The atomic shell model revisited At first H ww is neglected for each electron we get a hydrogen problem gt electronelectron interaction Due to Pauli principle each term can only be occupied with one electron gt This yeilds the Periodic table works regularly only for the first 18 el ID: 525901
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Slide1
Many electron systems
The atomic shell model revisited
At first H
ww is neglected, for each electron we get a hydrogen problem
=> electron-electron interaction
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 H
wwSlide2
Atomic shell model
Estimate the effect of W
ss 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)Slide3
Effective potential
showingScreening of the nuclear charge by the electronsSlide4
Alkali atom
: consist of a full noble gas configuration with an additional
valance
electron = “Leucht” electron
quantum defect
with = mass of the noble gas coreSlide5
Level-scheme of Li
Model of an Alkali-atom
valence electron
core
Table: Quantum defect
note:for large the quantum defect disappearsSlide6
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 functionSlide7
Symmetrical
Antisymmetrical
Space wave function of two particles:
Probability density for both casesSlide8
level
Spin wave function of the two electronic system
level
Total spin wave function is symmetrical
Total spin wave function is antisymmetric
Total wave function is product wave function of space and spin part and always antisymmetricSlide9
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 Slide10
a. for singulet s=0 ground state
due to the second electron
Effect of the electron-electron interaction
note: The good agreement between calculated and experimental valueSlide11
b. for the first excited state of the singulet respectively triplet system:
The exchange energy is ~ 0.4ev, Spin Triplet state is lower
direct
ExchangeSlide12
Energy levels of the excited-terms of the helium,
shown is the effect of the direct integral J and the exchange integral KSlide13
Doubly excited states in helium
larger than -24.6 eV the one electron ionization of heliumSlide14
Helium atom
Para helium S=0Ortho helium S=1The allowed electric dipole transitions
are indicated