abg decay theory
Skip this Video
Download Presentation
abg Decay Theory

Loading in 2 Seconds...

play fullscreen
1 / 32

abg Decay Theory - PowerPoint PPT Presentation

  • Uploaded on

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?

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about ' abg Decay Theory' - hamish-burton

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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

Nuclear Physics Lectures

a decay theory
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


radial wave function in alpha decay



barrier (negative KE)

small flux of real α




Exponential decay of y

Nuclear Physics Lectures

qm tunnelling
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





Nuclear Physics Lectures

a decay

DEsep≈6MeV per nucleon for heavy nuclei

DEbind(42a)=28.3 MeV > 4*6MeV





Nuclear Physics Lectures

alpha decay rates
Alpha Decay Rates
  • Gamow factor
  • Number of hits, on surface of nucleus radius R ~ v/2R.Decay rate

Nuclear Physics Lectures

experimental tests
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

experimental tests1
Experimental Tests






EnergyE (MeV)

Nuclear Physics Lectures

fermi b decaytheory











( )


Fermi b DecayTheory
  • Consider simplest case: n decay.
  • At quark level: du+W followed by decay of virtual W.

Nuclear Physics Lectures

fermi theory
Fermi Theory
  • 4 point interaction (low energy approximation).

Nuclear Physics Lectures

fermi theory1
Fermi Theory
  • e distribution determined by phase space (neglect nuclear recoil energy)
  • Use FGR : phase space & M.E. decay rate

Nuclear Physics Lectures

kurie plot
Kurie Plot

Tritium b decay


Coulomb correction  Fermi function K(Z,p)

Continuous spectrum neutrino

End point gives limit on neutrino mass



Electron energy


Electron energy (keV)

Nuclear Physics Lectures

selection rules
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

electron capture
Electron Capture
  • Can compete with b+ decay.
  • For “allowed” transitions.
  • Only l=0. n=1 largest.

Nuclear Physics Lectures

electron capture 2
Electron Capture (2)
  • Density of states:
  • Fermi’s Golden Rule:

Nuclear Physics Lectures

anti neutrino discovery
Anti-neutrino Discovery
  • Inverse Beta Decay
  • Same matrix elements.
  • Fermi Golden Rule:

Nuclear Physics Lectures

anti neutrino discovery 2
Anti-neutrino Discovery (2)
  • Phase space factor
  • Neglect nuclear recoil.
  • Combine with FGR

Nuclear Physics Lectures

the experiment
The Experiment
  • For E~ 1MeV s~10-47 cm2
  • Pauli prediction and Cowan and Reines.

Liquid Scint.

1 GW Nuclear Reactor




Nuclear Physics Lectures

parity definitions
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

parity conservation
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


<Op> = 0 QED

Nuclear Physics Lectures

is parity conserved in nature
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

mme wu s cool experiment
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

the experiment1
The Experiment

Nuclear Physics Lectures

improved experiment
Improved Experiment

q is angle wrt spin of 60Co.

Nuclear Physics Lectures

g decays
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

energy levels for mo and tc
Energy Levels for Mo and Tc

b decay leaves Tc in excited state.

Useful for medical imaging

Nuclear Physics Lectures

g decay theory beyond syllabus
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

g decays1
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

forbidden transitions
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

internal conversion
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