Nuclear Physics Lectures 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 Summary: Alpha decays: understand rates from QM tunneling and simple picture of alpha pre-formed in nucleus. Crude but explains orders of magnitude change in rate with E(alpha). Beta decays: Need neutrino hypothesis to explain continuous e energy spectra. Fermi theory (low energy approximation) 4 point interaction. Explains shape of e energy spectra. Inverse beta decay. Same theory  cross section. Experimental observation of anti-neutrinos Parity violation What is parity Experimental evidence for parity violation. Gamma decays When they occur. Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures

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

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures

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

Nuclear Physics Lectures Tony Weidberg Nuclear Physics Lectures

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

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures Experimental Tests 1018 Half-life (s) 10-6 4 9 Energy E (MeV) Tony Weidberg Nuclear Physics Lectures

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

Nuclear Physics Lectures Fermi Theory 4 point interaction (low energy approximation). Tony Weidberg Nuclear Physics Lectures

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

Nuclear Physics Lectures 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) Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures

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

Nuclear Physics Lectures Electron Capture (2) Density of states: Fermi’s Golden Rule: Tony Weidberg Nuclear Physics Lectures

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

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

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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. Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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). Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures <Op> = 0 QED Tony Weidberg Nuclear Physics Lectures

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

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. Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures The Experiment Tony Weidberg Nuclear Physics Lectures

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

Nuclear Physics Lectures 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. Tony Weidberg Nuclear Physics Lectures

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

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 Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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. Tony Weidberg Nuclear Physics Lectures

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 Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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. Tony Weidberg Nuclear Physics Lectures