Muon_Lifetime_F11 - Muon Lifetime Experiment Introduction...

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1 Muon Lifetime Experiment Introduction Charged and neutral particles with energies in excess of 10 23 eV from Galactic and extra Galactic sources impinge on the earth. Here we speak of the earth as the terrestrial mass and its captive atmosphere. These cosmic rays are mostly hadrons which undergo strong interactions and therefore interact in the earth’s atmosphere producing showers of charged and neutral particles that in turn interact resulting in many charged mesons with short lifetimes that eventually decay yielding many high energy muons. At the earth’s surface we are bombarded by muons of positive ( µ + ) and negative ( µ ) charge at the rate of about one particle per square centimeter per minute. Muons belong to a class of particles called leptons. They are spin ½ particles with a rest mass m 0 = 105.658469 ± 0.000009 MeV or about 200 times the mass of an electron, which is also a lepton as is the much heavier τ . The muon lifetime is measured to be τ µ = (2.19703 ± 0.00004) x10 -6 s . These charged members of the lepton family do not interact strongly. They have only electromagnetic and weak interactions and that is why we observe them at the earth’s surface. The stopped muon will decay into an electron or positron depending on the initial charge of the muon and two neutrinos. For example ° + ± + + ² ³ + ² ´ and ° → ± + ²̅ ³ + ² ´ with a distribution of decay times given by N(t) ~ exp(-t/ τ µ ) , Where N(t) is the number of decays between t and t+dt. The measurement of the lifetime is complicated by the fact that negative muons can be captured by a nucleus via the following reaction: ° + µ → ¶ + ² ´ , with considerable energy carried off by the neutrino. In this case the nucleus is left in an excited state, and the muon absorption is followed by gamma and/or beta decay from the nucleus, which can be sensed by the detector. This additional channel for negative muons has the consequence that the measured ° lifetime can be significantly shorter than the measured ° + lifetime. The effect of nuclear absorption is strongly dependent on the atomic number Z . For higher elements, the absorption probability is roughly proportional to · 4 . This rule may be explained by the mechanism of absorption, where the trapped muon first enters a K shell of the atom, and then the overlap of the muon wave function with the protons in The bar over the neutrino symbol indicates it is an antineutrino.
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2 nucleus governs the absorption probability. Positive muons cannot enter into an electron- like orbital state around a nucleus, and so they do not get absorbed. Since we do not have a magnetic field to bend positive and negative particles in opposite directions to identify the charge we cannot tell if a given muon stopping in our detector is a positive or negative muon. The ratio of positive to negative cosmic muons striking the earth’s surface is N( µ + ) / Ν (µ ) ≅ 1.225
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Muon_Lifetime_F11 - Muon Lifetime Experiment Introduction...

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