Nuclear Analysis and Radiography Department High-energy calibration data for neutron activation analysis L. Szentmiklósi 1, Zs. Révay 2, B. Maróti 1, D. Párkányi 1, I. Harsányi 1 1 Nuclear Analysis and Radiography Department, Centre for Energy Research, Hungarian Academy of Sciences, 29-33 Konkoly-Thege Miklós street, 1121 Budapest, Hungary. E-mail: szentmiklosi.laszlo@energia.mta.hu 2 Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRM II), Lichtenbergstraße 1 D-85747 Garching, Germany
Motivation In neutron activation analysis (NAA), there is a need to calibrate the HPGe detectors up to about 3.1 MeV, in order to properly analyse elements like Na (E=2754.0 kev), Ca (E=3084.4 kev) and S (E=3103.4 kev). In practice, if there is a disagreement bw. high- and low-energy lines of a multi-line isotope, we tend to discard the high-energy line, even though it is well separated and has not too bad statistical precision Commercially available, common radioactive sources cover the energy range only up to about 2.2 MeV, but not beyond. Cyclotron-created sources (Co-57, Ga-66) emitting high-energy gamma rays are useful, but expensive, too short-lived and not generally available to the NAA community With activation in the reactor, however, several radionuclides can be produced at low additional cost having high-energy gamma lines, such as Ga-72, Mn-56, In-116 and Na- 24. The application of such isotopes for calibration is hindered by imprecise or confronting nuclear data (energies, intensities).
Proposed solution: synergy of PGAA & NAA At a PGAA station, where the detector calibration is done on a routine basis up to 11 MeV with a precision of about < 1% for efficiency and < 0.01 kev for energy measurement, one can find ideal conditions to derive accurate energies and relative intensities for such high-energy gamma emitters. A joint effort at the Budapest PGAA facility and at the PGAA station of FRM II Garching is reported to produce a coherent dataset of such nuclides and apply them for efficiency and nonlinearity calibration. If the identical sources are counted at PGAA and NAA, it goes back to ratios of peak areas, expected to be reliable In combination with Monte Carlo calculations, this could form a basis of a more advanced detector calibration procedure in NAA. 3
Efficiency curve of the Budapest PGAA station up to 12 MeV We code this info in form of an activated sample and propagate to the NAA lab 4
Workflow Identify a good reference source: many lines, broad energy range, well-known data, well-characterized source Activate the targets in a neutron field: intense guided beam (FRM II) or vertical channel (Budapest). The target shall be as point-like as possible Measure the gamma lines of the activated target in repeated runs at a PGAA station. Splitting the counting time helps to check the self-consistency (internal vs external unc) and the uncertainty budget (statistical vs systematic unc).
Intensities Peak areas, after correcting with the established PGAA efficiency, will give emission probabilities of useful peaks relative to the most intense peak That can be used at an NAA detector in a relative way, no need to make the emission probabilities absolute. Peaks within and over an existing calibration range are needed to append them to the existing curve (Hypermet, Hyperlab can do this) as relative data Derive peak area ratio: peak of interest relative to the most intense peak of the same isotope, you get a number [0 1]. If repeated runs are available (taken using a Genie 2000 custom script) make weighted average of these peak area ratios from the successive spectra (with error propagation), only afterwards involve the efficiency correction (systematic error). Otherwise we underestimate the efficiency curve s contribution to the uncertainty budget. Not very wise to average (specific) activities 6
R i = WA s Intensities for efficiency calibration A i A 0, for the i th line of an isotope, through the s available spectra. This has only statistical unc., i.e. good as weight in weighted averaging. I i = R i to correct for the PGAA efficiency. Here ε ratio,i efficiency ratio is enough, i.e. without the unc. attributed to certified activities of sources Make it absolute by multiplying with a literature P γ, but in fact it is not required here 7
