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Absorption Cross Sections (Mihalas Chapter 4)

Absorption Cross Sections (Mihalas Chapter 4). Bound-bound transitions (Einstein relations) Bound-free transitions (Einstein-Milne relations). Bound-Bound Transitions. Balance transitions between two levels Upwards absorption Downwards by spontaneous or stimulated emission. j. h ν ij. i.

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Absorption Cross Sections (Mihalas Chapter 4)

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  1. Absorption Cross Sections(Mihalas Chapter 4) Bound-bound transitions(Einstein relations)Bound-free transitions(Einstein-Milne relations)

  2. Bound-Bound Transitions • Balance transitions between two levels • Upwards absorption • Downwards by spontaneous or stimulated emission j hνij i

  3. Energy Absorption Rate: Bij = Einstein coefficient for absorption

  4. Return Rates: Aji=Einstein coeff. spontaneous em.Bji=Einstein coeff. stimulated em. (isotropic) (same direction as Iν)

  5. *Thermodynamic Equilibrium: Iν=Bν

  6. b-b Transfer Equation

  7. b-b Transfer Equation

  8. Transition Rates • Calculate or measure cross section

  9. Transition Rates: Hydrogen • H transitions n'→n

  10. Einstein-Milne Relations forBound-Free Transitions

  11. Einstein-Milne Relations:energy and velocity Replace v dv increment in recombination term with this.

  12. Einstein-Milne Relations:#photoionizations=#recombinations

  13. Denominator Term:Maxwell dist. ne(v); Saha eq. n0/n1 …….=1. ……

  14. b-f Transfer Equation T.E.: αν=pνhν , ne=Maxwellian, n0*/n1*=Saha, G(v)/pν above …

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