abg Decay Theory

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# abg Decay Theory - PowerPoint PPT Presentation

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
• 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
• Consider 232Th Z=90 R=7.6 fm  E=34 MeV
• Energy of a Ea=4.08 MeV
• Question: How does the a escape?

Nuclear Physics Lectures

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

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

DEsep≈6MeV per nucleon for heavy nuclei

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

a-decay

Protons

Alphas

Neutrons

Nuclear Physics Lectures

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

Nuclear Physics Lectures

Experimental Tests
• Predict log decay rate proportional to (Ea)1/2
• Agrees ~ with data for e-e nuclei.
• Angular momentum effects:
• 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 Tests

1018

Half-life(s)

10-6

4

9

EnergyE (MeV)

Nuclear Physics Lectures

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

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

Nuclear Physics Lectures

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

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

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

Nuclear Physics Lectures

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

Nuclear Physics Lectures

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

Nuclear Physics Lectures

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

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

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.

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).

Nuclear Physics Lectures

<Op> = 0 QED

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.

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.

Nuclear Physics Lectures

The Experiment

Nuclear Physics Lectures

Improved Experiment

q is angle wrt spin of 60Co.

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.

Nuclear Physics Lectures

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)
• 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.
• Absolutely forbidden (why?): 00

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.

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

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.

Nuclear Physics Lectures