Hello, every friend.
As the title says, I have gotten the distribution of counts of events vs scattering angle. Could you please teach me how to get the angular distribution describred by d{sigma}/d{Omega} vs scattering angle? I heard that one can do Monte- Carlo simulation to get solid angles.
Many thanks!
Unless your geometry is very complicated, you should be able to CALCULATE the solid angles. If you need more precise answers you should provide more details (how many particles you shot, type of target and its density, angle measurement, distance target-to-detectors, detector size, detector efficiency,...)
With the information you provided, Dr. Paolo Finocchiaro's answered is also all I have to say. Did you perform scattering experiment?
Dear Prof. Paolo Finocchiaro and Prof. B. Lalremruata,
Thank you very much for your answers.
Now I have done a Monte-Carlo simulation to calculate solid angles, using a small C code written by myself. I have only considered the GEOMENTRY of the system, the incident angle distribution, and the beam position distribution on the first PPAC. If one particle impinges onto the target, sample uniformly the scattering angle. Then, if the outgoing particle impinges onto PSD, record the event. Repeat the process. At last, calculate the numbers of particles in each scattering angle bins, and get the solid angle corresponding to them, using this formula:
d#Omega = 4 * #Pi * N_{theta}/N_{total},
where, N_{theta} is the number of in each scattering angle bin, and N_{total} is the number of total number of samples. (Chin. Phys. Lett. 21(11): 2151 ( 2004))
Is my procedure is correct??
Best wishes,
Liyuan
Well, from your reply, I believe that your main interest is knowing your solid angle using Monte Carlo simulation. In that situation, generate your particle from your target geometry(uniformly throughout the Carbon target with the same incident beam diameter) uniformly in 4pi. Set up your detector(same dimension and at the same distance from target as in your experiment) and record the number of particles falling on your target. Then Ndet(Number of particles recoded by your detector) divided by the total number of particles generated should give you your geometric efficiency/solid angle. Does this answer your question?
Dear Prof.B. Lalremruata,
Thank you!
I think that our procedures are mostly same. Besides, I have also taken the incident beam direction into account as well.
Should I construct the whole telescope detector? In the data analysis, I have to use the whole telescope to identify the particles. However, I only use PSD to get outcoming direction. So is it necessary to construct that stopping detector?
I would suggest to keep the different contributions separated.
Solid angle (geometrical efficiency x4pi) has to be calculated by simply emitting particles isotropically from the target, and counting how many hit the effective area of your detector.
Then you should define the efficiency of your detector, i.e. the fraction of hitting particles that give rise to a valid signal (in both layers). This will also be a function of the electronic thresholds you set, and of the particle type and energy.
Another point is the efficiency of the beam/target system: this is the fraction of beam particles effectively and fruitfully hitting the target.
All these quantities can be obtained independently of each other, possibly as a function of some parameter. Afterwards you can combine them by multiplying the single efficiencies. In case you want to explore a different scenario, you will not need to re-run the whole simulation.
All this, of course, holds for the angular distribution in the lab reference frame! If you want to get it in the CM frame the situation gets more complicated...
...if the target-detector distance d is much larger than the target size, your geometrical efficiency will not be much different from det_area/(4 x pi x d^2)
Dear Prof. Paolo Finocchiaro,
Thanks a lot for your detailed explanation. :)
I will calculate the differential cross section in LAB frame by the following formula:
d#sigma/d#Omega = dN /( I * N_{s} * d#Omega)
using the solid angles, calculated by Monte Carlo simulation, for each angle bins.
So can I only calculate geometry efficiency here?
...and be careful if you wrote your Monte Carlo code yourself: one of the most common mistakes when generating isotropic distribution in the whole solid angle is related to the polar coordinates (and the WRONG use of uniform distributions). If this is your case just try generating say one million particles and count how many fall into equal detectors placed at different theta and phi on a sphere. All the detectors should see the same number of hits (apart from statistical fluctuations). If not, just contact me again!
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