u/H Charge Ratio at Ground Level Our measurement of the muon lifetime in plastic scintillator is an average over both negatively and positively charged muons. We have already seen that us have a lifetime somewhat smaller than positively charged muons because of weak interactions betweer negative muons and protons in the scintillator nuclei. This interaction probability is proportional to Z, where Z is the atomic number of the nuclei, so the lifetime of negative muons in scintillator and carbon should be very nearly equal. This latter lifetime tc is measured to be t=2043+0.003 usec. [Reiter, 19601 It is easy to determine the expected average lifetime t_obs of positive and negative muons in plastic scintillator. Let n be the decay rate per negative muon in plastic scintillator and let n be the corresponding quantity for positively charged muons. If we then letn and n represent the number of negative and positive muons incident on the scintillator per unit time, respectively, the average observed decay rate n and its corresponding lifetime t_obs are given by N+at+N-A Tks=(1+p)(+# (1+p)+m where p≡NN,τ≡(λ) is the lifetime of negative muons in scintillator and t'=() is the corresponding quantity for positive muons Due to the Z effect, t =to for plastic scintillator, and we can set t equal to the free space lifetime value tu since positive muons are not captured by the scintillator nuclei Setting p=l allows us to estimate the average muon lifetime we expect to observe in the scintillator We can measure p for the momentum range of muons that stop in the scintillator by rearranging the above equation Muon physics9 Muon Physics µ+/µ− Charge Ratio at Ground Level Our measurement of the muon lifetime in plastic scintillator is an average over both negatively and positively charged muons. We have already seen that µ − ’s have a lifetime somewhat smaller than positively charged muons because of weak interactions between negative muons and protons in the scintillator nuclei. This interaction probability is proportional to Z4 , where Z is the atomic number of the nuclei, so the lifetime of negative muons in scintillator and carbon should be very nearly equal. This latter lifetime τc is measured to be τc = 2.043 ± 0.003 µsec. [Reiter, 1960] It is easy to determine the expected average lifetime τ_obs of positive and negative muons in plastic scintillator. Let λ − be the decay rate per negative muon in plastic scintillator and let λ + be the corresponding quantity for positively charged muons. If we then let N− and N+ represent the number of negative and positive muons incident on the scintillator per unit time, respectively, the average observed decay rate
λ and its corresponding lifetime τ_obs are given by where ρ ≡ N+ /N− , τ − ≡ (λ − ) −1 is the lifetime of negative muons in scintillator and τ + ≡ (λ + ) −1 is the corresponding quantity for positive muons. Due to the Z4 effect, τ − = τc for plastic scintillator, and we can set τ + equal to the free space lifetime value τµ since positive muons are not captured by the scintillator nuclei. Setting ρ=1 allows us to estimate the average muon lifetime we expect to observe in the scintillator. We can measure ρ for the momentum range of muons that stop in the scintillator by rearranging the above equation: