Distorted wave second Born

Dewangan, D.P. and Walters, H.R.J. (1977). The elastic scattering of electrons and positrons by helium and neon the distorted-wave second Born approximation. J. Phys. B At. Mol. Phys. 10 637-661. 

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).

In applying the distorted-wave second Born approximation we have the same difficulty as in calculating the optical potential. We must calculate the spectrum of the Green s function of (6.87). The first iteration of (6.87) is written as... 

Madison and Callaway (1987) compared the results of pseudostate calculations with those of explicit distorted-wave second-Born calculations, omitting exchange amplitudes. They concluded that it is possible to find basis sets of a managable size whose results are quite close to the second-Born results at the energy of detailed investigation and which give close results also at diflFerent energies. 

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).

McCarthy, 1992). Circles 3s, McClelland, Kelley and Celotta (1989) circles 3p, Kelley et al. (1992). Differential cross sections (multiplied by asymmetries) are squares, Srivastava and Vuskovic (1980) diamonds, Lorentz and Miller (1991). Full curves, coupled channels optical long-dashed curves, 15-state coupled channels short-dashed curves, distorted-wave second Born (Madison et al., 1992). 

The direct amplitudes involving are analogous to the distorted-wave Born approximation and are calculated by (10.31). The T-matrix element in the second amplitude of (10.51), which has the observed resonances, is calculated by solving the problem of electron scattering on He" ". The solution consists of half-on-shell T-matrix elements at the quadrature points for the scattering integral equations (6.87). The same points are used for the k integration of (10.51). 

Distorted wave Born approximation resonance energies and widths were calculated numerically using Equation 17. for the reduced-dimensionality hamiltonian given by Equation 35. and employing Equation 36. for V (r,t) up to second order. The coefficients a(t) and b(t) were determined numerically from the ab imitio potential surface. Zero-order wavefimctions X,(t) Xj(t) were deter-... 

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