Workshop on DECAY DATA EVALUATION

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Discrepant Data. Program LWEIGHT Edgardo Browne
Decay Data Evaluation Project WorkshopMay 12
14, 2008Bucharest, Romania
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Statistical Analysis of Decay Data
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• Relative g-ray intensities
• a-particle intensities
• Electron capture and b intensities
• Recommended standards for energies and
  intensities
• Statistical procedures for data analysis
• Discrepant data

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Relative g-ray Intensities

• Ig A e(Eg)
• A DA Spectral peak area
• De Detector efficiency
• Several measurements with Ge detectors
• Ig1 A1 e1, Ig2 A2 e2,
• e1, e2, are determined with standard
  calibration sources, thus they are not
  independent quantities.
• Best value of Ig is a weighted average of Igi. A
  realistic uncertainty Dig should not be lower
  than the lowest uncertainty in the input values.
• Same criterion applies to g-ray energies.

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Precise half-life values are important for g-ray
calibration standards

• The IAEA Coordinated Research Programme (CRP)
  gives
• dT1/2/T1/2 ? 0.00144 T1/2 /T1, where
• T1 is the maximum source-in-use period for a
  given radionuclide (15 years or 5 half-lives),
  whichever is shorter. Then the contribution to
  the uncertainty in the radiation intensity
  calibration using this radionuclide will not
  exceed 0.1.
• Example 133Ba - T1/2 10.57 0.04 y - T1 15
  y, then
• dT1/2/T1/2 0.00144 x 10.57/15 0.0010,
• Experimental value is 0.04/10.57 0.0039.
• The contribution to the uncertainty is gt0.1.

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(No Transcript)
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A A1(434) A2(614) A3(723) The
areas of the individual peaks are not
independent of each other. DO NOT use A1(434),
A2(614), and A3(723) to determine T1/2(434),
T1/2(614), and T1/2(723), respectively, and
then average these values to obtain T1/2.
Use A to determine T1/2.
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2. a-particle Intensities

• Ia A e
• A DA Spectral peak area
• e ..Geometry (semiconductor
  detectors)
• e is the same for all a-particle energies.
• Best value of Ia is a weighted average of Iai.
• Uncertainty is the external (multiplied by c)
  uncertainty of the average value.
• Same criterion applies to a-particle energies,
  but because of the use of standards for energy
  calibrations, a realistic uncertainty should not
  be lower than the lowest uncertainty in the input
  values.

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Electron Capture and b Intensities
Most electron capture and b intensities are
from g-ray transition intensity balances.
Ib or Ie OUT - IN
Ib,e
IN
OUT
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4. Recommended Standards for Energies and
Intensities

• Recommended standards for g-ray energy
  calibration (1999), R.G. Helmer, C. van der Leun,
  Nucl. Instrum. and Methods in Phys. Res. A450, 35
  (2000).
• Update of X Ray and Gamma Ray Decay Data
  Standards for Detector Calibration and Other
  Applications, IAEA-Report, Vienna 2007.
• Recommended Energy and Intensity Values of Alpha
  Particles from Radioactive Decay, A. Rytz, Atomic
  Data and Nuclear Data Tables 47, 205 (1991)

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I strongly suggest reading the following paper

• Decay Data review of measurements, evaluations
  and compilations, A.L. Nichols, Applied
  Radiations and Isotopes 55, 23 (2001).

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5. Statistical Procedures for Data Analysis

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Averages
Unweighted x(avg) 1 / n ? xi sx(avg)
1 / n (n 1) ? (x(avg) xi)21/2 Std. dev.
Weighted x(avg) W ? xi / sxi2 W 1 / ?
sxi-2 c2 ? (x(avg) xi)2 / sxi2 Chi sqr. cn2
1 / (n 1) ? (x(avg) xi)2 / sxi2 Red. Chi
sqr sx(avg) larger of W1/2 and W1/2 cn. Std.
dev.
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Discrepant Data

• Simple definition A set of data for which cn2 gt
  1.
• But, cn2 has a Gaussian distribution, i.e. it
  varies with the number of degrees of freedom (n
  1).
• Better definition A set of data is discrepant if
  cn2 is greater than cn2 (critical). Where cn2
  (critical) is such that there is a 99
  probability that the set of data is discrepant.

