Problems Related to Charge Collection Variations in Ge(Li) Detectors with Special Reference to Timing

Ge(Li) detectors used for gamma rays detection deliver signals with random parameters in noise. Timing studies with such pulses must take into account the two sources of errors; random shape and noise. This has not been made until now. In this paper, we use the "maximum likelihood method" which has been widely studied in communication theory. It mainly consists in the search of a set of parameters which maximizes the "likelihood function". This condition gives the minimum values of variances of estimated parameters. With the likelihood method we have determined, in the case of Ge(Li) detectors for a random shape (but sinqle interaction) and noise, the expression of the likelihood functions. If an electronic system could give this function as response to Ge(Li) pulses it would be the best pulse Forocessor, but it is obviously impossible to realize. However the method qives the bounds of accuracy of measurements theoretically possible : For planar pulses, this bound is found to be proportional to the inverse of the expectation of the energy of the delivered current. For coaxial pulses, one derives bounds in low and high electric field regions. Results are not so simple as in the previous case and additive terms appear in the formulas with the expectation of the energy of the current. Rather surprising results are obtained : timing nearly as good for planar pulses could be approached.