Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
High-Precision Half-life Measurement for theSuperallowed β+ Emitter 14O
Alex Laffoley
The 49th Winter Nuclear and Particle Physics ConferenceUniversity of Guelph
February 24, 2012
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 1 / 22
Introduction
Nuclear β Decay
• Two types of β decay, β− (electron)and β+ (positron).
• Nuclear β− decay occurs when aneutron decays into a proton, electronand anti-neutrino.
• Mediated by the weak nuclear force.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 2 / 22
Introduction
Hamiltonian
In the Standard Model, the β decay Hamiltonian has the V − A form
H =GF√
2[eγµ(1− γ5)νe uγµ(1− γ5)d ] + H.c.
The most general form of the effective Hamiltonian describing n→ pe−νe(β− decay) is
Hβ ' HV,A +HS +HT ,
where HV,A is the vector and axial-vector term,HS is a scalar contribution term, andHT is a tensor contribution term.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 3 / 22
Introduction
Hamiltonian
In the Standard Model, the β decay Hamiltonian has the V − A form
H =GF√
2[eγµ(1− γ5)νe uγµ(1− γ5)d ] + H.c.
The most general form of the effective Hamiltonian describing n→ pe−νe(β− decay) is
Hβ ' HV,A +HS +HT ,
where HV,A is the vector and axial-vector term,HS is a scalar contribution term, andHT is a tensor contribution term.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 3 / 22
Introduction
Hamiltonian
In the Standard Model, the β decay Hamiltonian has the V − A form
H =GF√
2[eγµ(1− γ5)νe uγµ(1− γ5)d ] + H.c.
The most general form of the effective Hamiltonian describing n→ pe−νe(β− decay) is
Hβ ' HV,A +HS +HT ,
where HV,A is the vector and axial-vector term,HS is a scalar contribution term, andHT is a tensor contribution term.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 3 / 22
Introduction
Scalar Currents
The Standard Model of particle physics is an incomplete theory, thus welook to extensions of the SM. In particular, to set limits on the existenceof fundamental or induced scalar interactions we turn to the ft values forsuperallowed Fermi β decays.
Definition
Superallowed Fermi β decays are beta decays between isobaric analoguestates (ie. Ti = Tf ) where the parent and daughter nuclei have Jπ = 0+.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 4 / 22
Introduction
Scalar Currents
The Standard Model of particle physics is an incomplete theory, thus welook to extensions of the SM. In particular, to set limits on the existenceof fundamental or induced scalar interactions we turn to the ft values forsuperallowed Fermi β decays.
Definition
Superallowed Fermi β decays are beta decays between isobaric analoguestates (ie. Ti = Tf ) where the parent and daughter nuclei have Jπ = 0+.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 4 / 22
Introduction
Why ft Values?
• Have confirmed the CVC hypothesis at the level of 1.3× 10−4
• Provide the most precise value for Vud to date
• After making theoretical QCD and QED corrections, corrected ftvalues, denoted Ft, are expected to be nucleus independent
• Set limits on the existence of a fundamental or induced scalarinteraction in the Standard Model
To place further constraints on possible extensions of the Standard Model:
ft value precision ≤ 0.1% → β decay half-life precision ≤ 0.05%.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 5 / 22
Introduction
Why ft Values?
• Have confirmed the CVC hypothesis at the level of 1.3× 10−4
• Provide the most precise value for Vud to date
• After making theoretical QCD and QED corrections, corrected ftvalues, denoted Ft, are expected to be nucleus independent
• Set limits on the existence of a fundamental or induced scalarinteraction in the Standard Model
To place further constraints on possible extensions of the Standard Model:
ft value precision ≤ 0.1% → β decay half-life precision ≤ 0.05%.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 5 / 22
Introduction
Corrected ft values
5 10 15 20 25 30 35Z of daughter
3060
3065
3070
3075
3080
3085
3090
Ft
(s)
74Rb
62Ga
54Co
50Mn
46V
42Sc
38K
m
34Ar
34Cl
26Al
m
22Mg
14O
10C
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 6 / 22
Introduction
Corrected ft values
5 10 15 20 25 30 35Z of daughter
3060
3065
3070
3075
3080
3085
3090
Ft
(s)
74Rb
62Ga
54Co
50Mn
46V
42Sc
38K
m
34Ar
34Cl
26Al
m
22Mg
14O
10C
= 0.002C
S
CV
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 6 / 22
Introduction
How do we measure ft Values?
In order to measure ft values, we must measure:
• Q-value, the total transition energy
• T1/2, the half-life of the parent
• β branching ratios
If the primary β branch emits a characteristic γ-ray we may measure thehalf-life via:
• direct β counting
• γ photopeak counting
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 7 / 22
Introduction
How do we measure ft Values?
In order to measure ft values, we must measure:
• Q-value, the total transition energy
• T1/2, the half-life of the parent
• β branching ratios
If the primary β branch emits a characteristic γ-ray we may measure thehalf-life via:
• direct β counting
• γ photopeak counting
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 7 / 22
Introduction Motivation
10C and 14O
One of the most precisely measured superallowed half-lives known is 14O.An unsettling systematic effect arises when comparing the results from thetwo experimental methods.
