1. 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

2. 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
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Nuclear Physics Lectures

3. 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
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Nuclear Physics Lectures

4. 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
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Nuclear Physics Lectures

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

6. Nuclear Physics Lectures
Tony Weidberg
Nuclear Physics Lectures

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

8. 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

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

10. 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
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Nuclear Physics Lectures

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

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

13. 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)
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Nuclear Physics Lectures

14. 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
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Nuclear Physics Lectures

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

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

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

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

19. 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
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Nuclear Physics Lectures

20. 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

21. 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

22. Nuclear Physics Lectures
<Op> = 0 QED
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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.
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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.
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Nuclear Physics Lectures

25. Nuclear Physics Lectures
The Experiment
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Nuclear Physics Lectures

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

27. 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

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

30. 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.
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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
Tony Weidberg
Nuclear Physics Lectures

32. 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