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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

Absorption Cross Sections(Mihalas Chapter 4)

Bound-bound transitions(Einstein relations)Bound-free transitions(Einstein-Milne relations)


Bound bound transitions
Bound-Bound Transitions

  • Balance transitions between two levels

  • Upwards absorption

  • Downwards by spontaneous or stimulated emission

j

hνij

i


Energy absorption rate b ij einstein coefficient for absorption
Energy Absorption Rate: Bij = Einstein coefficient for absorption


Return rates a ji einstein coeff spontaneous em b ji einstein coeff stimulated em
Return Rates: Aji=Einstein coeff. spontaneous em.Bji=Einstein coeff. stimulated em.

(isotropic)

(same direction as Iν)





Transition rates
Transition Rates

  • Calculate or measure cross section


Transition rates hydrogen
Transition Rates: Hydrogen

  • H transitions n'→n


Einstein milne relations for bound free transitions
Einstein-Milne Relations forBound-Free Transitions


Einstein milne relations energy and velocity
Einstein-Milne Relations:energy and velocity

Replace v dv increment in recombination term with this.


Einstein milne relations photoionizations recombinations
Einstein-Milne Relations:#photoionizations=#recombinations


Denominator term maxwell dist n e v saha eq n 0 n 1
Denominator Term:Maxwell dist. ne(v); Saha eq. n0/n1

…….=1. ……


B f transfer equation
b-f Transfer Equation

T.E.: αν=pνhν , ne=Maxwellian, n0*/n1*=Saha, G(v)/pν above …


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