Differential cross section single

A unifonn monoenergetic beam of test or projectile particles A with nnmber density and velocity is incident on a single field or target particle B of velocity Vg. The direction of the relative velocity m = v -Vg is along the Z-axis of a Cartesian TTZ frame of reference. The incident current (or intensity) is then = A v, which is tire number of test particles crossing unit area nonnal to the beam in unit time. The differential cross section for scattering of the test particles into unit solid angle dO = d(cos vji) d( ) abont the direction ( )) of the final relative motion is... 

Figure 2. Total differential cross-section versus laboratory scattering angle for vibrational ground state of hydrogen molecules in single collisioins with 30-eV protons.

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... 

Owing to the symmetry property of an optical dipole transition, the data analysis for a photodissociation study is greatly simplified. The center-of-mass differential cross-section for a single-photon, dissociative process can be expressed as38,39... 

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... 

By further integrations over the energy or angle of the emitted electron we obtain the single differential cross section as a function of the angle and energy of the emitted electron, respectively ... 

Normally these conditions are satisfied in fast highly charged ion-atom collisions. From Eq. (66) we can derive the equations for the singly differential cross sections with respect to the components of the longitudinal momentum distributions for the electron, recoil-ion, and projectile. The longitudinal electron momentum distribution da/dpe for a particular value of p, may be derived by integrating over the doubly differential cross section with respect to the electron energy Ek ... 

The longitudinal momentum projectile transfer da / dp P obtained by consideration of Eq. (66) is expressed as a function of the singly differential cross section of the emitted electron from the projectile ion by... 

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],...

The projectile scattering angle QP has always proved to be extremely difficult to measure experimentally due to the small deflection of the projectile. However, the singly differential cross section as a function of fIp contains a wealth of information on binary collisions between the projectile and the target electrons. This singly differential cross section is given by... 

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... 

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... 

Figure 11 A Platzman plot, the ratio of the experimental single differential cross section for electron emission from helium by 1-MeV protons to the corresponding Rutherford cross sections plotted as a function of RjE. The experimental cross sections are from Ref. 54 and the differential oscillator strength is taken from Ref. 43.

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.)...

Figure 15 The ratio of calculated and measured single differential cross sections for electron emission from N2 following proton impact to the corresponding Rutherford cross sections. The solid line is the result of the model of Rudd [62] experimental data are from Rudd (O) [64], Crooks and Rudd ( ) [65], Toburen (x) [48], and Stolterfoht ( ) [66],...

---