Overview

The purpose of the detector is to measure, in a manner which is independent of rate and emission angle, the time of decay for each muon. In order to minimize the systematic error caused by any residual, albeit tiny, muon polarization, a symmetric geometry covering a very large fraction of 4$\pi$ is desired. The detector should be sensitive to the whole energy spectrum of the decay positrons to avoid adverse affects due to time-dependence of pulse-height thresholds. Segmenting the detector will reduce the rate of pileup.

A number of critical design criteria are dictated by a careful analysis of systematic errors. They are detailed in a later section. The list below includes many of the main and general conclusions which we feel are important in the design.

• Geometrical coverage of a large fraction of $4\pi$ for efficient use of beam time. Detector should be as symmetric as possible.
• A coincidence system for each decay measurement. This ensures identification of decay positrons with low background .
• Overall detection threshold as low as possible; thin materials and detectors are implied.
• High segmentation commensurate with use of photomultiplier tubes and waveform digitizer readout channels. The segmentation number is strongly coupled to the next two items.
• Double-pulse resolution, $\Delta t$, as small as possible. Use of fast scintillator, PMTs, and a fine-sampling waveform digitizer can reduce $\Delta t$ to better than 10 ns.
• High light yield in order to obtain adequate rejection of events with two minimum ionizing particles (MIP) which occur due to particle pileup.
• Stability of the gains and thresholds to better than 1%.

We have considered several detector schemes and geometries to address these demands and have settled on a design which includes coincident timing elements made of fast plastic scintillators, each viewed by independent photomultiplier tubes. The advantage of scintillator is its large light output and relatively short signal duration. Experience with similar counters in 2 shows that MIPs as close together as 10 ns can be separated easily if appropriate sampling waveform digitizers are used as readout devices (as opposed to discriminators and TDCs). For quasi-monoenergetic pulses as we will encounter here, we believe this pulse-separation interval can be reduced, possibly to 5 ns. We further feel it is important that each decay positron time be authenticated by some kind of coincidence. This reduces any remnant beam-related backgrounds that could fall off with a decay time different from the muon lifetime. The DC primary beam at PSI should minimize this consideration compared to an environment with a high-energy time structured beam, however it is critical to ensure that each recorded event be associated with a positron from a muon decay, or with a background with no time dependence (e.g., cosmic rays). Part of our running plan will be to measure potential background sources, such as neutrons.