Distorted-wave Bom approximation

A number of improvements to the Bom approximation are possible, including higher order Born approximations (obtained by inserting lower order approximations to i jJ into equation (A3.11.40). then the result into (A3.11.41) and (A3.11.42)), and the distorted wave Bom approximation (obtained by replacing the free particle approximation for the solution to a Sclirodinger equation that includes part of the interaction potential). For chemical physics... 

Giant dipole resonance. Isovector giant resonances contain information about the SE through the restoring force. In particular the excitation of the isovector giant dipole resonance (GDR) with isoscalar probes has been used to extract A R/R [32], In the distorted wave Bom approximation optical model analysis of the cross section the neutron and proton transition densities are needed as an input. For example, in the Goldhaber-Teller picture these are... 

Distorted Wave Bom Approximation. Quantum scattering calculations are sometimes made using the distorted wave Bom approximation (15). Such calculations have the advantage of almost always being feasible numerically. For simple cases, one can also obtain some results analytically (16). However, the accuracy of the results is generally poor, for most molecular collisions. A... 

Shakeshaft, R. and Wadehra, J.M. (1980). Distorted-wave Bom approximation for inelastic collisions application to electron capture by positrons from hydrogen atoms. Phys. Rev. A 22 968-978. 

In finding an analytical expression to simulate the distorted-wave Bom approximation (DWBA)-generated EISICS data of the K- and L-shell ionization of atoms, Campos et al. [47] in their CVTS model have adopted the Bethe s asymptotic condition in a parameterized form to fit low-energy data. Their resultant expression is given by... 

The driving term of (6.87) is the distorted-wave Bom approximation (DWBA). If i 0 the T-matrix element in the DWBA is... 

For continuum channels the radial orbitals in (7.140) are not bounded and the integral is divergent. The choice of radial functions in (7.136) must be based on intuition obtained from a study of ionisation, which is treated in chapter 10. A necessary condition for a reasonable distorted wave in the distorted-wave Bom approximation for ionisation is that it should be orthogonal to the initial state in the ionisation amplitude. For computational simplicity we set Fop,7l equal to zero and orthogonalise the resulting Ricatti—Bessel functions to all the states of P space using (5.83). 

Fig. 10.1. Coplanar-asymmetric ionisation from the 3p orbital of argon at Eo = 1000 eV, Es = 120 eV (Avaldi et al, 1989). The fast and slow electrons are respectively indicated by the subscripts / and s on the diagram, (a) 6f = 20 (Bethe ridge), (b) Of = 14 , (c) Of = 8°. Full curve, distorted-wave Bom approximation.

Fig. 10.12 compares the distorted-wave Bom approximation with the experimental data of Muller-Fiedler et al. (1986) for Eq = 100 eV, 300 eV and 500 eV and different values of Ef. It is significant that a later experiment by Avaldi et al. (1987a), for one case, agrees much better with the calculation. 

Fig. 10.15. Total ionisation cross section for helium. Experimental data, de Heer and Jansen (1977) full curve, coupled channels optical (equivalent local) (McCarthy and Stelbovics, 1983a) broken curve, distorted-wave Bom approximation.

Here we use the convention that co > 0 for phonon annihilation and < 0 for phonon creation. For the differential reflection coefficient, or the fraction of incident atoms which are scattered into final solid angle dQf with energy Ef to Ef + dEf, the result from perturbation theory—as, for example, from the distorted wave Bom approximation [39, 41]—is that... 

The relative excitation probabilities for members of the rotational band were taken from the work of Back et al. (1972) who performed Distorted Wave Bom Approximation (DWBA) calculations for the (d,p) reaction at the same bombarding energy. The width of the Gaussians was set by the experimental resolution. 

The values and d y/dz look like the P-violating ones caused by the 7-even P-odd correlation O A. It was shown [24,27] that Ao- -p and Axl z have the analogous enhancement factors which lead to their increase by a factor of 10 -10. Now, following ref. [27], one can obtain the 7-violating P-violating part of the reaction matrix (using the distorted-wave Bom approximation in the CP-odd interaction) as... 

In the assumption that the TNPC interaction constant 1, and in analogy with the calculation of the P-odd amplitude method [27], we shall use the distorted wave Bom approximation in the first power of g,... 

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