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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) l2 V (r ) 1 4 0 r Ze 2 1 V (r ) 4 0 r Effective potential showing Screening of the nuclear charge by the electrons Alkali atom : consist of a full noble gas configuration with an additiona valance electron = “Leucht” electron (nl , l ) quantum defect EG me mEG me mEG with mEG = mass of the noble gas core Level-scheme of Li Model of an Alkali-atom valence electron core Table: Quantum defect (n, l ) l note:for large l 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= special case This holds for the symmetric spin function 1 => electrons) must be antisymmetric 2 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 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