Multiple gated-integrator as an effective tool for processing nuclear radiation detector signals

In a previous paper the double gated-integrator with exponential prefilter was investigated in detail [J. Gál, Nucl. Instr. and Meth. A 462 (2001) 506]. It was shown that it has very good noise characteristics. Its noise figure of demerit relating to the cusp shaping is 1.016. However, a more detailed analysis of the output of the double gated-integrator shows that the ballistic deficit of this signal, due to its sharp peaking, is not negligible, if the rise time constant of the detector pulse is comparable with the shaping time constant. In the present paper the theoretical study of the so-called multiple gated-integrator is presented. It will be shown that using multiple gated-integration and performing linear combination of the multiple integrated signals several pulse shapes can be realized. For example, by combining the outputs of the single and the double gated-integrators ramp or trapezoidal shaping can be implemented. The effect of the ballistic deficit on the spectral resolution is also discussed. The calculations confirm the well known fact that trapezoidal shaping is a good compromise when both the ballistic deficit and the system noise have comparable effect on the spectral resolution. At the same time, the multiple integrated signals can be used to derive such quantities which characterize the shape of the input signal. This makes it possible to realize pulse shape discrimination in order to identify particle type or to eliminate unwanted pulses appearing e.g., due to slow charge collection or due to pile-up. In the present paper the characteristics of a shape parameter deduced from the single and double gated-integrator outputs are investigated and the figure of merit of the pulse shape discrimination using this shape parameter is calculated.