Slater wavefunctions

A widely used approximate method of describing atomic states is the Slater atomic wavefunctions (Zener, 1930 Slater, 1930). In this section, we show that regarding STM, the Slater wavefunction is a convenient tool for describing localized atomic states at surfaces. 

To determine the image, the first step is to determine the distribution of tunneling current as a function of the position of the apex atom. We set the center of the coordinate system at the nucleus of the sample atom. The tunneling matrix element as a function of the position r of the nucleus of the apex atom can be evaluated by applying the derivative rule to the Slater wavefunctions. The tunneling conductance as a function of r, g(r), is proportional to the square of the tunneling matrix element ... 

Figure 2. Top Note that for simple (Slater) wavefunctions, the overlap between donor (D) and acceptor (A) decreases exponentially as distance (R) increases.

Using, for example, Slater wavefunctions for the initial and final states, this matrix element can be evaluated to yield a one-particle matrix element for the active electron and an overlap matrix element for the passive electrons (see equ. (2.4)). Of interest in the present discussion is the one-particle matrix element of the active electron ... 

The Hartree wavefunction (above) is a product of one-electron functions called orbitals, or, more precisely, spatial orbitals these are functions of the usual space coordinates x, y, z. The Slater wavefunction is composed, not just of spatial orbitals, but of spin orbitals. A spin orbital ij/ (spin) is the product of a spatial orbital and a spin function, a or / The spin orbitals corresponding to a given spatial orbital are... 

The Slater wavefunction differs from the Hartree function not only in being composed of spin orbitals rather than just spatial orbitals, but also in the fact that it is not a simple product of one-electron functions, but rather a determinant (Section 4.3.3) whose elements are these functions. To construct a Slater wavefunction (Slater determinant) for a closed-shell species (the only kind we consider in any detail here), we use each of the occupied spatial orbitals to make two spin orbitals, by multiplying the spatial orbital by a and, separately, by jl. The spin orbitals are then filled with the available electrons. An example should make the procedure clear (Fig. 5.2). Suppose we wish to write a Slater determinant for a four-electron... 

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). 

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]. 

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