• T1/2(γ) = 70.616(13) s
• T1/2(β) = 70.696(52) s] differ by 1.3σ, or 0.11%
Similarly, a systematic bias occurs with the 10C half-life where the preciseβ counting experiment disagrees at a level of 3σ, or 0.10% with the γcounting method.
These discrepancies provide the motivation for a simultaneous direct β andγ-ray counting experiment.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 8 / 22
Introduction Motivation
γ Photopeak Counting Direct β Counting70.2
70.3
70.4
70.5
70.6
70.7
Hal
f-lif
e of
14O
19.26
19.27
19.28
19.29
19.30
19.31
19.32H
alf-
life
of 10
C
T1/2 γ(
14O) = 70.616(13) s
T1/2 β(
14O) = 70.696(52) s
T1/2 γ(
10C) = 19.290(12) s
T1/2 β(
10C) = 19.310(4) s
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 9 / 22
Experiment & Facilities
TRIUMF & Superallowed Program
A strong superallowed program is in place at TRIUMF’s Isotope Seperatorand Accelerator (ISAC) facility, where the primary driver is a 500 MeVcyclotron which provides intense beams of up to 100 µA of protons tothick layered-foil targets which produce radioisotopes through spallation.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 10 / 22
Experiment & Facilities
Proposed Experiment
• A simultaneous γ and β counting experiment for 14O was run atTRIUMF in November 2011.
• The 8π facility was used to make the measurements.
• A new detector set-up, including the 8π Gamma-Ray Spectrometer,Scintillating Electron-Positron Tagging Array (SCEPTAR), andZero-Degree Scintillator (ZDS), is in place and it is being investigated.
• In follow-up experiments, the General Purpose Station (GPS) will beused for both 10C and 14O measurements.
• The half-life of 10C will also be measured at 8π in a simultaneous β-γexperiment.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 11 / 22
Experiment & Facilities
Proposed Experiment
• A simultaneous γ and β counting experiment for 14O was run atTRIUMF in November 2011.
• The 8π facility was used to make the measurements.
• A new detector set-up, including the 8π Gamma-Ray Spectrometer,Scintillating Electron-Positron Tagging Array (SCEPTAR), andZero-Degree Scintillator (ZDS), is in place and it is being investigated.
• In follow-up experiments, the General Purpose Station (GPS) will beused for both 10C and 14O measurements.
• The half-life of 10C will also be measured at 8π in a simultaneous β-γexperiment.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 11 / 22
Experiment & Facilities Detectors
8π Spectrometer
• Spherical array of 20Compton-supressedHPGe detectors
• Covers approximately13% of the 4π solidangle
• Detects γ-rays emittedfrom excited daughterstates
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 12 / 22
Experiment & Facilities Detectors
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 13 / 22
Experiment & Facilities Detectors
SCEPTAR
• Spherical array of 20thin plastic scintillatingβ detectors (10 perhemisphere) surroundingthe implantation point ofthe radioactive ion beaminside the centralvacuum chamber of 8π
• Each scintillator sits infront of a HPGe detectorto provide β-γcoincidence information
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 14 / 22
Experiment & Facilities Detectors
Zero-Degree Scintillator
• Fast plastic scintillatorbehind implantation site,replacing the back halfof SCEPTAR
• Detects β particlesdirectly
• Beam is implanted ontotape, data is recorded,tape is moved oncenucleus of interest hasdecayed
• It has never been usedfor high-precisionhalf-life measurements
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 15 / 22
Experiment & Facilities Detectors
Zero-Degree Scintillator
• Fast plastic scintillatorbehind implantation site,replacing the back halfof SCEPTAR
• Detects β particlesdirectly
• Beam is implanted ontotape, data is recorded,tape is moved oncenucleus of interest hasdecayed
• It has never been usedfor high-precisionhalf-life measurements
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 15 / 22
Experiment & Facilities S1140
Experiment Overview
• Experiment run in November 2011 using the 8π, SCEPTAR & ZDS
• 95 runs were performed where each run consisted of:1 min background — 3 min beam on — 23 min decay
• Beam of 12C14O with 26Na contaminant
• Various settings such as deadtime and shaping time were variedrun-by-run to investigate systematics
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 16 / 22
Analysis
Deadtime Corrections
• Five multichannel scaler modules were used to independently recordthe ZDS decay data.
• Fixed, nonextendable deadtimes (chosen to be longer than the seriesdeadtimes of the system) were applied to each MCS.
• The deadtimes were measured via the source-plus-pulser method tobe 1.981(3) µs, 5.002(4) µs, 10.001(4) µs, 20.006(7) µs, and29.991(9) µs.
