Differential cross section hydrogen

Schnieder L, Seekamp-Rahn K, Wede E and Welge K H 1997 Experimental determination of quantum state resolved differential cross sections for the hydrogen exchange reaction H -r D2 -> HD -r D J. Chem. Phys. 107 6175-95... 

In Figure 2, we show the total differential cross-section for product molecules in the vibrational ground state (no charge bansfer) of the hydrogen molecule in collision with 30-eV protons in the laboratory frame. The experimental results that are in aibitrary units have been normalized to the END... 

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

Calculations using the CDW-EIS model [38] are shown to be in good accord with 40-keV protons incident on molecular hydrogen and helium, and at this energy both theory and experiment show no evidence of any saddle-point enhancement in the doubly differential cross sections. However, for collisions involving 100-keV protons incident on molecular hydrogen and helium the CDW-EIS calculations [39] predict the existence of the saddle-point mechanism, but this is not confirmed by experiment. Recent CDW-EIS calculations and measurement for 80-keV protons on Ne by McSherry et al. [41] find no evidence of the saddle-point electron emission for this collision. 

Fig. 4.7. The differential cross sections for positronium formation into the ground state and the nPS = 2 excited states in positron-hydrogen collisions at...

Fig. 5.8. The triple differential cross section for positron impact ionization of atomic hydrogen, expressed as a function of the energy of the ejected electron. The scattered positron and electron both emerge in the direction of the incident...

Recently, Kover and Laricchia (1998) reported the first measurement of d3(Tj+ /riOidQ2d/f. the triple differential cross section for positron collisions. Molecular hydrogen was chosen as the target for positrons at... 

Brauner, M. and Briggs, J.S. (1991). Structures in differential cross sections for positron impact ionization of hydrogen. J. Phys. B At. Mol. Opt. Phys. 24 2227-2236. 

The differential cross section at 33° near an elastic resonance is illustrated in fig. 4.5 for a calculation of electron scattering by the hydrogen atom. This resonance has L = 1 with the electrons in a state of total spin S = 1. 

Fig. 4.5. The differential cross section at 33° near a resonance Eo=9J7 eV, F=8.9 X 10 eV, L = 1, S = 1 in a calculation of electron—hydrogen elastic scattering.

Because our description of differential cross sections for momentum transfer in a reaction initiated by an electron beam depends on our ability to describe both the structure and the reaction mechanism, scattering provides much more information about bound states. This is even more true of ionisation. The information is less accurate than from photon spectroscopy and is obtained only after a thorough understanding of reactions, the subject of this book, is achieved. The understanding of structure and reactions is of course achieved iteratively. A theoretical description of a reaction is completely tested only when we know the structure of the relevant target states with accuracy that is at least commensurate with that of the reaction calculation. The hydrogen atom is the prototype... 

Fig. 8.2. Differential cross section for the elastic scattering of electrons on hydrogen. Circles, Williams (1975) solid curve, coupled-channels-optical calculation long-dashed curve, one channel with discrete polarisation potential only short-dashed curve, one channel without polarisation potential. Adapted from Bray et al. (1991h).

Fig. 8.3. Differential cross section for electron scattering to the Is, 2s and 2p states of hydrogen at 54.4 eV. Experimental data for Is are interpolated (Williams, 1975), for 2s and 2p they are taken from Williams (1981). Calculations are solid curve, convergent close coupling (Bray and Stelbovics, 1992h) long-dashed curve, coupled channels optical (Bray et al, 1991c) short-dashed curve, distorted-wave second Born (Madison et al, 1991) chain curve, intermediate-energy R matrix (Scholz et al, 1991) dotted curve, pseudostate method (van Wyngaarden and Walters, 1986).

Table 8.1. The ratio of n=I to n=2 differential cross sections for hydrogen.

Fig. 8.8. Differential cross section at 30 and 90 for electron—hydrogen elastic scattering below the n = 2 threshold. Experiment, Williams (1976f>) solid curve, coupled channels optical (equivalent local) (McCarthy and Shang, 1992). From McCarthy and Shang (1992).

Fig. 10.2 shows that the plane-wave impulse approximation is as good for relative helium differential cross sections at different energies as it is for hydrogen. Here p) is the Hartree—Fock orbital. For helium there is an absolute experiment by van Wingerden et al. (1979) for 0 = 0 in symmetric kinematics at different total energies. Fig. 10.3 shows that the plane-wave impulse approximation using the Ford T-matrix element is consistent with the experiment. 

Brauner, Briggs and Klar (1989) have performed the first calculation of differential cross sections that uses an approximation in which the boundary condition (10.15) is explicitly satisfied. The target was hydrogen. Their calculation may be considered in terms of (10.25). The first term is omitted. The second term is evaluated with the choice (10.26) for the auxiliary state )(k/,ks)) and Ui =0. 

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