True coincidences and a Decent Currie

Transcription

1 True coincidences and a Decent Currie Lars-Erik De Geer FOI, Swedish Defence Research Agency, Stockholm, Sweden ledg@foi.se NKS GammaSem2010, Lillestrøm, Norway, 28 September 2010

2 Radionuclide Particulate Station Network TBD

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4 SAUNA Swedish Automatic Unit for Noble gas Acquisition

5 The CTBT Verification Regime

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7 % 210 Pb 109 Cd 57 Co 139 Ce 203 Hg Sn 137 Cs 88 Y 60 Co 88 Y kev

8 % 139 Ce Y 60 Co 88 Y kev

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15 The Lead Picker

16 The Lead Picker

17 Sinnko Debertin Aaltonen, Ugletveit Shaman GESPECOR Korsum ISOCS, LabSOCS VGSL

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19 p-type cylindrical crystal, positive on the mantle and negative on the inner surface

20 120 ns later Saturated drifting velocities for both holes and electrons around 7.5 cm per μs imply a preamplifier rise time of about 400 ns. About and secondary electrons drift towards the mantle and the same number of holes drift towards the center hole [sic].

21 400 ns ns

22 ~1 tc ~2 tc ~1 tc ~5 tc Time constant tc = 3 μs

23 ~1 tc ~2 tc Multiply time by 10 9 ~1 tc ~5 tc Everything nuclear happened in a 1 sec flash at breakfast this morning Charge collection finished after eating a sandwich for less than 10 minutes The useful part of the main amplifier pulse will be ready by lunch time The ADC will deliver the count to the spectrum late tonight At 10 cps we can expect next event in November 2013 At 100 cps we can expect next event in mid-february next year. Time constant tc = 3 μs

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25 Investing in the laboratory

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31 Bi K α1 + K α2 Bi K α1 + K α1 Bi K α2 + K α2 Bi K α1 + K β1 Bi K α2 + K β Bi K α1 + K β1

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41 Efficiency curve after half a minute

42 Efficiency curve after 7.6 minutes

43 Running an experiment

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50 Applying the Currie SCA to gamma spectra Number of counts in a Single Channel Analyzer = e.g.5% k 5% L C = k % True Mean = B

51 Applying the Currie SCA to gamma spectra Number of counts in a Single Channel Analyzer k 5% k 5% L D = 2k % True Mean = B = e.g.5%

52 Lloyd Currie s classical paper from 1968 L C = k B ( 1 + 1/m) L D = k 2 + 2L C

53 Applying the Currie SCA to a gamma spectrum peak

54 Applying the Currie SCA to a gamma spectrum peak FWHM

55 Applying the Currie SCA to a gamma spectrum peak FWHM

56 Applying the Currie SCA to a gamma spectrum peak FWHM

57 Applying the Currie SCA to a gamma spectrum peak Commonly used width: 2.5 FWHM FWHM

58 Calculating the channel-width that gives the lowest relative uncertainty

59 L C = k B ( 1 + 1/m) With the SCA-width (and thus μ B ) reduced by a factor of 2 and m considered large instead of 1, L C is reduced by a factor of 2. This can be compensated by doubling k, which is equivalent to reducing α, the risks for errors of the first and second kind, from e.g. 5% to 0.05%. Still L D = 2L C This is much more consistent with experience, as we normally see just around five false positives in a 8192 channel spectrum and not hundreds of them which we would if the risk was really 5%.

60 So how do we now utilize this in a spectrum where we a priori don t know where all peaks are? 1. Pick all clear and nice peaks away from the spectrum. 2. We need a good background line and we can now get one by smoothing the picked spectrum. 3. Assume all channels are the centroid of a small peak. 4. Add the channels within 1.25 FWHM of each channel in the spectrum and write the sum into the centroid channel. This involves also partial channels at each end of the SCA. 5. Compare with the L C criterion. If channel content is > L C it s part of a peak, otherwise not.

61 Lawnmower operation

62 Lawnmower operation

63 Lawnmower operation

64 Lawnmower operation

65 Lawnmower operation

66 Lawnmower operation

67 Lawnmower operation

68 Lawnmower operation

69 Lawnmower operation

70 Lawnmower operation

71 Lawnmower operation

72 Lawnmower operation

73 Lawnmower operation

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79 Lawnmower operation

80 Lawnmower operation

81 Lawnmower operation

82 Lawnmower operation

83 Lawnmower operation

84 Lawnmower operation

85 Lawnmower operation

86 SAINT opening window

87 SAINT spectrum picked

88 SAINT SCAC-LCC

89 SAINT SCAC-LCC

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103 How do we decide what risks we should take? 1. The PEAKMAKER and PLATEMAKER Mathematica programs provide interfaces between mathematics and what we think we see on the display. 2. Gain experience. Murray has worked on this for a while in Romano s L C -GUI and I think I hear Murray vote for an between % and 0.001%. 3. To keep the quality pressure on the stations everything stays the same if the SCA width is set to 1.25 FWHM, m to and to 0.05%, when the barium-140 detection limit is analyzed.

104 The Lawnmower algorithm To solve the first problem we should cut as most we can the spectrum peaks before smoothing. The following algorithm can be used: For each channel j we define a channel interval j 1, j + 2 where 1 and 2 are the equivalent in channels of 2*FWHM(j). If the channel j happens to be the one with maximum counts in this interval, it is a good candidate to be the centroid of a potential peak. In this case the original spectrum in the selected interval is replaced with a straight line from j 1 to j + 2. After 2 o 3 times of application of this algorithm all the peaks will be cut out. International Data Centre / Radionuclide Section

105 Application Coupling the smoothing and the Lawnmower algorithm we have a very good baseline for all the energies with the exception of some structures like saw teeth where only the smoothing is applied. Compton edges are preserved. In The the smoothing case algorithm of multiplets is the most the straightforward width of the way to structure calculate the is baseline, larger itthan FWHM, consist in setting therefore counts the to a loop given a smooth-lawnmower channel as the average of the will neighbor give channels a final structure for a given interval of a plateau width. far from the right baseline. To solve this problem, on the X-rays region, the Lawnmower algorithm is applied many times before smoothing. International Data Centre / Radionuclide Section

106 Application: the recipe Due to the large amount of multiplets in the X-rays region I distinguish two regions: 1) kev 2) E max 1) 2 loops with 1 smoothing and 80 Lawnmowers each. 2) 4 loops with 1 smoothing and 4 Lawnmowers each. International Data Centre / Radionuclide Section

107 The smoothing The smoothing algorithm is the most straightforward way to calculate the baseline, it consists in setting the counts to a given channel as the average of the neighbouring channels for a given interval width. This algorithm, applied in the baseline calculation for The smoothing algorithm is the most straightforward way to calculate the baseline, it consist gamma in setting spectra, the counts works to a given fine a channel in the as the absence average of of the peaks neighbor channels for a given interval width. structure, since the baseline should not consider the peak counts but only the ones coming from the background. The baseline itself should follow the shape of certain spectrum structures not recognizable as peaks like Compton edges or saw teeth from (n,n ) reactions. International Data Centre / Radionuclide Section

108 The smoothing The smoothing algorithm is the most straightforward way to calculate the baseline, it consists in setting the counts to a given channel as the average of the neighbouring channels for a given interval width. The baseline itself should follow the shape of certain spectrum structures not recognizable as peaks like Compton edges or saw teeth from (n,n ) reactions.