Weak Interactions in the Nucleus II

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Weak Interactions in the Nucleus II

• Summer School, Tennessee
• June 2003

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Recoil effects in EM
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
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Recoil effects in Weak decays
Recoil effects
gS and gWM Conservation of the Vector Current
I1 form factors in VEM are identical to form
factors in VWEAK
gT Second Class Currents breaking of G-parity
gPS Partial Conservation of the Axial
Current (plus pion-pole dominance)
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Conservation of the Vector Current I1 form
factors in VEM are identical to form factors in
VWEAK
Width of M1 and (e,e) cross-section determine
ltgWMgt for EM
I1,Jp0
14O
I1,Jp0
I1,Jp0
14C
14N
Shape of beta spectrum, t, determines ltgWMgt for
WEAK
Potential for checking CVC at fraction of level

• Garcia and B.A. Brown,
• Phys Rev. C 52, 3416 (1995).

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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
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gT Second Class Currents breaking of G-parity
In 1970s evidence that (ft)/(ft)- changed
linearly with end-point energy
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From R. D. McKeown, et al.Phys. Rev. C 22,
738-749 (1980)
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From Minamisono et al. Phys. Rev. Lett. 80,
4132(1998).
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Angular momentum and Rotations
Rotating the coordinate system
Invariance
For any rotation
Invariance under rotations imply conservation of
J
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Isospin
Notice nn, np, pp hadronic interactions are
very similar.
Use spin formalism to take into account Pauli
exclusion principle etc.
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Weak Decays of Quarks
Once upon a time
Weak interactions needed neutral component to
render g sinq e.
m-
m
But the process KL0?mm- could not be observed.
Why not??
Z0
s
d
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Weak Decays of Quarks
G.I.M. proposed
The neutral weak currents go like
No strangeness-changing Neutral Currents
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Weak Decays of Quarks
G.I.M. proposed
The neutral weak currents go like
n
The process KL0?mm- actually goes through
this diagram
u c
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Finding J/Psi confirmed the existence of the c
quark and gave validity to the G.I.M. hypothesis
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Weak decays in the Standard Model
I
u
e
ne
1/2
W
d
1/2
Ke3 0.220
nm
e
From nuclear 0.974
0.080
ne
m
CKM matrix Is it really Unitary?
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In order to measure Vud we compare intensities
for semi-leptonic to purely leptonic decays
e
d
ne

• Fermis Golden rule
• t -1 a ltf H igt2 f(E)
• Then
• ltf I igt2 Vud2 ? ftm /ftquarks

u
nm
e
ne
m
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Example decay of 14O
Level density not high so Isospin config. mixing
very small.
I1 Iz1, Jp0
14O easy to produce and half-life convenient for
separating from other radioactivity.
14O (t1/270.6 s)
I1 Iz0, Jp0
branch lt1
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
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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

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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
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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
p
n
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Radiative and isospin breaking corrections have
to be taken into account.
From Hardy et al, Nucl. Phys. A509, 429 (1990).
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The complication of isospin-breaking
correctionscan be circumvented by looking at
1) p?p0 e n2) 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).
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Determinnig Vud from neutron b decay

• Disadvantage Vm and Am contribute to this
  Jp1/2 ? 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.
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Cold-Neutron Decay
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J.C. Hardy, 2003
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Beta asymmetry with beam of Cold Neutrons (v ?
500 m/s)
e-
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, 211801 (2002).
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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, 272501

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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.
• GravityAluminum detector window

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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, 272501

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Neutrons in Magnetic Field
In a frame rotating with freq. w
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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
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Neutrons in Magnetic Field
In S motion is precession around Be with angular
velocity a -w Be