Proportional counters have a moderate energy resolution. The energy resolution is mainly determined by the statistics of the initial ionization process and the statistics of charge multiplication. The variation of the number N of electron-ion pairs created by the ionizing event is less than that estimated from Poisson statistics, because the collisions of the ionization process are not statistically independent. The Fano factor F is an empirical constant to adapt the experimental observed variance to the predicted one .
For large values of multiplication, the variance of the amplification A of a single electron is :
Therefore, the energy resolution of a proportional counter is:
These estimates give a limit for the best achievable energy resolution. Gas impurities, tolerances of anode wire diameter, and loss of electrons at the entrance window can deteriorate the energy resolution of the proportional counter.
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