Herman-Skillman potential

Figure 2.12 Radial integrals and phases for 2p photoionization in neon as functions of the kinetic energy of the photoelectron. The radial integrals R d2p and R s2p and the corresponding phases refer to the photoionization channels 2p - sd and 2p -> ss, respectively. Instead of the total phase 2p the individual contributions are shown (equ. (7.27)), namely the Coulomb phases <7ed2p and

The MPIB and VIB [35] models attempt to improve the aeeuraey of the earlier models and to overcome some of the difficulties associated with the use of Hartree-Fock wave functions. We have already stated some of the advantages of using the density functional approach to obtain ionic wave-functions they were amply demonstrated by the PIB model which replaced the Hartree-Fock equation with a density functional implementation of the Dirac equation [21]. The MPIB is so called because it also adopts the density functional approach to obtain ionic charge densities (specifically anon-relativistic version derived from the Herman-Skillman [48],but replaces the potential inside the Watson shell with the spherical average of the potential due to the rest of the material, IF (r)[36] ... 

Fig. 11.3 illustrates the relative momentum profile of the 15.76 eV state in a later experiment at =1200 eV, compared with the plane-wave impulse approximation with orbitals calculated by three different methods. The sensitivity of the reaction to the structure calculations is graphically illustrated. A single Slater-type orbital (4.38) with a variationally-determined exponent provides the worst agreement with experiment. The Hartree-Fock—Slater approximation (Herman and Skillman, 1963), in which exchange is represented by an equivalent-local potential, also disagrees. The Hartree—Fock orbital agrees within experimental error. 

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