Normalization of an isotropic flux in space

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Dear all,

I am simulating the interaction of a space telescope with the cosmic ray environment and, after a long discussion with my colleagues, I am a bit confused on the normalization process that translates the number of counts in my detector in unity of counts/cm^2 sec.

So I really appreciate if somebody could help me to clarify this topic!

I show here what is my normalization way.

I have an isotropic proton flux F:

F = prot /cm^2 sec sr

I run the protons from a sphere of radius R within an half cone angle q to increase the statistics. My spacecraft is placed within the emission angle, that is the spacecraft is placed within the sphere of radius r, with

r = tan(q) x R

The GPS macro is:

/gps/particle proton

/gps/pos/type Surface

/gps/pos/shape Sphere

/gps/pos/radius 50.0 m ---> R

/gps/pos/centre 0.0 0.0 0.0 mm

/gps/ang/type iso

/gps/ang/mintheta 0 rad

/gps/ang/maxtheta 0.01 rad ---> q

while the spectral shape is made via /gps/hist .

At the end of the run, I detect a number of counts C on the focal plane. If N is the number of emitted protons, we call the fraction of detected/emitted particles Eff:

Eff = C/N

In order to trasform the number C to a rate P in counts/sec, I apply this formula:

P = Eff x F x (4 x PI) x PI x r^2 counts/sec

Then I divide the count rate P by the detecting area Adet, and the final flux B is given by:

B = P/Adet counts/cm^2 sec

The same normalization can be achieved using the simulation time:

D = F x A_sphere x omega prot/sec

where:

- A_sphere = 4 x PI x R^2 (the source sphere)

- omega = 2 x PI x (1 - cos(q)) (solide angle of the emission cone)

Then we calculate the simulated time:

Time = N/D (sec)

The flux B on the focal plane is given by:

B = C/(Time x Adet) counts/cm^2 sec

My normalization way is based on what shown by Sullivan (1971).

Now my question is: is this the right way?

Thank you all for the help!

Best regards, Valentina