Transcript Phys1401 - Texas A&M University

Experimental Aspects in the
Precise Superallowed
Nuclear Beta Decay
Measurements
V.E. Iacob
Cyclotron Institute, Texas A&M University
09:03
• Standard Model finalized in the mid 70’s
• Testing a Model via precise measurements
o Hafele–Keating experiment testing the
relativistic puzzle of the twins with
macroscopic clocks:
Gravitational
Kinematic
Net effect
Observed
Eastward
144 14
184 18
40 23
59 10
Westward
179 18
96 10
275 21
273 21
Non-relativistic velocities
Atomic clocks (cesium beam atomic clocks)
09:03
J.C. Hafele and R. E. Keating, Science 177, 166 (1972)
Superallowed 0+ → 0+ β decay
Experiment
0+,1
precision: 0.1%
t1/2
Weak Decay Equation
f  f( Z , QEC )
ft 
K
G 
2
V
t  f(t1/ 2 , BR)
2
BR
QEC
0+,1
GV  coupling constant
  matrix element
radiative
nuclear structure
CVC
K
F t  ft (1     NS )(1   C ) 
2GV2 (1   R )
'
R
|Vud |=GV /Gμ
nuclear (&neutron) decays
muon decay
0.97425±0.00022
±0.00010 exp’t
constant
CKM Matrix and Unitarity, 2010
Vud2  Vus2  Vub2  0.9999  0.0006
Towner, Hardy, Rep. Prog. Phys. 73 (2010) 046301
Requirements for Precision Measurements
•
Primary Data Quality (design of the experiment)
 optimized Signal-to-Noise
•
Acquisition System
 dedicated electronics
 simple primary-data observable relation
 easy to understand, systematically tested
•
Data reduction
 accurate methods
 test resuts for all conceivable inconsistencies
 generate a complete & detailed error budget
09:03
T1/2(26Si): The radioactive 26Si beam
Momentum Achromat Recoil Separator
Tape Transport System
i ty
c
o
l
Ve
D3
Q5
r
D2
V1
S1
Q3
P Slits
Faraday Cup
D1 Q2
Q1
T
SW
2
H2 Gas
Target
Q4
25.2A MeV 26Si
>99.3%
0
te
l
i
F
5
Scale (meters)
Emittance
Slits
SW1
QY Q
X
27
Al
30A MeV
1H(27Al,2n)26Si
• Reaction:
• 26Si Beam Purity: > 99.3%
• 26Si Beam Intensity: ~ 4×104 part/s
R. E. Tribble et al., Nucl. Instr. Meth. A 285, 441 (1989), Nucl. Instr. Meth. B 56/57, 956 (1991),
Nucl. Phys. A701, 278 (2002).
09:03
move
beam
detect
• Beam time: ~2 t1/2
• Move time: ~0.175s
• Detect time: ~20 t1/2
MARS
beam-line
1 cycle
time
Aluminum degraders &
Thin plastic scintillator
deck #2
4π proportional
gas counter
Aluminized
Mylar tape
Fast Tape Transport (Half-life Set-up)
09:03
deck #1
tape
Implantation Profile (purity refinement)
26Si
beam
impurities
Implantation depth (mm)
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-125 mV ... -200 mV
Gas
PA
counter
PS-6950
80ns
TFA
nonextending dead-time
ORTEC-579
+ 2400 ... + 2750 V
Gate
(PS794)
threshold
bias
Gate
(PS794)
Multi-scale events
Integrate time (dead-time)
IMPORTANT FEATURES
• Rapid transport (~175 ms) to shielded
counting position (Very low background)
• Extremely high source purity
(separation by Z/A and range)
• Decay data stored cycle-by-cycle so actual instantaneous
rate can be used in analysis.
• Dominant dead-time, fixed and measured.
09:03
The decay of 26Si
(2.1×108 decays)
Counts per 90 ms
t1/2(26Si) = 2.243(4) s
(free-fit)
106
26Si
26Alm
26Mg
105
0+
0+
0+
104
0
10
20
30
40
Time [s]
Survey Average: t1/2=2.234(12)s Hardy, Towner, PRC 71, 055501 (2005)
09:03
Data Reduction: Maximum Likelihood vs c2
•
Gaussian Data: c2 is equivalent to ML
•
Poissonian Data: dedicated ML analysis
•
Modified Poissonian Distribution
 Variable rate
 Dead-time distortion
09:03
Poisson-versus-Gauss Statistics
𝑒 −𝝁 𝝁𝒏
𝑷 𝒏; 𝝁 =
𝒏!
G(x; 𝝁, 𝝈) =
𝟏
− 𝒙−𝝁 𝟐 /𝝈𝟐
𝑒
𝟐𝝅𝝈
𝝁 = 𝟑; 𝝈 = 𝟑
09:03
Poisson-versus-Gauss Statistics
(𝒙𝟏 ; 𝝈𝟏 ) = 𝟏𝟔, 𝟒
(𝒙𝟐 ; 𝝈𝟐 ) = 𝟐𝟓, 𝟓
𝒙𝟏
𝒙𝟐
+
𝝈𝟏 𝟐 𝝈𝟐 𝟐
𝒙=
𝟏
𝟏
+
𝝈𝟏 𝟐 𝝈𝟐 𝟐
= 𝟏𝟗. 𝟓𝟏 (!? )
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𝑒 −𝝁 𝝁𝒏
𝑷 𝒏; 𝝁 =
𝒏!
G(x; 𝝁, 𝝈) =
𝟏
− 𝒙−𝝁 𝟐 /𝝈𝟐
𝑒
𝟐𝝅𝝈
𝝁 = 𝟐𝟓; 𝝈 = 𝟐𝟓
Dead Times
Extendable (PA, TFA); Nonextendable (GG)
threshold
09:03
Free Fit
Sit
tot (t )  C ' e
Al t
 C "e
t1/2=2.2430(40)s
(0.2%)
Constrained Fit
Rtot (t )  C e
 Si t
ke
  Al t
  Bgd
 Si
where k  f (Si , Al ,
, tbeam , tmove )
 Al
t1/2=2.2253(7) s
09:03
(<0.1%)
The decay of 26Si
(2.1×108 decays)
Counts per 90 ms
t1/2(26Si) = 2.2453(7) s
106
26Si
26Alm
26Mg
105
0+
0+
0+
104
0
10
20
30
40
Time [s]
fit: Maximum Likelihood using Distorted Poissonian Statistics 
Modified Gaussian c2 → asymptotic convergence, limited value
09:03
Influence of Detection Efficiencies
(our proportional counter)
26Alm
26Si
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Influence of Detection Efficiencies
Our result vs Matea et al , EPJ A37, 151 (2008)
0.012
26Si
26Si
0.01
26Alm
26Alm
Yield
0.008
Matea et al Cut-Off
0.006
0.004
0.002
0
0
1
2
3
4
Energy [MeV]
εav = 90%; ε(26Si)/ε(26Al)=1.0075; 2.2283(27)s ↗ 2.240 s (?)
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26Si
Half Life
Test for Possible Systematic Errors
2.26
t1/2(26Si) = 2 243.77 ± 0.51 ms
0.1%
Half Life [s]
2.25
2.24
Detector Bias:
2550V ▲
2650V ■
Discriminator Threshold:
2.23
0
10
20
150mV
30
Run Number
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2750V ●
2850V ▼
200mV
40
250mV
50
60
26Si
Half Life
Test for Possible Systematic Errors
09:03
Error Budget
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Results
• High purity & intense radioactive beam
– Main contaminant: 25Al (25Al/26Si <10-4)
• No systematic error could be identified
– No short lived isomers
– No rate dependencies (dead-time correction)
– No electronic set-up dependencies
• T1/2(26Si) = 2.2430(40) / 2.2453(7) s
(free / restricted fit)
– Current precision: ~0.03%
09:03
move
beam
detect
• Beam time: ~1-2 t1/2
• Move time: ~0.175s
• Detect time: ~2 t1/2
MARS
beam-line
1 cycle
deck #2
time
Aluminum degraders &
Thin plastic scintillator
HPGe
Absolute efficiency
0.2% for 50-1400 keV
Aluminized
Mylar tape
Plastic
Scintillator
deck #1
09:03
Fast Tape Transport (Branchig Ratio Set-up)
Branching Ratio (Experimental Method)
2mm
d=151 mm


