular dipole. In addition, the mass spectrum is orientation-dependent for example, in the ionization of CH3CI the ratio CHjCriCHj depends on the molecular orientation. There are both similarities in and differences between the effect of orientation on electron transfer (as an elementary step in the harpoon mechanism) and electron impact ionization, but there is a substantial effect in both cases. It seems likely that other types of particle interactions, for example, free-radical chemistry and ion-molecule chemistry, may also exhibit a dependence on relative spatial orientation. The information emerging from these studies should contribute one more perspective to our view of particle interactions and eventually to a deeper understanding of complex chemical and biological reaction mechanisms. 

Fig. 3.31. Distributions (i)/(Ee) dEe of electron energy (E ) for a low-pressure HF-plasma (suffix pi, Maxwellian with temperature = 80000 K) and an electron beam (suffix eb, simplified to Gaussian shape with 40 eV half-width) (ii) rTx (Ej) ofthe Ej dependent electron impact ionization cross-section for X=Ti...

Quantum mechanical and selected semiclassical and semiempirical methods for the calculation of electron impact ionization cross sections are described and their successes and limitations noted. Experimental methods for the measurement of absolute and relative ionization cross sections are also described in some detail. Four theoretical methods, one quantum mechanical and three semiclassical, have been used to calculate cross sections for the total ionization of the inert gases and small molecules and the results compared with experimental measurements reported in the literature. Two of the theoretical methods, one quantum mechanical and one semiclassical, have been applied to the calculation of orientation-dependent electron impact ionization cross sections and the results compared with recent experiments. 

The EM method has been tested on the inert gases and a range of small molecules and gives good agreement with experimental results in almost all cases.17 This method will be discussed further in relation to the orientation dependence of the electron impact ionization cross section in a later section. The semiempirical polarizability method described below was developed to calculate and to use it with the amax values obtained from this method in order to calculate the energy dependence of the cross section. 

A multitude of semiempirical and semiclassical theories have been developed to calculate electron impact ionization cross sections of atoms and atomic ions, with relatively few for the more complicated case of molecular electron impact ionization cross sections. One of the earlier treatments of molecular targets was that of Jain and Khare.38 Two of the more successful recent approaches are the method proposed by Deutsch and Mark and coworkers12-14 and the binary-encounter Bethe method developed by Kim and Rudd.15,16 The observation of a strong correlation between the maximum in the ionization efficiency curve and the polarizability of the target resulted in the semiempirical polarizability model which depends only on the polarizability, ionization potential, and maximum electron impact ionization cross section of the target molecule.39,40 These and other methods will be considered in detail below. 

This expression reproduces the experimentally measured ionization efficiency curves surprisingly well, considering the simplicity of the model on which it is based. There is a discontinuity in the function at the maximum (when X = Xmax) but this affects only a small region of the ionization efficiency curve, and satisfactory values of the cross section are still obtained over this region. A great advantage of this method is that it is very simple to apply, depending on only three parameters the molecular polarizability volume, the ionization potential, and the maximum electron impact ionization cross section. These can be measured or calculated values (from the ab initio EM method described above, for example). 

We note that because the electron impact ionization cross section for a neutral polyatomic fragment depends on its vibrational and electronic excitations, the TOF mass spectrum obtained for a neutral fragment in a mass spectrometric experiment is not expected to correspond exactly to the true neutral TOF distribution. Thus, the kinetic energy distribution derived by the TOF mass spectrometric measurement is an approximation of the true distribution. 

Reactions of Complex Ions. For reactions of systems containing H2 or HD the failure to observe an E 1/2 dependence of reaction cross-section was probably the result of the failure to include all products of ion-molecule reaction in the calculation of the experimental cross-sections. For reactions of complex molecule ions where electron impact ionization probably produces a distribution of vibrationally excited states, kinetic energy transfer can readily open channels which yield products obscured by primary ionization processes. In such cases an E n dependence of cross-section may be determined frequently n = 1 has been found. 

Theoretical models of the electron impact ionization process have focused on the calculation of the ionization cross section and its energy dependence they are divided into quantum, semiclassical and semiempirical. Methods for the calculation of the ionization cross section and experimental techniques developed for the measurement of absolute ionization cross sections will be described in more detail below. Cross sections calculated using the semiempirical additivity method developed by Deutsch and Mark (DM) and their coworkers,12-14 the binary-encounter-Bethe (BEB) method of Kim and Rudd,15 16 and the electrostatic model (EM) developed by Vallance, Harland, and Maclagan17,18 are compared to each other and to experimental data. 

In the classical treatment of near-threshold electron impact ionization developed by Wannier (1953), the repulsion between the two electrons causes them to emerge with very similar energies but in opposite directions along the so-called Wannier ridge. This effect is depicted in Figure 5.6, where it is contrasted with the case for positron impact described below. According to this theory the energy dependence of the ionization cross section for electron impact is predicted to be... 

