Knoll's book says "An estimate can be made of the amount of inherent fluctuation by assuming that the formation of each charge carrier is a Poisson processes".
What is the basis of Poisson process?
Does this assumption holds true in every detector, if not why does it fail?
A Poisson distribution means that the detected events are equally distributed in time. If you have, let's say, in average one event per second, using the Poisson distribution you can estimate the probabilities you have n (0,1,2,3,4,5,...) events during one second. This is true for every detector because it does not depend on any physical properties but is pure statistics.
@Strub My concern is about pulse height distribution which involves the formation of different number of charge carriers due to single enrgy. Why that distribution is Poisson?
That's analogue. You have aan average number of events (ionizations) that are independent from each other and occur in a certain region (of time or of space) and the number can not be lower than zero.
the basis of the radiation detection by a detector is to deposit the charged particle's energy and convert the deposited energy to a large number of charge carriers.
for example, when the energy of a compton recoiled electron is 100keV and deposited in HpGe, it will produce about 30k e-h pairs. The number of 30k is determined by the the many collisions of the 100keV electron with the atoms of Ge in HpGe. If the number of collisons is very large and the probability of producing an e-h pair in each collision is very low, the number (here: 30k ) of total e-h produced by the 100keV would obey poisson statistics.
In fact, the production of the 30k e-h paris is not independant, i.e., some e-h paris are the "son " or "grandson" of others, then the 30k is not exactly the poisson distribution. Fano distribution give the right result. Usually, for gaseous and semiconductor detectotor, fano factor is less than 1 and for scintillator detection , fano factor is about 1.
So, the "poisson assumption" does not hold for gaseous and semiconductor detectors, and approximately hold for scintillator detector..
The Poisson distribution is usually the best model for counting events that have a stable average rate over the time of counting, but the events are independent and random. The base distribution is the binomial, but the Poisson is a good approximation if the events are rare.
A pulse height distribution is counts sorted by bins. The counts in each bin are collected at an average rate for each bin, regardless of the width of the bin. The shape of the spectrum will depend upon several factors, original energy distribution, type of detector, and electronics.
The standard deviation of the counts in each bin or sum of several bins is the square root of the total counts in the bin or sum.
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