Distorted wave approximation

Blaha, M. Davis, J. Electron Ionization Cross Sections in the Distorted Wave Approximation. N.R.L. Memorandum Report 4245, Naval Research Laboratory, Washington, DC, 1980. 

The cross sections have been obtained through a quantum mechanical calculation of the transition matrix elements in the distorted-wave approximation, for low and ultra-low collisional energies. 

Various forms of distorted-wave approximation have been used to investigate the excitation cross sections in helium. Parcell, McEachran and Stauffer (1983, 1987) used this approximation to investigate the 2 S and 21 P excitation of helium over the energy range from near the threshold up to 150 eV. Their results for the 21 S excitation were found to be in rather poor agreement with the corresponding experimental results of Sueoka (1982), which prompted Parcell, McEachran and Stauffer (1987) to question whether these measurements were for this transition alone,... 

Guha, S. and Mandal, P. (1980). Model potential approach for positron-atom collisions I. Positronium formation in ground state in alkali atoms Na, K, Rb and Cs using the distorted-wave approximation. J. Phys. B At. Mol. Phys. 13 1919-1935. 

Nesbet, R.K. (1984). Asymptotic distorted-wave approximation for electron-molecule scattering. J. Phys. B 17, L897-L900. 

The observed temperature dependence departs from the theoretical predictions increasingly as the mass of the incident particle increases, a result which probably reflects increasing error with increasing m in the distorted-wave approximation. Helium is found to be more efficient at room temperature in deactivating the 7 = 2 level than is H2, while neon is more efficient than either helium or argon. This behavior was also observed at 170°K by Jonkman et al. [71,73]. 

Fig. 7.2. Distorted-wave approximations to a two-channel (CC) calculation of electron—sodium scattering. UDWB, unitarised distorted-wave Bom DWSB, distorted-wave second Born DWBA, distorted-wave Born (Bray et al., 1989).

The kinematic treatment is generally used to interpret surface diffraction data. However, one must remember that the total external reflection effect is dynamial in nature so that the kinematic treatment is strictly not applicable. However, as has been pointed out by Vineyard, a simple distorted wave approximation ean be used, and this can be quite adequately treated in a kinematical approach. This last point greatly simplifies data interpretation. 

Several distorted wave approximations were explored by Gilbert and George (1973). Their best results were obtained by fitting the Porter-Karplus... 

Bennewitz et al. (1964) were the first to get this information on the AIP from total collision cross section measurements. In the last three sections we shall confine ourselves to this type of measurements and discuss a more recent experimental set up (Section IV) and the results obtained so far (Section VI). In Section V we shall discuss the theory which connects the AIP with the orientation dependent part of the total collision cross section. Our main technique will be the first order distorted wave approximation (d.w.a.). 

Recently Bandrauk (1972) has shown that the time dependent equations coupling the two-state amplitudes have an analytic solution for a constant potential crossing a Coulombic one, together with a Coulombic Hl2(R). For systems with a large reduced mass (such as K + Br) he finds agreement again with a distorted wave approximation and with the LZS theory. 

Theoretically, Vineyard described GIXD with a distorted-wave approximation in the kinematical theory of x-ray diffraction [4]. In terms of the ordinary dynamical theory of Ewald [5] and Lane [6], Afanas ev and Melkonyan [7] worked out a formulation for the dynamical diffraction of x-rays under specular reflection conditions and Aleksandrov, Afanas ev, and Stepanov [8] extended this formalism to include the diffraction geometry of thin surface layers. Subsequently, the properties of wave Adds constructed during specularly diffracted reflections have been discussed in more detail by Cowan [9] and Sakata and Hashizume [10]. Meanwhile, a geometrical interpretation of GIXD based on a three-dimensional dispersion surface has been proposed by Hoche, Briimmer, and Nieber [11]. 

Vineyard, G.H., Grazing-incidence diffraction and the distorted-wave approximation for the study of surfaces, Phys. Rev. B 26, 4146, 1982... 

Recursive distorted wave approximation. Several linear and quadratic methods have been proposed to obtain the wave operator by limiting the divergence of Eq. (40) (23,25-30). In the applications presented below, a recursive treatment, proposed by Jol-icard (31-33) and called the recursive distorted wave approximation (RDWA) has been used. Such an approach leads to the equations ... 

We solve the hydrogen-antihydrogen scattering problem in a distorted wave approximation based on the separation of the leptonic and hadronic motions as implied by the Born-Oppenheimer approximation. The total wave function of the system is written as... 

A. Gelb and R.J. Suplinskas. Influence of the distorted wave approximation in calculations of chemical reaction cross sections Ar i HD. J. Chem. Phys.. 53. 2249-57 (1970). 

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