A rather different theory of electron impact ionization was developed by Temkin (1982) it was based on the assumption that one of the electrons remains closer to the core than the other, so that the outer electron moves in the dipole field produced by the inner electron and the core. According to this Coulomb-dipole theory the ionization cross section has a modulated quasi-linear energy dependence of the form... 

Schneider et al. (1993) developed their group s technique further in order to assign an absolute scale to the ionization cross sections by electron and positron impact for the K-shell of silver and the L3-shell of gold. Magnitudes were of the order of 10-23 cm2 and 10-22 cm2 respectively, though strongly energy dependent as the relevant threshold is approached. 

Bell et al. [33] proposed an analytical formula, widely known in the literature as the Belfast ionization (BELI) formula [34] that contains the dipole interaction term for the electron-impact ionization of atoms and ions. It has been applied to light atomic and ionic targets with species-dependent parameters. Godunov and Ivanov [34] applied the BELI formula to the El ionization of Ne 1 ions. Here also no generality as to parameters of the formula was provided regarding the species-dependent parameters. Moreover, the BELI formula does not make any allowance for relativistic effects. Haque et al. [35-38] have proposed a modification of this BELI model for evaluating the El K-, L-, and M-shell ionization cross sections of atoms. The relativistic and ionic effects are also incorporated in their modified BELI (MBELL) [35-38] model in addition to generalizing the species-independent... 

D.H.H. Hoffmann, C. Brendel, H. Genz, W. Low, S. Muller, A. Richter, Inner-shell ionization by relativistic electron impact, Z. Phys. A 293 (1979)187 D.H.H. Hoffmann, H. Genz, W. Low, A. Richter, Z and E dependence and scaling behaviour of the K-shell ionization cross section for relativistic electron impact, Phys. Lett. A 65 (1978) 304. 

Figure 19-4. Open and solid symbols are the measured quantum yields (events per incident electron) for the induction of single strand breaks (SSB) (a) and double strand breaks (DSB) (b) in DNA films by 4-100 eV electron impact. The solid curves through the data are guides to the eye. The dotted curves symbolize general electron energy dependence of the cross sections for various nonresonant damage mechanisms, such as ionization cross sections, normalized here to the measured strand break yields at lOOeV...

The collinear model (Eq. (15)) has been successfully used in the semiclassical description of many bound and resonant states in the quantum mechanical spectrum of real helium [49-52] and plays an important role for the study of states of real helium in which both electrons are close to the continuum threshold [53, 54]. The quantum mechanical version of the spherical or s-wave model (Eq. (16)) describes the Isns bound states of real helium quite well [55]. The energy dependence of experimental total cross sections for electron impact ionization is reproduced qualitatively in the classical version of the s-wave model [56] and surprisingly well quantitatively in a quantum mechanical calculation [57]. The s-wave model is less realistic close to the break-up threshold = 0, where motion along the Wannier ridge, = T2, is important. 

The rate coefficient for electron impact ionization depends very sensitively on the ionization energy, as is demonstrated in Fig. 8. We calculated the ratio of the rate coefficients for total ionization of silane for different electron temperatures using the total ionization cross sections of Chatham et al. (1984) and Krishnakumar and Srivastava (1995). The primary difference between the two cross-section data sets at low energies is a 0.6-eV difference in the measured ionization energy [with Chatham et al. (1984) reporting the lower value]. As expected, the... 

The orbiting and the classical and semiclassical impact parameter models have been used to interpret inelastic scattering data in chemiionization, the dependence of ionization cross-section on collision energy and electron energy spectra, in order to gain information about the potential curves, V and V, and the autoionization width, (/ ). 

Fig. 4.12. The single (non dissociative) ionization cross section for positron impact on Hj (renormalized as mentioned in the main text) of Knudsen et al. [3.45] compared with corresponding data of Rapp and Englander-Golden [4.26] for electron impact and with a curve showing a power law dependence with > = 1.3.

If the single-ionization cross sections measured for impact of protons and equivelodty positrons, or for antiprotons and equivelodty electrons, are compared, the effect of the large mass difference between the two kinds of particles can be studied. Sudi a comparison is shown in fig. 4.18 for a He target. For the largest projectile velodties, there is no difference between measured with light and heavy projectiles. This is in accordance with the prediction of the first Bom approximation eq (4.3) which (at high velodty) does not depend on the projectile mass. 

In asymmetric collisions the lowest orbital, the Isa, connects the Is orbital of 2 with the Is of Z. This is illustrated in Fig. 1 for the 35Br-i oZr system. When the system is sufficiently asymmetric the 2pa is far removed from Isa radial coupling between the two is weak and the only way to form a vacancy in the Is shell of the high Z collision partner is by Coulomb ionization from the Isa. Since Coulomb ionization cross sections are dependent on the electron binding energy, measurements of the impact parameter depen-... 

Charge exchange is important all along the high-LET tracks. The effective ionic charge is determined by cross sections of electron capture and loss, which depend predominantly on the ionic velocity. Electron loss may be simply described by an ionization of the incident ion in its own reference frame due to the impact of medium electrons and nuclei. Following Bohr (1948), Mozumder et al. (1968) wrote the cross section for this process as1... 

---