HpGe detector
Plastic
scintillator
N   N decays   
N  
09:03


 N decays     BR    
N  
N
 BR   
5.2714 y
5+
0
60
27Co
Q =2823.9
99.925%
< 0.0022%
0.057%
7.5
> 13.3
15.02
4+
2+
2+
2.0
99 10 -6
0.0.90
25
0.0 076 1173 05
0.00111 346.237E4
.
07
99
6 215 93 E2(+
.98
8
M3
26 8.57
20
)
.
0
6
13
32
M1E2
.50
+E
1
2
E2
Cross-over gammas
0+
1332.516 0.713 ps
0
60
28Ni
09:03
2505.765 0.30 ps
2158.64 0.59 ps
stable
-delayed -rays observed in coincidence
with positrons following the decay of 34Ar
10 5
0.8438(4)s
β+
SE
DE
3129
2580
461
34Cl
2
SE
10
665
10 3
2580
3129
461
10 4
665
34Ar
10 1
0
10
0
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1000
2000
3000
Random Coincidences
2 1-Na Time Sp ectrum
100
Time-Spectrum
Background
10
1
09:03
0
100
200
300
400
Results
0.8438(4)s
N 
BR 
k
N 
Random coincidence summing 0.3%
Errors
461
Real coincidence summing 0.1%
666
-detector cut-off 0.2%
2580
Dead times 0.5%
3129
Corrections
34Ar
34Cl
Statistics ±1.3%
Σ(BR*) = 5.64(8)%
ε ±0.7% (position:±0.5mm)
BRGS = 94.36(8)%
09:03
ε ±0.3%
(preliminary)
Credits:
•
•
•
•
•
•
•
09:03
A. Banu
J.C. Hardy
V.V. Golovko
N. Nica
H.I. Park
L. Trache
R.E. Tribble
09:03
-delayed -rays observed in coincidence
with positrons following the decay of 10C
β+
1022
10B
10 1
1740
718 +
1022
10 2
718 + 511
1022
10 3
718
10 4
1740 (<0.2%)
10C
718
10
19.312(3)s
5
BR718+BR1740=99.51(68)%
0
10
0
09:03
500
METHOD
✓
1000
1500
2000