B.R.S. Simpson and W.M. van Wyngaardt
National Metrology Institute
of South Africa
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Introduction
• Measurements made for the 32P international comparison
• Utilized liquid scintillation counting (LSC)
• Three phototube detection system
• Method: followed the decay, with the following variations
• collected double- and triple-coincidence data
• fresh counting sources weekly → rates per unit mass analyzed
• established the counting efficiency by two independent methods,
namely:
1) Efficiency tracing with a quench-matched Ni-63 source
2) TDCR efficiency calculation
Most of the uncertainty was due to the analysis (fitting).
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Method, results and uncertainties
at time t :
λ
•
33P
count rate at time t : C2(t) = C2 exp(-λ2t)
•
35S
count rate at time t : C3(t) = C3 exp(-λ3t)
•
All we can do is measure the total count rate C(t) :
•
C(t) = C1(t) + C2(t) + C3(t) …………………………………….(1)
•
Therefore must follow the decay over time and determine the best
fit to the data using expression (1). This extracts the count rates
C1, C2 and C3 at the reference date chosen.
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wi[Ci – C1 exp(-λ1ti) – C2 exp(-λ2ti) – C3 exp(-λ3ti) ]2
Q is minimised by differentiating with respect to the coefficients
C1, C2 and C3 and equating to zero.
This gives rise to a set of linear algebraic equations that can be
expressed in matrix form. The solution is given by a matrix
inversion technique. This gives the values and uncertainties for
the three coefficients C1, C2 and C3.
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Thus
=
i.e.
X⋅c=v
where X11 = Σ wi exp(-2λ1 ti), etc. (wi are the weights = 1
and
V1 = Σ wi Ci exp(-λ1 ti), etc.
The
are estimates of C1, C2 and C3 giving the best fit.
Solving, c = X-1 ⋅ v such that X-1 =
.
Variances: var(C1) = c11 , var(C2) = c22 , var(C3) = c33
cov(C1, C2) = c12 = c21
cov(C2, C3) = c23 = c32
,
cov(C1, C3) = c13 = c31
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)
decay constant λ = 0.693
½
alf-life.
32P:
T½ = 14.284 days, λ = 0.0485, N1 = 25000 c/s at time t = 0
33P:
T½ = 25.383 days, λ = 0.0273, N2 = 1800 c/s at time t = 0
35S:
T½ = 87.32 days, λ = 0.0079, N3 =
555 c/s at time t = 0
Days
32P
33P
35S
Total
28
6425
838
444
7712
35
4574
692
420
5685
42
3257
572
398
4221
49
2319
472
376
3171
56
1651
390
356
2396
63
1176
322
337
1836
70
837
266
318
1422
Program gives: 32P = 25147
33P = 1683
35S =
579
178 c/s
140 c/s
28 c/s
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COUNTING SYSTEM
Electronic modules for
pulse processing and the
data acquisition system
(CAMAC interval timer and
32-channel scaler under
computer control).
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EXPERIMENTAL DATA
These are
double-tube
coincidence
rates.
Count rate per unit mass (s-1 g-1)
96000
95500
95000
94500
94000
93500
93000
0.0
0.2
0.4
0.6
0.8
1.0
Time interval (days)
This plot shows the cluster of data points collected on day
one. Expressed as count rate given by the master solution.
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Extracted
double count rate
concentrations
(s-1 g-1) :
N1 = 93970
N2 = 2355
N3 =
134
Count rate per unit mass (s-1 g-1)
1e+5
LOCAL ref. date: 09-03-05
(36.0 days after comparison
ref. date)
8e+4
6e+4
4e+4
2e+4
0
0
10
20
30
40
50
Time interval (days)
A plot of the 106 data points collected over six weeks.
Red line: 32P
Blue line: 33P
Black line: 32P + 33P + 35S
(Reduced Chi-square = 1.28)
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The uncertainties from counting statistics/fitting are:
32P
33P
35S
93970
2355
134
173 ( 0.18 %)
231 ( 9.8 %)
75 (56.0 %)
cov(32P, 33P) = -39360
cov(32P, 35S) = 12512
cov(33P, 35S) = -17250
Correlation coeff.
r(32P, 33P) = - 0.9875
r(32P, 35S) = + 0.9627
r(33P, 35S) = - 0.9921
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Other main contributors to the uncertainty budget
Half-life
For 32P: T1/2 = 14.284 0.036
This bound changes the 32P activity by
0.18 %.
For 33P: T1/2 = 25.383 0.040
This bound changes the 32P activity by
0.004 %.
For 35S: T1/2 = 87.32 0.16
This bound changes the 32P activity by
0.0001 %.
Adsorption
A correction of 0.2 % was made to account for adsorption
to the counting vials. Uncertainty taken as
%.
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A quench-matched 63Ni source was used to characterize the
system in terms of the figure-of-merit P.
Using P, the efficiencies εd (and εt) were determined:
32P
= 99.39 % (99.26),
P-32
33P
= 84.6 % (81.6),
Double Activity Triple
rate
conc.
rate
(s-1 g-1) (Bq/g) (s-1 g-1)
Activity
conc.
(Bq/g)
93970 94547 93862
173
172
94562
35S
= 75.2 % (70.6)
Impurity as
fraction of
P-32 (%)
P-33
2355
231
2783
1708
230
2093
2.2 – 2.9
(1.0 – 1.4) comp. ref. date
S-35
134
75
179
311
75
441
0.2 – 0.5
(.04 – .11) comp. ref. date
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Then
ε t (P ) N t
=
ε d (P ) N d
is solved for P.
Activity conc. (Bq g)
Alternative 32P efficiency determination by the
TDCR technique
Triple and
96000
double rates
corrected for
95500
33P and 35S
95000
contributions.
94500
94000
93500
93000
0
Mean efficiency = 0.9951
Mean activity conc. = 94490
10
20
30
Time interval (days)
44 Bq/g
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40
50
UNCERTAINTY COMPONENTS FOR 32P
weighing
% of activity conc. (1σ)
0.02
dead time
0.01
background
0.01
resolving time
0.005
adsorption to vial
0.10
tracer
0.006
half life
0.18
fit to decay data sets
0.18
satellite pulses
0.015
COMBINED
0.28
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CONCLUSIONS
• Application of the decay method successfully
extracted the 32P activity content in the presence
of pure beta-emitting impurities.
• The two schemes adopted to convert count rates
into activities produced consistent results.
• The main contributions to the uncertainty were
due to the fit to the decay data sets, the
uncertainty in the half-life and adsorption of
radioactive material to the glass counting vials.
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Publication:
B.R.S. Simpson and W.M. Van Wyngaardt, Activity measurement of
phosphorus-32 in the presence of pure beta-emitting impurities. South African
Journal of Science, July/August 2006 – Vol. 102, No. 7 / 8, 361-364.
Electronic reprint available from:
[email protected]
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