GENERAL-METHOD TO DETERMINE THE POSITION-CHARGE RELATIONSHIP FOR POSITION-SENSITIVE DETECTORS WITH VARIOUSLY-SHAPED RESISTIVE ANODES

A new approach using the Green function instead of the method of Fouri er expansion is presented to determine the position-charge relationshi p for radiation detectors employing a charge division on the resistive anode bordered by an additional resistive line. The resistive anode w ith a polygonal shape is considered as a general case. Theoretical con sideration shows that the position of radiation incidence in the posit ion-sensitive detectors is represented in the integral form containing the Green function if the total charge generated in the detector is a ssumed to be collected over an infinite time. Anodes with the geometri es of a triangle, square, circle or spherical triangle are described a s practical shapes. It is shown that, when the shape of the anode is ( spherical) triangular or square, the relationship between the position and charge is determined by a harmonic function obtained from a simpl e geometric consideration.