1. At first Hww is neglected, for each electron we get a hydrogen problem
Many electron systems
The atomic shell model revisited
=> electron-electron interaction
At first Hww is neglected, for each electron we get a hydrogen problem
Due to Pauli principle, each term can only be occupied with one electron => This yeilds the Periodic table, works regularly only for the first 18 electrons. After the 3p the 4s and not the 3d shell is filled.
This is due to Hww

2. Atomic shell model Estimate the effect of Wss
For small distances r->0, the electron sees the unshielded nucleas
for large distances the nucleus and (Z-1) electrons form an almost spherical charge distribution(core)

3. Effective potential showing
Screening of the nuclear charge by the electrons

4. : consist of a full noble gas configuration with an additional
Alkali atom
: consist of a full noble gas configuration with an additional
valance electron = “Leucht” electron
quantum defect
with = mass of the noble gas core

5. Model of an Alkali-atom
Level-scheme of Li
valence electron
core
Table: Quantum defect
note:for large the quantum defect disappears

6. The Helium atom = simplest many electron atom= 2 electrons
For time being let us neglect V, or set V=0
Write eigen function as a product of hydrogen functions
The total wave functin for Femions (particles with s= => electrons) must be antisymmetric
special case
This holds for the symmetric spin function

7. Space wave function of two particles:
Symmetrical
Antisymmetrical
Probability density for both cases

8. Spin wave function of the two electronic system
level
Total spin wave function is symmetrical
level
Total spin wave function is antisymmetric
Total wave function is product wave function of space and spin part and always antisymmetric

9. Wave Function of the ground state of helium with S=0
note: changing the direction of the spin costs ≈ 40eV and this is
happening without a spin dependance of the Hamilton operator

10. Effect of the electron-electron interaction
a. for singulet s=0 ground state
due to the second electron
note: The good agreement between calculated and experimental value

11. The exchange energy is ~ 0.4ev, Spin Triplet state is lower
b. for the first excited state of the singulet respectively triplet system:
direct
Exchange
The exchange energy is ~ 0.4ev, Spin Triplet state is lower

12. Energy levels of the excited-terms of the helium, shown is the effect of the direct integral J and the exchange integral K

13. Doubly excited states in helium
larger than eV the one electron ionization of helium

14. Helium atom Para helium S=0 Ortho helium S=1
The allowed electric dipole transitions
are indicated