1. (and some things about the weak interaction)
Nuclear b-Decay
(and some things about the weak interaction)
Tomas Janssen
Povh/Rith: Chapter (Weak interaction)
Chapter 15.5 (b-decay of the neutron)
Chapter 17.6 (Nuclear b-decay)

2. Overview of the talk Weak Interaction V-A coupling Cabibbo angle
b-decay of the neutron
Phase space
Fermi and Gamow-Teller transitions
Nuclear b-decay
Different decay types (allowed, forbidden, …)
Physics beyond the standard model

3. V-A coupling Parity is not conserved Spin flip should be possible
Neutrino has a definite handedness
 V -A

4. Cabibbo angle 1 Quarks from one family: weak isospin doublet
Operator I+ changes weak isospin
I+|u> = |d> ; I+|d> = |u> ; I+|s> = |c> ; etc. N
No mixing of family’s!
General weak decay involving quarks:
Quark emits W+/- and changes it’s weak isospin.
W+/- decays to:
Lepton / anti-lepton (semi-leptonic)
Quark / anti-quark (non-leptonic)

5. Cabibbo angle 2 So mixing of family’s should be possible!W- p  -
So mixing of family’s should
be possible!
Mixing matrix of eigenstates of the same weak isospin. W-
T+ = I+cosC d u W-
T+ = I+sinC s u

6. b-Decay of the neutron 1 Phase space

7. b-Decay of the neutron 2 Fermi transitions
Case 1: pure vector transitions (“Fermi”)
 No spin flip; DJ=0
Independent of nuclear structure!

8. b-Decay of the neutron 3 Gamow-Teller transitions
Case 2: pure axial transitions (“Gamow-Teller”)
Spin flip; DJ=0, ±1
Matrix element depends on overlap of spin-wavefunctions
Use:

9. b-Decay of the neutron 4 Total matrix element
We cannot measure individual quarks, so we need the complete nucleon wave functions and

10. Nuclear b-decay 1 Nucleon is contained in a nucleus
Matrix element contains overlap of nuclear wave functions
Difference in binding energy fixes phase space
Phase space is modified by Coulomb interaction

11. Nuclear b-decay 2 Phase Space
Fermi function:
Coulomb parameter for :

12. Nuclear b-decay 3 ft-Value
Since
We can define ft-value: only a function of the matrix element
ft-value ranges from 103 – 1022 sec. !
The difference between vector and axial transitions can’t explain this
 Look at orbital angular momentum.

13. Nuclear b-decay 4 l-dependence
Plane wave:
For spinless particle: partial wave:
So we can associate each term in the plane wave
expansion with a unit of l

14. Nuclear b-decay 4 Types of decay
Since p ~ MeV, x ~ fm px ~10-2
The matrix element occurs squared in the decay rate,
So each unit of l suppresses the decay with 10-4
l = 0
DP=0
Allowed
l = 1
DP=1
Forbidden
l = 2
Double forbidden
l =3
Triple forbidden
e.g: 1-  0+ : Once forbidden Gamow-Teller

15. Nuclear b-decay 5 Superallowed b-decay
Initial and final states overlap perfectly
Proton and neutron have the same q-numbers
Initial and final states are in the same isospin
multiplet
“Only” with b+
Decay to highly
excited state

16. Nuclear b-decay 6 Forbidden b-decay
Due to selection rules: the allowed decays are ruled out.

17. Nuclear b-decay 7 Kurie Plot
Gives:
 Straight line, if Mfi is constant (only if l=0; allowed)

18. Beyond the standard model 1 Measuring the neutrino mass
Nonzero neutrino mass alters phase space:
Gives:
The intersection with the K=0 axis gives the
neutrino mass
Also puts a limit on the tau and muon neutrino’s
(neutrino oscillations)

19. Beyond the standard model 2 Measuring a S or T coupling
If the neutrino is massive, we need righthanded neutrino’s
We can’t have pure V-A
Consider Fermi decay: DJ=0.
Can only happen with V or S
Angular dependence of Matrix element:
Where:

20. Beyond the standard model 2 Measuring a S or T coupling
But we can’t measure so instead look at:

21. Summary (please think of some questions!)