09nuclei2 - Nuclear Decays Unstable nuclei can change N,Z.A...

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P461 - nuclear decays 1 Nuclear Decays • Unstable nuclei can change N,Z.A to a nuclei at a lower energy (mass) • If there is a mass difference such that energy is released, pretty much all decays occur but with very different lifetimes. • have band of stable particles and band of “natural” radioactive particles (mostly means long lifetimes). Nuclei outside these bands are produced in labs and in Supernovas nuclei can be formed in excited states and emit a gamma while cascading down. ν β α / : : 1 4 2 4 2 + + + ± ± e N N He N N A n Z A Z A n Z A Z
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P461 - nuclear decays 2 General Comments on Decays • Use Fermi Golden rule (from perturbation theory) • rate proportional to cross section or 1/lifetime • the matrix element connects initial and final states where V contains the “physics” (EM vs strong vs weak coupling and selection rules) the density of states factor depends on the amount of energy available. Need to conserve momentum and energy “kinematics”. If large energy available then higher density factor and higher rate. • Nonrelativistic (relativistic has 1/E also. PHYS684) dVolume V V V rate f i if f if ψ ρ π = = * 2 | | 2 h particle each dE dp p i i i f 2
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P461 - nuclear decays 3 Simplified Phase Space • Decay: A b a + b + c …. . • Q = available kinetic energy • large Q b large phase space b higher rate • larger number of final state products possibly means more phase space and higher rate as more variation in momentums. Except if all the mass of A is in the mass of final state particles • 3 body has little less Q but has 4 times the rate of the 2 body (with essentially identical matrix elements) ) ( state final m Mass Q i A = MeV Q body D B MeV Q body D B 2505 139 770 1865 5279 3 2644 770 1865 5279 2 0 0 0 = = = = + + + + π ρ
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P461 - nuclear decays 4 Phase Space:Channels • If there are multiple decay channels, each adds to “phase space”. That is one calculates the rate to each and then adds all of them up • single nuclei can have an alpha decay and both beta+ and beta- decay. A particle can have hundreds of possible channels • often one dominates • or an underlying virtual particle dominates and then just dealing with its “decays” • still need to do phase space for each…. mesons K s e d u W W s c + τν μν ν , , ,
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P461 - nuclear decays 5 Lifetimes • just one channel with N(t) = total number at time t • multiple possible decays. Calculate each (the “partial” widths) and then add up • Measure lifetime. long-lived ( τ >10 -8 sec). Have a certain number and count the decays 2 ln 1 ) 0 ( ) ( 2 / 1 τ λ = = = = = = t life half t e N t N N dt dN t width gamma Rate = = Γ = = 1 Γ Γ = Γ + Γ + Γ = Γ = i i fraction branching K 3 2 1 1 1 / = N dt dN
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P461 - nuclear decays 6 Lifetimes • Measure lifetime.
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This note was uploaded on 10/02/2009 for the course PHYS 460 taught by Professor Johnson,c during the Spring '08 term at Northern Illinois University.

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09nuclei2 - Nuclear Decays Unstable nuclei can change N,Z.A...

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