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

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)

Effective potential showing Screening of the nuclear charge by the electrons

: 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

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

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

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

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

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

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

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

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

Doubly excited states in helium larger than -24.6 eV the one electron ionization of helium

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