Dear @Alexy,
Thank you for your question. I proceed to answer to the different points:
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In your input file, USRYIELD is set to calculate d2N/dE/dtheta/cos(theta), but unfortunately this option is discontinued as you can see in the FLUKA forum (7.22.94. USRYIELD — FLUKA Manual). Moreover, please note that in USRYIELD, the fluence is calculated as the proyection of the particle trajectory with respect to a fixed direction, instead of to the surface normal, which is probably what you may be looking for. Therefore, perhaps USRBDX might yield the desired result: d2N/dE/dtheta where theta is the solid angle between the normal and the particle, and theta bins is set to 1.
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The results of the USRBDX mentioned above produce an effective dN/dE, which can be used as input in the second leg of a two-step simulation. You need to use the source routine where the energy is sampled from an histogram.
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USRBDX outputs the double differential of the particle fluence as a function of the energy and solid angle. Setting the solid angle bins as 1 and proper maximum and minimum angles with respect to the normal, the result could indeed be considered as the vertical muon flux over the interval.
Please let me know if this is helpful.
Regards
Mario