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question of CR nuclei injection function https://galprop.stanford.edu/forum/viewtopic.php?f=19&t=217 
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Author:  lw840305 [ Wed Sep 09, 2015 11:05 am ] 
Post subject:  question of CR nuclei injection function 
Dear all, I want to understand the injection function of heavier nuclei. In 5.5.1 of the manual, in normalization of the nucleon primary source function, the source abundance of heavier nuclei is X = Q_A/Q_1 = A*C_A/C_1 ..., C_A/C_1 = X*A^(gamma1)*Z^gamma Why there is one more A here ? If it is like this: q_A(p_A) dp_A = q_A(p_A) *dp_A/dEk_n *dEk_n, where Ek_n is the kinetic energy per nucleon, and dp_A/dEk_n = A/beta Then in flux I(Ek) = c/4pi *n *A, and at last both of A are cancelled actually. And for the corresponding secondary particle, there is one more A is formula 13 for secondary positron. And for secondary electron and antiproton. Maybe A_j ? But in secondary nuclei, there is no A, for example formula 20. Because it is the integral in p_A space? Here I have a question. In some literature, people assumed hard sphere approximation, i.e. before and after spalltion, kinetic energy per nucleon is conserved. But here in 19 and 20, it seems that you don't use that assumption. Right? How large is the difference between both two? Thank you very much for your reply! Wei 
Author:  strong [ Wed Sep 09, 2015 11:38 pm ] 
Post subject:  Re: question of CR nuclei injection function 
Thanks for your questions, I will prepare a reply. Such comments are very useful! 
Author:  lw840305 [ Thu Sep 10, 2015 7:05 am ] 
Post subject:  Re: question of CR nuclei injection function 
I read manual again, I find in spallation, galprop still applies hard sphere scattering approximation. but just in momentum space. 
Author:  strong [ Thu Sep 10, 2015 7:33 am ] 
Post subject:  Re: question of CR nuclei injection function 
yes it does that approximation. The grid is aligned on kinetic energy per nucleon for this reason, although the propagation is done in momentum. So that is correct. 
Author:  lw840305 [ Thu Sep 10, 2015 7:51 pm ] 
Post subject:  Re: question of CR nuclei injection function 
thank you very much for getting back to me! 
Author:  lw840305 [ Thu Sep 10, 2015 10:24 pm ] 
Post subject:  Re: question of CR nuclei injection function 
in decayed cross section, when spallation, rather decay, is branching_ratio = 1？ what is its vlaue? or it has value when decay appear? thank you very much ! 
Author:  strong [ Fri Sep 11, 2015 5:21 am ] 
Post subject:  Re: question of CR nuclei injection function 
re: X = Q_A/Q_1 = A*C_A/C_1 ..., this is from (8) since p' = p_A /A Q_A(p')dp'=q_A(p_A)dp_A Q_A(p')=q_A(p_A)dp_A/dp'=Aq_A(p_A) The algebra seems correct. The relation p' = p_A /A should be written explicitly, I will do that in the next version. For the fragmentation the sitiuation is similar, going from 'per nucleon' to 'per nucleus'. I agree the formulation is confusing, and should be clarified, and checked too (comments like yours help!). We need to think more carefully about how abundances are defined in fact. 
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