Nuclear Instruments and Methods in Physics Research A 362 (1995) 423-433 zyxwvutsrqponmlkjihgfedcbaZYXWVU NUCLEAR INSTRUMENTS BMETNOUS IN PHVStCS EISEVIER Light pulses to photomultiplier tubes from extended scintillators S. Albergo a, D. Boemi b, Z. Caccia a, S. Costa a, A. Insolia a, S. Panebianco a, R. Potenza a, N. Randazzo a, S. Reito a, J. Romanski ‘, G.V. Russo a,* , C. TuvC a zyxwvutsrqponmlkji a Department of Physics, Universiv of Catania, and INFN, I-95129 Catania, Italy ’ CSFNeSM, 1-95129 Catania, Italy ’ The Svedberg Laboratory, University of Vppsala, S751-21 Uppsala, Sweden Received 31 January 1994; revised form received 7 March 1995 zyxwvutsrqponmlkjihgfedcbaZYXWVU Abstract Light pulses seen by photomultiplier tubes (PMTs) after propagation within long scintillator slats or rods, or large disc-shaped scintillators are investigated and compared with those from point-like scintillators. Results of experimental tests for the disc-shaped configuration, performed with the single photon counting technique, are presented and compared with numerical calculations. These calculations were performed describing the light pulse shape by means of a new, quite general analytical method based on the geometrical optics concepts of virtual light paths and images. The associated electric pulses produced by the PMTs coupled to the scintillators are then discussed with particular emphasis on their dependence on the distance between light source and photocathode. 1. Introduction Long scintillator slats coupled to photomultiplier tubes (PMT), either directly or through light pipes, have been used for a long time in many experiments as position sensitive detectors (PSD) for time of flight (TOF) measure- ments. Recently, large disc-shaped scintillators coupled to a suitable number of PMTs have been proposed as PSDs [l]. Scintillator fibers have also been extensively used for the same purposes. They have almost exclusively the form of cylindrical rods. When time resolutions better than 100 ps are required, it is important to carefully investigate how the geometry of the scintillator and the location of the particle impact point influence the pulses produced by the PMTs. This investigation is needed not only when leading edge discriminators (LED) are used, which gives rise to the well known slew effect [2], but also when constant fraction discriminators (CFD) are used in systems where photon paths are largely variable from event to event. In addition, jitter effects, due to statistical fluctuations of the pulse shape, affect the time resolution of both types of discriminators especially when the amount of light col- lected is small. * Corresponding author. Tel. f39 95 7195 240, fax +39 95 383023, e-mail vrusso@infnct.infn.it. As a matter of fact, CFDs give the correct time only if all pulses have the same shape. But, when the scintillator to which the PMTs are coupled is rather long or wide, assuming that no diffusion takes place at the edges, the combined effect of reflections and absorptions in the scin- tillator causes the light pulse shape to vary with the distance between source of light and PMT window. As a consequence, the electric pulses from fast PMTs vary also. This can disrupt the accuracy of the CFD response if no correction is applied. A suitable correction requires knowledge of how the pulse shape changes with the scintillator geometry. This in turn is possible if reflec- tions and/or absorptions, but not diffusions, take place at the edges of the scintillator and provided the scintillator is sufficiently uniform so that no diffusion takes place along the light paths. Due to its intrinsically statistical origin, diffusion causes pulses to jitter. The larger the scintillator, the more pronounced becomes the jitter effect. The same considerations hold for the correction of the slew effect when using LEDs, which cannot account for amplitude fluctuations, especially in a large dynamic range. Now, assuming diffusion is absent and provided the shape of the light pulses from point-like scintillators is known (see Section 2.1), it is relatively easy to calculate the probability per unit time P(t, D) that photons emitted from a light source point inside an extended scintillator reach the photocathode at time f from a distance D. This can be done in a very compact and almost general way, 0168-9002/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-9002(95)00292-E