Amplitude ratio method

The first method takes advantage of the fact that the lifetime of the muon is different in hydrogen and gold, being about 2.2 s and 70 ns, respectively. The electron time spectrum is measured with a pair of electron scintillation counters surrounding the target chamber (En1, En2, and Ege), and with NE213 neutron detectors (N1 and N2) with their fast dynode output (Tel1 and Tel2) in coincidence with the scintillator pair hit in front of them.

The time of the first hit among En1, En2, or Ege (first E), as well as the first hit of Tel1 and Tel2 (first Tel), are also histogrammed, which if we accept only one muon at a time, and if the effect of background is small, should equal to the sum of En1, En2 and Ege, or Tel1 and Tel2 respectively.

The recorded time spectra were fitted to exponential functions with a
constant background^{}. The general form of the fitting
function, taking into account capture and other muon losses, as well as the
finite size of the time bin, is derived in Eq. 6.4 in
Appendix C:

where for

Let us consider the specific case of ** M=2** (two exponentials), where we
assume all observed muon decay takes place in one of the two
materials. Also we take

the superscript ``

which would equal

- Electron scintillator measurements
- Electron telescope measurements
- Corrections to in the amplitude ratio method