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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

r

nucleus

barrier (negative KE)

small flux of real α

I

iII

iI

Exponential decay of y

Nuclear Physics Lectures

• 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

• Gamow factor

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

Nuclear Physics Lectures

• 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

1018

Half-life(s)

10-6

4

9

EnergyE (MeV)

Nuclear Physics Lectures

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

• 4 point interaction (low energy approximation).

Nuclear Physics Lectures

• e distribution determined by phase space (neglect nuclear recoil energy)

• Use FGR : phase space & M.E. decay rate

Nuclear Physics Lectures

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

• 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

• Can compete with b+ decay.

• For “allowed” transitions.

• Only l=0. n=1 largest.

Nuclear Physics Lectures

• Density of states:

• Fermi’s Golden Rule:

Nuclear Physics Lectures

• Inverse Beta Decay

• Same matrix elements.

• Fermi Golden Rule:

Nuclear Physics Lectures

• Phase space factor

• Neglect nuclear recoil.

• Combine with FGR

Nuclear Physics Lectures

• 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

• 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

• 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

Nuclear Physics Lectures

• Feynman’s bet.

• Yes in electromagnetic and strong interactions.

• Big surprise was that parity is violated in weak interactions.

Nuclear Physics Lectures

• 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

Nuclear Physics Lectures

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

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

• 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

• 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