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abg Decay Theory

abg Decay Theory. Previously looked at kinematics now study dynamics (interesting bit). QM tunnelling and a decays Fermi theory of b decay and e.c. g decays. a Decay Theory. Consider 232 Th Z=90 R=7.6 fm  E=34 MeV Energy of a E a =4.08 MeV Question: How does the a escape?

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abg Decay Theory

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  1. abg Decay Theory • Previously looked at kinematics now study dynamics (interesting bit). • QM tunnelling and a decays • Fermi theory of b decay and e.c. • g decays Nuclear Physics Lectures

  2. a Decay Theory • Consider 232Th Z=90 R=7.6 fm  E=34 MeV • Energy of a Ea=4.08 MeV • Question: How does the a escape? • Answer: QM tunnelling Nuclear Physics Lectures

  3. radial wave function in alpha decay r nucleus barrier (negative KE) small flux of real α I iII iI Exponential decay of y Nuclear Physics Lectures

  4. QM Tunnelling • B.C. at x=0 and x=t for Kt>>1 and k~K gives for 1D rectangular barrier thickness t gives T=|D|2=exp(-2Kt) • Integrate over Coulomb barrier from r=R to r=t V E t 0 Nuclear Physics Lectures

  5. DEsep≈6MeV per nucleon for heavy nuclei DEbind(42a)=28.3 MeV > 4*6MeV a-decay Protons Alphas Neutrons Nuclear Physics Lectures

  6. Nuclear Physics Lectures

  7. Alpha Decay Rates • Gamow factor • Number of hits, on surface of nucleus radius R ~ v/2R.Decay rate Nuclear Physics Lectures

  8. Experimental Tests • Predict log decay rate proportional to (Ea)1/2 • Agrees ~ with data for e-e nuclei. • Angular momentum effects: • Additional barrier • Small compared to Coulomb but still generates large extra exponential suppression. Eg l=1, R=15 fm El~0.05 MeV cf for Z-90  Ec~17 MeV. • Spin/parity DJ=L parity change=(-)L Nuclear Physics Lectures

  9. Experimental Tests 1018 Half-life(s) 10-6 4 9 EnergyE (MeV) Nuclear Physics Lectures

  10. p d n u d u u e- d ne ( ) W- Fermi b DecayTheory • Consider simplest case: n decay. • At quark level: du+W followed by decay of virtual W. Nuclear Physics Lectures

  11. Fermi Theory • 4 point interaction (low energy approximation). Nuclear Physics Lectures

  12. Fermi Theory • e distribution determined by phase space (neglect nuclear recoil energy) • Use FGR : phase space & M.E. decay rate Nuclear Physics Lectures

  13. Kurie Plot Tritium b decay (I(p)/p2K(Z,p))1/2 Coulomb correction  Fermi function K(Z,p) Continuous spectrum neutrino End point gives limit on neutrino mass Intensity 18 Electron energy (keV) Electron energy (keV) Nuclear Physics Lectures

  14. Selection Rules • Fermi Transitions: • en couple to give 0 spin: DS=0 • “Allowed transitions” DL=0  DJ=0. • Gamow-Teller transitions: • en couple to give 1 unit of spin: DS=0 or ± 1. • “Allowed transitions” DL=0  DJ=0 or ± 1. • “Forbidden” transitions: • Higher order terms correspond to non-zero DL. Therefore suppressed depending on (q.r)2L • Usual QM rules give: J=L+S Nuclear Physics Lectures

  15. Electron Capture • Can compete with b+ decay. • For “allowed” transitions. • Only l=0. n=1 largest. Nuclear Physics Lectures

  16. Electron Capture (2) • Density of states: • Fermi’s Golden Rule: Nuclear Physics Lectures

  17. Anti-neutrino Discovery • Inverse Beta Decay • Same matrix elements. • Fermi Golden Rule: Nuclear Physics Lectures

  18. Anti-neutrino Discovery (2) • Phase space factor • Neglect nuclear recoil. • Combine with FGR Nuclear Physics Lectures

