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Nuclear Decays

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.

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Nuclear Decays

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  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. 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. PHYS584) P461 - nuclear decays

  3. Simplified Phase Space • Decay: A  a + b + c ….. • Q = available kinetic energy • large Q  large phase space  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) 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…. 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 (t>10-8sec). Have a certain number and count the decays P461 - nuclear decays

  6. Lifetimes • Measure lifetime. medium-lived (t>10-13sec). Decay point separated from production point. Measure path length. Slope gives lifetime • short-lived (10-23 < t <10-16 sec). Measure invariant mass of decay products. If have all  mass of initial. Width of mass distributions (its width) related to lifetime by Heisenberg uncertainty. 100 10 1 Dx P461 - nuclear decays

  7. Alpha decay • Alpha particle is the He nucleus (2p+2n) • ~all nuclei Z > 82 alpha decay. Pb(82,208) is doubly magic with Z=82 and N=126 • the kinematics are simple as non-relativistic and alpha so much lighter than heavy nuclei • really nuclear masses but can use atomic as number of electrons do not change P461 - nuclear decays

  8. Alpha decay-Barrier penetration • One of the first applications of QM was by Gamow who modeled alpha decay by assuming the alpha was moving inside the nucleus and had a probability to tunnel through the Coulomb barrier • from 1D thin barrier (460) for particle with energy E hitting a barrier potential V and thickness gives Transmission = T • now go to a Coulomb barrier V= A/r from the edge of the nucleus to edge of barrier and integrate- each dr is a thin barrier P461 - nuclear decays

  9. Alpha decay-Barrier penetration • Then have the alpha bouncing around inside the nucleus. It “strikes” the barrier with frequency • the decay rate depends on barrier height and barrier thickness (both reduced for larger energy alpha) and the rate the alpha strikes the barrier • larger the Q larger kinetic energy and very strong (exponential) dependence on this • as alpha has A=4, one gets 4 different chains (4n, 4n+1, 4n+2, 4n+3). The nuclei in each chain are similar (odd/even, even/even, etc) but can have spin and parity changes at shell boundaries • if angular momentum changes, then a suppression of about 0.002 for each change in L (increases potential barrier) P461 - nuclear decays

  10. Alpha decay-Energy levels • may need to have orbital angular momentum if sub-shell changes (for odd n/p nuclei) • Z= 83-92 1h(9/2) N=127-136 2g(9/2) Z=93-100 2f(7/2) N=137-142 3d(5/2) • so if f(7/2)  h(9/2) need L>0 but parity change if L=1  L=2,4 • or d(5/2)  g(9/2) need L>1. No parity change L=2,4 • not for even-even nuclei (I=0). suppression of about 0.002 for each change in L (increases potential barrier) s 0 p 1 d 2 f 3 g 4 h 5 P461 - nuclear decays

  11. Parity + Angular Momentum Conservation in Alpha decay • X  Y + a. The spin of the alpha = 0 but it can have non-zero angular momentum. Look at Parity P • if parity X=Y then L=0,2…. If not equal L=1,3… • to conserve both Parity and angular momentum P461 - nuclear decays

  12. Energy vs A Alpha decay P461 - nuclear decays

  13. Lifetime vs Energy in Alpha Decays Perlman, Ghiorso, Seaborg, Physics Review 75, 1096 (1949) 10 log10 half-life in years 0 -10 5 7 Alpha Energy MeV P461 - nuclear decays

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