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I am trying to work out the integrals of the ionisation equilibrium equations to obtain the density of neutral hydrogen NH0 (r) and protonNp(r), but I am able to figure it out. The equations are in the slide 19 in http://www.astro.physik.uni-potsdam.de/~lida/TEACH.DIR/ism3.pdf

{Equation of ionization equilibrium

NH0R2 ∞πFν(R)ae−τνdν=NNα(H0,T) r2 ν0 hν ν e p B

τν(r) = r NH0 (r′)aνdr′ = aν τ0(r) 0 aν0

These two equations are integrated outwards to find

NH0 (r), Np(r), Ne(r)}

Please help me if anyone got an idea on it, thanks in advance.

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# How to solve the ionisation equilibrium equation?

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