• To correct the data for the deadtime effects, the following equationwas used:
yi =ni
1− ni (τtb
)
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 17 / 22
Analysis
Fit Function
The data was then fit with a two exponential decays, a contaminant of26Na (with a half-life fixed at its central value of 1.07128 s) and the 14O,plus a constant background. The fit function, of four free parameters, canbe expressed as:
yfit(t) =
tf∫ti
a1 exp
(− ln 2 t
a2
)︸ ︷︷ ︸
14O
+ a3 exp
(− ln 2 t
a4
)︸ ︷︷ ︸
26Na
+a5 dt
The level of contamination of the 26Na was relatively large (&10%), butby waiting several seconds after the beam turned off most of the sodiumdecayed leaving a relatively pure (≥99.9%) sample of 14O.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 18 / 22
Analysis Direct β Counting — ZDS
PRELIMINARY Sample Fit
0 50 100 150 200Bin # (6 s/bin)
1e+05
1e+06
Cou
nts
All Runs (summed)MCS24 (2 µs deadtime)
0 50 100 150 200Bin # (6 s/bin)
-3
-2
-1
0
1
2
Res
idua
l (y i-y
fit)/
σ iT
1/2(14
O) = 70.580(20) s, χ2/ν = 1.17
Accepted T1/2
= 70.620(15) s
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 19 / 22
Analysis Direct β Counting — ZDS
PRELIMINARY
0 10 20 30 40 50 60 70 80 90 100Run Number
69
69.5
70
70.5
71
71.5
72
72.5
14O
Hal
f-lif
e (s
)14
O Half-lifeMCS24 (2 µs deadtime)
Average T1/2
(14
O) = 70.572(19) s, χ2/ν = 1.11
Accepted T1/2
= 70.620(15) s
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 20 / 22
Summary & Future Work
Results & Conclusions
• The feasibility of the Zero Degree scintillator for high-precisionhalf-life measurements is being investigated.
• The analysis is still in preliminary stages and more in-depth work mustbe done in the coming months.
• We are preparing for the rerunning of this experiment in Fall/Winterand the 10C superallowed Fermi β decay experiments in the future.
• After obtaining high statistics experiments at 8π and GPS we will beable to address the current systematic bias existing from experimentalmethod used.
• These experiments will help test the limits of induced andfundamental scalar interactions and extensions of the Standard Model.
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 21 / 22
Summary & Future Work
Acknowledgments
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 22 / 22
Summary & Future Work
Acknowledgments
University of Guelph TRIUMF GANILA. Diaz-Varela G. C. Ball G. F. GrinyerR. Dunlop A. Garnsworthy H. BouzomitaP. Finlay G. HackmanP. Garrett S. Ketelhut CEN Bordeaux-GradignanB. Hadinia E. Tardiff B. BlankD. S. Jamieson C. Unsworth J. GiovinazzoK. G. LeachC. E. Svensson SFU SMU
C. Andreoiu R. A. E. AustinQueen’s University D. CrossJ. R. Leslie
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 22 / 22
Appendix Fermi’s Golden Rule
Determining the ft Values
From Fermi’s Golden Rule, we have that
ft =K
|Mf ,i |2G 2v
Assuming isospin is a perfect symmetry, |Mf ,i |2 for β± decay from 0+ → 0+
states is the expectation value for the isospin lowering (raising) operator.
|Mf ,i |2 =∣∣⟨T ,T3 ∓ 1|τ∓|T ,T3
⟩∣∣2= (T ± T3)(T ∓ T3 + 1)
Specifically, both 10C and 14O are T = 1, Tz = −1 β+ emitters. Thus, we clearlysee
|Mf ,i |2 = (1 + 1)(1− 1 + 1) = 2 .
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 23 / 22
Appendix Fermi’s Golden Rule
The phase space integral, f , is defined as
f =
W0∫1
p W (W0 −W )2 F (Z ,W ) S(Z ,W ) dW ,
where W is the electron total energy in electron rest-mass units, W0 is themaximum value of W , p is the electron momentum, Z is the charge number ofthe daughter nucleus, F (Z ,W ) is the Fermi function, and S(Z ,W ) is theshape-correction factor.
The partial half-life, t, is defined as
t =ln 2
λi→f=
T1/2
Bf.
Combining all of this we have that
ft =2π3~7 ln 2
|Mf ,i |2 G 2V m5
ec4
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 24 / 22
Appendix Source-Plus-Pulser
To measure the deadtime (τ) of a system we use two sources, A and B, that wecount independently and in combined form C . Generally, we use artificial periodicpulses (of frequency n0
p) for one of the random sources and a random source ofrate nr when counted alone.
Once combined, the recording rate for periodic pulses is
np = n0p(1− nrτ) ,
while the random rate is
n′r = nr (1− npτ) = nr [1− n0p(1− nrτ)τ ] .
The total combined counting rate, nrp, is just the sum of the np and n′r
nrp = n0p(1− nrτ) + nr [1− n0
p(1− nrτ)τ ]
= n0p + nr − 2n0
pnrτ + n2r n0
pτ2 ,
or
τ =n0p + nr − nrp
2n0pnr (1− nrτ/2)
which can be solved by iteration.Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 25 / 22
Appendix Deadtime
Deadtime Effects
100 150 200Bin (0.1 s/bin)
10000
20000
30000
40000
50000
60000
Cou
nts
Deadtime CorrectedRaw Data
Alex Laffoley (University of Guelph) Half-life Measurement of 14O February 24, 2012 26 / 22