Static-exchange approximation

The summation over spins in equation (7.14) does not, of course, include the spins of the positron and the fth electron. The form of for positronium-hydrogen scattering in the static-exchange approximation is given in equation (7.18) below. 

Fig. 7.12. Cross sections for positronium-hydrogen scattering in the static-exchange approximation (Hara and Fraser, 1975). A, elastic scattering B, ortho-to para-positronium conversion.

Takatsuka, K. and McKoy, V. (1981). Extension of the Schwinger variational principle beyond the static exchange approximation, Phys. Rev. A 24, 2473-2480. 

So far no approximation for a form of the optical potential U has been made. At this point we assume static-exchange approximation defined by the eq. (4). First two terms of eq. (4) describe electrostatic interaction consisting of nuclear attraction and static repulsion with the bound electrons. Corresponding matrix elements for the static part Us come out as a Fourier transform of the charge density ... 

Static Exchange Approximation (Complex basis functions for scattering electron only) 0.76 1.11... 

Representative examples of resonances in molecular partial-channel photolonlzatlon cross sections are described and discussed in this section. Comparisons are made between calculations, largely in static-exchange approximation (14,15), and measurements in selected cases, and Stleltjes orbitals are presented in three-dimensional... 

Studies of valence-shell photolonlzatlon cross sections in N2O in static-exchange approximation aid in identification of the presence of the 8o(a ), 9o(a ), and 3ir(ii ) virtual valence orbitals in the dipole spectrum of this compound (29). The a orbitals are found positioned in the ionization continuum in a manner similar to that in... 

Figure 10. Stieltjes orbitals in tenth-order for (5a-+ka)b n ionization of NO in static-exchange approximation (28). Layout as in Figure 7.

Figure 12, Occupied canonical Hartree-Fock and 5th-order Stieltjes orbitals In static-exchange approximation for 5a- -ko ionization of CO (20). Layout as in Figure 7, with the carbon nucleus on the left, the oxygen on the right.

Figure 13. Occupied canonical Hartree-Fock and 5th-order Stieltjes orbitals in static-exchange approximation for 5ai- ka2 ionization of H2CO (20). Results shown refer to orbital values in a molecular plane of dimension 6 by 16 Sq, with the hydrogen nucleii on the left of the figure.

Ekstrom U, Norman P, Carravetta V. Relativistic four-component static-exchange approximation for core-excitation processes in molecules. Phys Rev A. 2006 73 022501. 

Ekstrom U, Ottosson H, Norman P. Characterization of the Chemisorption of Methylsi-lane on a Au( 1,1,1) Surface from the Silicon K- and L-Edge Spectra A Theoretical Study Using the Four-Component Static Exchange Approximation. J Phys Chem C. 2007 111 13846-13850. 

Villaume S, Ekstrdm U, Ottosson H, Norman P. Near sulfur L-edge X-ray absorption spectra of methanethiol in isolation and adsorbed on a Au(lll) surface a theoretical study using the four-component static exchange approximation. Phys Chem Chem Phys. 2010 12 5596-5604. 

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