  19. The Experiment • For E~ 1MeV s~10-47 cm2 • Pauli prediction and Cowan and Reines. Liquid Scint. 1 GW Nuclear Reactor H20+CdCl2 PMTs Shielding Nuclear Physics Lectures

  20. Parity Definitions • Eigenvalues of parity are +/- 1. • If parity is conserved: [H,P]=0  eigenstates of H are eigenstates of parity. If parity violated can have states with mixed parity. • If Parity is conserved result of an experiment should be unchanged by parity operation. Nuclear Physics Lectures

  21. Parity Conservation • If parity is conserved for reaction a+b c+d. • Nb absolute parity of states that can be produced from vacuum (e.g. photons) can be defined. For other particles we can define relative parity. e.g. define hp=+1, hn=+1 then can determine parity of other nuclei. • If parity is conserved <pseudo-scalar>=0 (see next transparency). Nuclear Physics Lectures

  22. <Op> = 0 QED Nuclear Physics Lectures

  23. Is Parity Conserved In Nature? • Feynman’s bet. • Yes in electromagnetic and strong interactions. • Big surprise was that parity is violated in weak interactions. Nuclear Physics Lectures

  24. Mme. Wu’s Cool Experiment • Align spins of 60Co with magnetic field. • Adiabatic demagnetisation to get T ~ 10 mK • Measure angular distribution of electrons and photons relative to B field. • Clear forward-backward asymmetry  Parity violation. Nuclear Physics Lectures

  25. The Experiment Nuclear Physics Lectures

  26. Improved Experiment q is angle wrt spin of 60Co. Nuclear Physics Lectures

  27. g decays • When do they occur? • Nuclei have excited states cf atoms. Don’t worry about details E,JP (need shell model to understand). • EM interaction << strong interaction • Low energy states E < 6 MeV above ground state can’t decay by strong interaction  EM. • Important in cascade decays a and b. • Practical consequences • Fission. Significant energy released in g decays. • Radiotherapy: g from Co60 decays. • Medical imaging eg Tc. Nuclear Physics Lectures

  28. Energy Levels for Mo and Tc b decay leaves Tc in excited state. Useful for medical imaging Nuclear Physics Lectures

  29. g Decay Theory (Beyond Syllabus) • Most common decay mode for nuclear excited states (below threshold for break-up) is g decay. • Lifetimes vary from years to 10-16s. nb long lifetimes can easily be observed unlike in atomic. Why? • Angular momentum conservation in g decays. • intrinsic spin of g is1 and orbital angular momentum integer  J is integer. • Only integer changes in J of nucleus allowed. • QM addition of J: • Absolutely forbidden (why?): 00 Nuclear Physics Lectures

  30. g Decays • Electric transitions • Typically k~1 MeV/c r~ 1 fm k.r~1/200  use multipole expansion. Lowest term is electric dipole transitions, L=1. • Parity change for electric dipole. Nuclear Physics Lectures

  31. Forbidden Transitions • If electric dipole transitions forbidden by angular momentum or parity can have “forbidden” transitions, eg electric quadropole. • Rate suppressed cf dipole by ~ (k.r)2 • Magnetic transitions also possible: • Classically: E=-m.B • M1 transition rate smaller than E1 by ~ 10-3. • Higher order magnetic transitions also possible. • Parity selection rules: • Electric: Dp=(-1)L • Magnetic: Dp=(-1)L+1 Nuclear Physics Lectures

  32. Internal Conversion • 00 absolutely forbidden: • What happens to a 0+ excited state? • Decays by either: • Internal conversion: nucleus emits a virtual photon which kicks out an atomic electron. Requires overlap of the electron with the nucleus only l=0. Probability of electron overlap with nucleus increases as Z3. For high Z can compete with other g decays. • Internal pair conversion: nucleus emits a virtual photon which converts to e+e- pair. Nuclear Physics Lectures

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