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# Absorption Cross Sections (Mihalas Chapter 4) - PowerPoint PPT Presentation

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)

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

• Balance transitions between two levels

• Upwards absorption

• Downwards by spontaneous or stimulated emission

j

hνij

i

Energy Absorption Rate: Bij = Einstein coefficient for absorption

Return Rates: Aji=Einstein coeff. spontaneous em.Bji=Einstein coeff. stimulated em.

(isotropic)

(same direction as Iν)

• Calculate or measure cross section

• H transitions n'→n

Einstein-Milne Relations forBound-Free Transitions

Einstein-Milne Relations:energy and velocity

Replace v dv increment in recombination term with this.

Einstein-Milne Relations:#photoionizations=#recombinations

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

…….=1. ……

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