Chapter2_8 - τ . Consider particles that are at rest in...

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PHY3063 R. D. Field Department of Physics Chapter2_8.doc University of Florida The Lifetime of Unstable Particles There are only a few stable elementary particles (protons, antiprotons, photons, electrons, positrons, and neutrinos). All other elementary particles are unstable and eventually decay into stable particles. The table below gives the “proper-mean-life” of a few particles: Particle Mean-Life τ 0 c τ 0 Primary Decay Mode π + 2.6×10 -8 sec 780 cm µ ν + + π 0 0.8×10 -16 sec 25 nm γ + µ - 2.2×10 -6 sec 660 m + + e e n 896 sec 2.7×10 8 km e e p + + The rate at which a given type of particle decays is proportional to the number of particles, N, as follows: N dt dN α = and hence τ / 0 0 ) ( t t e N e N t N = = , where τ = 1/ α is the “mean-life” of the particle. The “mean-life” of a particle at rest is called the “proper-mean-life”,
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Unformatted text preview: τ . Consider particles that are at rest in the O'-frame which is moving at speed V relative to the O-frame . In the O-frame In the O'-frame ) /( / ) ( γτ t t e N e N t N − − = = / ' ) ' ( t e N t N − = where = and 2 1 / 1 / β − = = c V . Suppose the particles are created at rest in the O'-frame at x = x' = 0 at t = t' = 0 then the number of particles as a function of x (in the O-frame ) is ) /( ) ( V x V e N x N − = and the “mean-distance” traveled (in the O-frame ) is V x = ∆ y x z y' z' x' V Particle at rest in the O'-frame O O' Classical Result ∆ x = V τ...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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