|Message: Re: Normalization of an isotropic flux in space||Not Logged In (login)|
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the paper by Sullivan is indeed a good starting point for normalisation issues.
I tend to agree on your 1st final formula.
I see a problem in your macro, as you use "iso" for the angular distribution. In fact, if you want to generate an isotropic source in a volume starting from a surface, you have to bias the angular distribution with a cosine-law function, that means using "cos" in GPS.
Some time ago I tried to summarise all this in some diagrams, you can find a presentation at: http://geant4.in2p3.fr/2007/prog/GiovanniSantin/GSantin_Geant4_Paris07_Normalisation_v07.ppt
There, the final formula I get at slide #10 is equivalent to your first one, if you substitute Xs=C/Adet , q=thetamax , F=Phi
At the last slide, I include a couple more useful references.
Also, it seems to me that the 2nd formula you propose is a factor 2 different from the 1st one (am I right?). Indeed, that might come from the fact that you should integrate the cosine-biased emission, not an isotropic one.
In my calculations, also, if I limit the max emission angle theta to a certain q, I normally get a sin2(q) instead of (1 - cos q), as a result of the integration of the cos-biased distribution.
I hope this can help you, and I am interested in comments from your side
Kind regards, Giovanni
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