Hartree Slater

Douglas, A. S., Proc. Cambridge Phil. Soc. 52, 687, "A method for improving energy-level calculations for series electrons." Inclusion of a polarization potential in the Hartree-Slater-Fock equation. 

The x-ray models used have been generated by a Hartree-Slater code [5,6] of J. Scofield s. Radiative recombination rates are calculated from the photoionization crossections. Information for the optical models has been drawn from a wide variety of sources. The ions included in the present calculation are Fel, n, HI, IV, V, VI Col, II, in, IV, V OI, n, HI, IV and Hel, H. Many important ions are not included, particularly in the intermediate Z range near Si. To minimize (but not eliminate) the effects of these... 

Relativistic Hartree-Slater values of the X-ray emission rates for the filling of K- and L-shell vacancies in berkelium have been tabulated (78). X-ray emission rates for the filling of all possible single inner-shell vacancies in berkelium by electric dipole transitions have been calculated, using nonrelativistic Hartree-Slater wavefunctions (79). 

In Fig. 2 we compare the 6s orbitals obtained for the two different couplings of the ion core. The difference in the calculations for these two orbitals is that the A a-coefficient for the exchange-correlation term in the Hartree-Slater Hamiltonian is varied to shift the calculated orbital energy to agree with the respective binding energy. The Hartree-Slater orbital for the 6s [ Fi/2 core] is also shown in Fig. 2. The inner nodes in this orbital are removed to obtain the 6s pseudoorbital. 

Fig. 2. Orbitals for the [5p (3/2)]6s [light solid line) and the [5p (l/2)]6s [heavy solid line) pseudoorbitals from which the j-wave effective potentials were determined The 6s Hartree-Slater orbital is also shown [heavy dashed line)...

Figure 4. Calculated partial photoionization cross sections for the K-shell of N2 over a broad energy range. The dashed line represents twice the K-shell photoionization cross section for atomic nitrogen, calculated using a Hartree-Slater potential.

This is called a Fermi hole and is the first example we encounter of a particle being dressed (i.e. having its properties modified) by many-body forces. Strictly speaking, the Fermi hole differs for each electron, but the interaction can be made local by averaging it over different orbitals, and this is referred to as the Hartree-Slater approximation. ... 

There exist several SCF codes for the solution of radial equations the Hartree-Fock [16] equations are only one example, and the case described above is that of the single configuration approximation, in which each electron has well-defined values of n and l. There exist several other possibilities as stressed above, in Hartree s original method, the exchange term was left out in the Hartree-Slater method [17], an approximate expression is used for the form of the exchange term. The Cowan code [20] is a pseudorelativistic SCF method, which avoids the complete four-component wavefunctions by simulating relativistic effects. 

JH Scofield, Hartree-Slater photoionization cross-sections at 1254 and 1487 eV. Journal of Electron Spectroscopy and Related Phenomena 8, 129-137, 1976. 

The analysis can also be carried out using the standard computer code. However, the procedure for analysis is the same as described earlier. PIXEF (for PIXE-fit) the Livermore PIXE spectrum analysis package has been developed by Antolak and Bench (1994). This software initially computes an approximation to the background continuum, subtracts from the raw spectral data and the resulting X-ray peaks are then fitted to either Gaussian or Hy > ermet distributions. The energy dependent ionization cross-sections for each element s K-shell or L-subshell are procured from the analytical functional fit, while the subshell and total photoelectric cross-sections are determined directly from the Dirac-Hartree-Slater calculations of Scofield. Schematic of a typical PIXE spectrum is as shown in Fig. 1.16. 

Figure 17. Theoretical K-shell photoabsorption cross section of Argon showing the hydro-genic (Hyd), Hartree-Slater (HS) and relativistic random phase approximation (RRPA) results (From Ref 69 )...

J.H. Scofield, Hartree-Slater subshell photo-ionisation cross-sections at 1254 and 1487eV, J. Electr. Spectr. Relat. Hienom. 8 (1976) 129-137. 

Similar calculations using non-relativistic Hartree-Slater wavefunctions [61] and relativistic Hartree-Slater theory [62] have also provided data for californium. The atomic form factors, the incoherent scattering functions [63], and a total Compton profile have been tabulated for californium [64]. 

SCO Scofield, J. H. Hartree-Slater subshell photoionization cross-sections at 1254 and 1487 eV J. Electron. Spectrosc. Relat. Phenom. 8 (1976) 129. 

Desclaux [11] performed true relativistic Dirac-Fock calculations with exchange to obtain orbital binding energies for every atom. Relativistic Hartree-Fock-Slater calculations were made by Huang et al. [12] and later improved by ab initio Dirac-Hartree-Slater wave functions for elements with Z = 70 to 106 in [13]. 

Detailed numerical results of a theoretical relativistic treatment of the electrons moving in a Hartree-Slater central potential are given in [1], see references therein up to 1973. 

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