1. Weak Interactions in the Nucleus II
Summer School, Tennessee
June 2003

2. Recoil effects in E&M g p Hadrons exchange gluons
so need to include most general
Lorentz-invariant terms in
interaction
Recoil effects
Has to be zero to allow
conservation of charge:
Anomalous magnetic moment

3. Recoil effects in Weak decaysne d W u
gS and gWM: Conservation of the Vector Current:
I=1 form factors in VE&M are identical to form factors in VWEAK
gPS: Partial Conservation
of the Axial Current
(plus pion-pole dominance):
gT: Second Class Currents:
breaking of G-parity

4. Conservation of the Vector Current:
I=1 form factors in VE&M are identical to form factors in VWEAK
Width of M1 and (e,e’)
cross-section
determine <gWM>
for E&M
I=1,Jp=0+
14O
I=1,Jp=0+
I=1,Jp=0+
14C
14N
Shape of beta spectrum,
t, determines <gWM>
for WEAK
Potential for checking CVC
at fraction of % level
Garcia and B.A. Brown,
Phys Rev. C 52, 3416 (1995).

5. gPS: Partial Conservation of the Axial Current
(plus pion-pole dominance):
Approximation should hold very well : u and d quarks are very light
chiral symmetry: V. Bernard et al. Phys. Rev. D 50, 6899 (1994).
Measure intensity of m + p =n + n + g
Radiative m capture
Ordinary m capture

6. gT: Second Class Currents:
breaking of G-parity
In 1970’s evidence that (ft)+/(ft)- changed linearly with end-point energy

9. From R. D. McKeown, et al. Phys. Rev. C 22, 738-749 (1980)

10. From Minamisono et al.
Phys. Rev. Lett. 80, 4132(1998).

11. Angular momentum and Rotations
Rotating the coordinate system:
Invariance:
For any rotation:
Invariance under rotations imply conservation of J

12. Isospin Notice n+n, n+p, p+p hadronic interactions are very similar.
Use spin formalism to take into account Pauli exclusion principle etc.

14. Weak interactions needed neutral component to render g sinq = e.
Weak Decays of Quarks
Once upon a time:
Weak interactions needed neutral component to render g sinq = e. m- m+
But the process
KL0m+m-
could not be observed.
Why not?? Z0 s d

15. No strangeness-changing
Weak Decays of Quarks
G.I.M. proposed
The neutral weak
currents go like:
No strangeness-changing
Neutral Currents

16. Weak Decays of Quarks G.I.M. proposed The neutral weak
currents go like: s d W m+ m- n
The process
KL0m+m-
actually goes through
this diagram
u c

17. Finding J/Psi confirmed the existence of the c quark and
gave validity to the G.I.M. hypothesis

18. CKM matrix: Is it really Unitary?
Weak decays in the Standard Model Q -1
+2/3
-1/3 I u e+ ne
1/2 d W
1/2 Ke nm e+
From nuclear
0.974
0.080 ne m
CKM matrix: Is it really Unitary?

19. In order to measure Vud we compare intensities for semi-leptonic to purely leptonic decaysne
Fermi’s Golden rule:
t -1 α |<f H i>|2 f(E)
Then:
|<f I i>|2 Vud2  ftm /ftquarks u nm e+ ne m

20. Example: decay of 14O 14O (t1/2=70.6 s) 14N Level density not high
so Isospin config.
mixing very small.
I=1 Iz=1, Jp=0+
14O easy to produce
and half-life convenient
for separating from other
radioactivity.
14O (t1/2=70.6 s)
I=1 Iz=0, Jp=0+
branch <1%
Additional branches so
small that beta intensity
can almost be obtained
directly from 14O half-life
14N
Many features contribute
to allowing a precise
determination of ft

21. Nuclear weak decays are driven by two currents : Vm and Am
Nuclear weak decays are driven by two currents : Vm and Am. Vm is conserved (in the same sense that the electromagnetic current is conserved).
Initially most precise results came from decays for which only Vm can contribute:
Jp(Initial nucleus)=0+  Jp(Final nucleus)=0+

22. From Hardy et al, Nucl. Phys. A509, 429 (1990).
Note this
range is
only 0.5%
Nuclear 0+  0+ decays:
2.3s away from 1

23. Complication: Isospin symmetry breaking
Nuclei do have charge and
To understand it we can separate it into effects at two different levels:
1) decaying proton and new-born neutron sample different mean fields. E
2) shell-model configurations are mixed n p

24. Radiative and isospin breaking corrections have to be taken into account.
From Hardy et al, Nucl. Phys. A509, 429 (1990).

25. The complication of isospin-breaking corrections can be circumvented by looking at: 1) p+p0 e+ n 2) n  p e- n
1) p+p0 e+ n has a very small branch (10-8);
2) n  p e- n is a mixed transition (Vm and Am contribute).

26. Determinnig Vud from neutron b decay
Disadvantage: Vm and Am contribute to this Jp=1/2+  1/2+ decay. Consequently need to measure 2 quantities with precision.
Advantage: Simplest nuclear decay. No isospin-breaking corrections.
Neutron t already well known: need to determine b asymmetry (e- angular distribution) from polarized neutrons.

28. Cold-Neutron Decay

29. J.C. Hardy, 2003

30. Beta asymmetry with beam of Cold Neutrons (v  500 m/s)
vacuum
beam pipe
neutron
momentum
neutron
spin
B field decreases to
decrease transverse
component of momentum
which lowers backscattering
Abele et al.
Phys. Rev. Lett. 88, (2002).

31. Ultra-Cold Neutron Source Layout (LANL)
SS UCN Bottle
58Ni coated stainless guide
Liquid N2
Flapper
valve
Be reflector
LHe
Solid D2
UCN Detector
77 K poly
Tungsten Target
Saunders, 2003
C. Morris et al, PRL 89,

32. Line C Measurements Saunders, 2003 C. Morris et al, PRL 89, 272501 UCN
Detector
Cold Neutron
Detector
Proton
Beam
Line C results show reduced ( 100) UCN production.
D2 frost on guide windows and walls.
Gravity+Aluminum detector window

33. Solid D2 in a “windowless” container
Grown from a gas phase at 50 mbar
Cooled through the triple point
Saunders, 2003
C. Morris et al, PRL 89,

35. Neutrons in Magnetic Field
In a frame rotating with freq. w:

36. Neutrons in Magnetic Field
Field B1 rotating
with freq. w
around B0 .
In a frame rotating with freq. w:
strength of B0
freq. of B1
strength of B1

37. Neutrons in Magnetic Field
In S’ motion is precession around Be with angular velocity a = -w Be