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Multielectron Atoms

Multielectron Atoms. Eisberg & Resnick, Ch 10. Exchange Symmetry. SO AS FAR AS SPATIAL DISTANCES ARE CONCERNED:. Indistinguishable SYM spatial wavefns are closer together in space. Indistinguishable ASYM spatial wavefns

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Multielectron Atoms

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  1. Multielectron Atoms Eisberg & Resnick, Ch 10

  2. Exchange Symmetry

  3. SO AS FAR AS SPATIAL DISTANCES ARE CONCERNED: IndistinguishableSYMspatial wavefns are closer together in space IndistinguishableASYMspatialwavefns are farther apart in space than for Distinguishable particles

  4. Helium Summary exchange-related Repulsion (spin) 1P1 ℓ-related repulsion spin-singlet 3P0,1,2 spin-triplet 1s2p n-related repulsion spin-singlet 1S0 H-basis functions spin-triplet 3S1 1s2s 1s2* 1s2* *=s,p 1S0 spin-singlet x 1s1s 1s1s 1s1s

  5. Hartree-Fock Methods Choose initial shape For Coulomb Potl V(r) Solve Schro Eqn for EnYn Insert fine structure corrections Build atom according to This set of orbital energies En Loop until V(r) doesn’t change much Use the collection of Yn*Yn to Get new electron charge distrib Use Gauss’ Law to get new V(r) shape

  6. Note: This shows how the orbitals shift as viewed from the perspective of an s-orbital.

  7. Hartree-FockEffective Charge Effects r2 ~ n2 ao / Zeff En ~ (Zeff2/n2) ( -13.6 eV )

  8. Hierarchy of Interactions • Hartree-Fock Central Coulomb • Residual Coulomb • Stot ordering • Ltot ordering • Spin-Orbit • …

  9. Impact upon a 3d4p basis config ( sample )

  10. Zeeman

  11. Weak Field Zeeman • Hartree-Fock Coulomb • Residual Coulomb • stot effects • ℓtot effects • Fine Structure • spin-orbit ( jtot becomes important ) • relativistic • Zeeman H’Zeeman = - mtot * Bext

  12. Weak Field Zeeman mtot

  13. Weak Field Zeeman Jtot mtot project average mtot onto Jtot g

  14. Weak Field Zeeman Jtot monto J projection of mtot onto J onto B Bext H’Zeeman = - mtot * Bext

  15. stot=0

  16. Strong Field Zeeman • Hartree-Fock Coulomb • Residual Coulomb • stot effects • ℓtot effects • Zeeman • Fine Structure • spin-orbit • relativistic H’Zeeman = - mtot * Bext

  17. Strong Field Zeeman Ltot Stot Bext H’Zeeman = - mtot * Bext

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