Resonance Potential

Consider the three electron system shown below.  The nucleus in black has charge 2, there are electrons in blue at y = ¾ and z = ¾.   The potential seen by the third electron at r along the x axis is zero for r large.  At r = ¾, the potential is .  At r = 0.1, the potential is   

Thus crudely, the potential seen by the third electron is

                This is the kind of potential considered by Siegert in his discussion of resonances. Resonances\Siegert-mod.doc.

Zeff

The charge seen by an electron at a distance r from the nucleus is

For the k shell the wave function is  as given above.

The mid point trap rule integral from 0 to h is given by the single

point evaluated at h/2,  That from 0 to 2h by the value at h plus the single point at 3h/2,

Note that I am approximating the density given by the 2p electrons by that given by the 2s electrons.

The code is for/PLOTZEFF.FOR.  The 1s orbital yields

Figure 1 Integral of electron density from 0 to r as a function of r (Bohr radii) for K shell.

Figure 2  Number of electrons within a radius r for both the K and L (approsiate) shells of hydrogen.

Figure 3 Z_eff(r)

                The code test.c  converts the data in zeff.out to a function.