Figure 1:Illustration of Tx (T30, T90) time differences
A closed-ended coaxial p-type HPGe-detector was employed to measure position dependent signal shapes. It has been irradiated by collimated gamma sources at different locations at the front and side faces. The pulse shapes have been scanned by a digital oscilloscope (10bit, 1GSa/s) in correlation with an energy measurement by a standard spectroscopy set-up.
Figure 1:Illustration of Tx (T30, T90) time differences
Different analysis methods have been employed, e.g. Fourier analysis, to extract the position information from the measured pulses. The most successful method was an analysis of the rise time differential parameterized by the time differences Tx defined as the rise time between 10 percent and x percent of the pulse heigth, see figure 1. The most pronounced effect is observable in a two-dimensional plot of T30 versus T90. In fig. 2 this correlation is shown for the Ge-crystal with a diameter of 7.5cm and a length of 7cm at a gamma-energy of 661 keV. For that case about 75% of the positions are assigned correct. The position resolution fluctuates between 4mm and 8mm.
Figurge 2:Two-dimensional plot of T30- versus T90-time for different
radii of irradiation.
The measured pulse shapes have been nicely reproduced by a computer model [1] which enables an accurate prediction of position dependent pulse shapes for arbitrary detector geometries. In our approach the interaction of gamma-rays with Ge-detectors is simulated for a predefined geometry using the Monte Carlo code GEANT3. The generated energy depositions in the Ge-crystal are used in a second program to obtain the pulse shapes from the electrical field distribution. Field gradients are derived from numerical solutions of the Poisson equation on a grid to account for the closed-ended geometry.
Figure 3:Simulated T30- and T90-time as a function of the radius of the
primary interaction
Figure 3 shows the calculated distribution of the T30 and T90 time differences as a function of the interaction radius of the gamma-ray. A comprehensive analysis of the calculated events reveals that the strong correlations at complementary radii correspond to primary interactions in the inhomogenious front part of the crystal (z<14mm), whereas the broad time distributions are due to primary interactions in the coaxial part (z>14mm). Moreover, subsequent interactions from multiple Compton scattering which is dominant for gamma-energies greater than 150keV has only a minor influence on the pulse shape.
[1] T. Kröll, I. Peter, Th. W. Elze, J. Gerl, Th. Happ, M. Kaspar, H. Schaffner, S. Schremmer, R. Schubert, K. Vetter and H.J. Wollersheim; Analysis of simulated and measured pulse shapes of closed-ended HPGe detectors.; Nucl. Instr. Meth. A 371 (1996) 489-496