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c2n (critical) nN-1

• n c2n (critical) n
  c2n (critical)
• -----------------------------------
• 1 6.6 11 2.2
• 2 4.6 12 2.2
• 3 3.8 13 2.1
• 4 3.3 14 2.1
• 5 3.0 15 2.0
• 6 2.8 16 2.0
• 7 2.6 17 2.0
• 8 2.5 18 - 21 1.9
• 9 2.4 22 - 26 1.8
• 10 2.3 27 - 30 1.7
• gt 30 1 2.33 ? 2/n

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Limitation of Relative Statistical Weight Method
(Program LWEIGHT)

• For discrepant data (c2n gt c2n(critical)) with
  at least three sets of input values, we apply the
  Limitation of Relative Statistical Weight method.
  The program identifies any measurement that has
  a relative weight gt50 and increases its
  uncertainty to reduce the weight to 50. Then it
  recalculates c2n and produces a new average and a
  best value as follows

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• If c2n ? c2n(critical), the program chooses the
  weighted average and its uncertainty (the larger
  of the internal and external values).
• If c2n gt c2n(critical), the program chooses
  either the weighted or the unweighted average,
  depending on whether the uncertainties in the
  average values make them overlap with each other.
  If that is so, it chooses the weighted average
  and its (internal or external) uncertainty.
  Otherwise, the program chooses the unweighted
  average. In either case, it may expand the
  uncertainty to cover the most precise input
  value.

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Simple Example
5001
1000100
X
nN - 1
X(avg) 500 5
2
c
2
c
(critical) 6.6 Data are discrepant
25,
n
n
We change to 500100 (Same statistical weights).
Then
X(avg) 750 250
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44Ti Half-life
T1/2REF HALF-LIFE 99Wi01 60.7 1.2 98Ah03
59.0 0.6 98Go05 60.3 1.3 98No06
62.0 2.0 90Al11 66.6 1.6 83Fr27 54.2
2.1



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44Ti Half-life (LWEIGHT)

• 44Ti Half-life Measurements
  
• INP. VALUE INP. UNC. R. WGHT chi2/N-1
  REFERENCE
• .607000E02 .120E01 .141E00 .826E-01
  99Wi01
• .590000E02 .600E00 MIN .563E00 .479E00
  98Ah03
• .603000E02 .130E01 .120E00 .163E-01
  98Go05
• .620000E02 .200E01 .507E-01 .214E00
  98No06
• .666000E02 .160E01 .792E-01 .348E01
  90Al11
• .542000E02 .210E01 .460E-01 .149E01
  83Fr27
• No. of Input Values N 6 CHI2/N-1 5.76
  CHI2/N-1(critical) 3.00
• UWM .604667E02 .164796E01
  unweighted average
• WM .599288E02 .450317E00(INT.)
  .108057E01(EXT.) weighted average
• INP. VALUE INP. UNC. R. WGHT chi2/N-1
  REFERENCE
• .607000E02 .120E01 .161E00 .563E-01
  99Wi01
• .590000E02 .681E00 .500E00 .487E00
  98Ah03
• Input uncertainty increased .114E01 times
• .603000E02 .130E01 .137E00 .663E-02
  98Go05
• .620000E02 .200E01 .580E-01 .188E00
  98No06
• .666000E02 .160E01 .907E-01 .334E01
  90Al11
• .542000E02 .210E01 .526E-01 .156E01
  83Fr27  

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I strongly suggest reading the following paper

• M.U.Rajput, T.D.Mac Mahon, Techniques for
  Evaluating Discrepant Data, Nucl.Instrum.Methods
  Phys.Res. A312, 289 (1992).