Energies for the nonlinearity calibration Measure the activated target in presence of the reference source to determine the energies of the two calibration lines. Choose peak couples where the reference isotope s peak is next to, or close to an intense peak of our isotope of interest. Here the energies can be propagated to the peaks with unknown energies without much risk for bias due to the nonlinearity. These two energies can be used for the previously taken spectra to generate accurate energies for high-energy part of the non-linearity. 8
Systematic and statistic components of energy uncertainties Let us consider two calibration peaks in a gamma spectrum with positions P and known literature energies E. Let us define quantity, a couple of a value (v) and its corresponding 1-sigma uncertainty (u), as follows: P 1 : = vp 1, up 1, P 2 : = vp 2, up 2, E 1 : = ve 1, ue 1, E 2 : = ve 2, ue 2, Define P 0, an internal variable, as the average of the two calibration poisitions: P 0 P 1+P 2 2 = 1 2 vp 1 + 1 2 vp 2, 1 2 up 1 2 + up 2 2 If we look for the linear energy calibration in an uncommon form of E = a + b P P 0 and solve the system of equations for a and b, we get: a = 1 2 ve 1 + 1 2 ve 2, 1 2 ue 1 2 + ue 2 2 b = ve1 ve2, (ve 1 ve 2 ) 2 up 2 1 + (ve ve 1 2 )2 up 2 2 + ue 2 1 + ue 2 2 vp1 vp2 (vp 1 vp 2 ) 4 (vp 1 vp 2 ) 4 (vp 1 vp 2 ) 2 (vp 1 vp 2 ) 2 These a and b are different for each repeated run. Term a is only systematic, whereas b contains statistical (up) and systematic components (ue) 9
How to obtain peak energies after calibration Let s consider a third peak somewhere in between P 1 and P 2, with fitted position P 3, where the nonlinearity is non-zero (N 3 ), then E 3 is: ve 3 = 1 2 ve 1 + 1 2 ve 2 + ve 1 ve 2 vp 3 + vn 3 1 2 vp 1 1 2 vp 2 vp 1 vp 2 ue 3 = 1 2 sqrt 4(vE 1 ve 2 ) 2 1 4 up 2 1 + 1 4 up 2 2 (vp 1 vp 2 ) 2 + ue 2 1 + ue 2 2 + 4 vp3 + vn3 1 2 vp 1 1 2 2 vp (ve1 ve 2 ) 2 2 up 1 2 (vp 1 vp2) 4 + (ve 1 ve 2 ) 2 2 2 2 up 2 ue 1 (vp 1 vp 2 ) 4 + (vp 1 vp 2 ) 2 + ue 2 (vp1 vp 2 ) 2 + 4(vE1 ve 2 ) 2 un 3 2 (vp 1 vp 2 ) 2 + 4(vE 1 ve 2 ) 2 up 3 (vp 1 vp 2 ) 2 2 10
Systematic vs statistical variance of E 3 Statistical variance: ve1 ve2 2 1 4 up12 + 1 4 up22 vp1 vp2 2 + ve1 ve2 2 up3 2 vp1 vp2 2 + vp3 + vn3 1 2 vp1 1 2 2 vp2 ve1 ve2 2 up1 2 vp1 vp2 4 + ve1 ve2 2 up2 2 vp1 vp2 4 Systematic variance: 1 4 ue12 + 1 4 ue22 + vp3 + vn3 1 2 vp1 1 2 2 vp2 + ve1 ve2 2 un3 2 vp1 vp2 2 ue1 2 vp1 vp2 2 + ue2 2 vp1 vp2 2 11
Ra-226 certified radioactive source Energy (kev) Unc (kev) Emission probalbility and unc origin in the decay chain 53.2275 0.0021 0.01066 0.00014 214Pb 186.211 0.013 0.03533 0.00028 226Ra 241.997 0.003 0.0719 0.0006 214Pb 295.224 0.002 0.1828 0.0014 214Pb 351.932 0.002 0.3534 0.0027 214Pb 609.316 0.003 0.4516 0.0033 214Bi 665.453 0.022 0.01521 0.00011 214Bi 768.367 0.011 0.04850 0.00038 214Bi 806.185 0.011 0.01255 0.00011 214Bi 934.061 0.012 0.03074 0.00025 214Bi 1120.287 0.01 0.1478 0.0011 214Bi 1155.19 0.02 0.01624 0.00014 214Bi 1238.110 0.012 0.05785 0.00045 214Bi 1280.96 0.02 0.01425 0.00012 214Bi 1377.669 0.012 0.03954 0.00033 214Bi 1401.516 0.014 0.01324 0.00011 214Bi 1407.993 0.007 0.02369 0.00019 214Bi 1509.217 0.008 0.02108 0.00021 214Bi 1661.316 0.013 0.01037 0.0001 214Bi 1729.640 0.012 0.02817 0.00023 214Bi 1764.539 0.015 0.1517 0.0012 214Bi 1847.420 0.025 0.02000 0.00018 214Bi 2118.536 0.008 0.01148 0.00011 214Bi 2204.071 0.021 0.0489 0.0010 214Bi 2447.673 0.01 0.01536 0.00015 214Bi IAEA: Update of X Ray and Gamma Ray Decay Data Standards for Detector Calibration and Other Applications, STI/PUB/1287 (ISBN:92-0-113606-4) (2007) http://www-pub.iaea.org/mtcd/publications/pdf/pub1287_vol1_web.pdf
In-116 @ 818 & 2112 kev vs Ra-226 @ 806 & 2118 kev Ra-226 806.185 +/- 0.011 kev Ra-226 2118.536 +/- 0.008
Mn-56 @ 846 and 2113 kev vs Ra-226 @ 806 & 2118 kev Ra-226 806.185 +/- 0.011 kev Ra-226 2118.536 +/-0.008
Na-24 1368 & 2754 kev vs Ra-226 @ 1377 & 2447 kev Ra-226 1377.669 +/- 0.012 Ra-226 2447.673 +/- 0.010 15
Ga-72 16
Na-24 Peak area ratios 2754/1368: 0.5806 0.5821 0.5832 0.5836 0.5837 0.5841 0.5844 0.5856 Weighted average: 0.5834 Empirical unc: 0.0014 Propagated unc: 0.0021 Ratios: 0.992 0.990 0.988 0.987 0.987 0.986 0.986 0.984 0.9876 0.0024 0.0064 Ratios: 0.997 0.990 0.992 0.994 0.993 0.002 0.012 Efficiencies: 2.89E-04 0.2 1.66E-04 0.5 Energies: 1368.591 0.020 2754.016 0.040 BIPM
Mn-56 Energy 846.741 Unc 0.022 Ratio 1 Unc 0.004 1810.669 0.029 0.2665 0.0013 2113.031 0.036 0.1418 0.0008 2522.793 0.051 0.01019 0.00017 2657.389 0.054 0.00682 0.00010 2959.776 0.066 0.00316 0.00007 3369.643 0.080 0.00205 0.00005
In-116 ENERGY RATIO Value Unc Value Unc 1293.494 0.031 1 0.0071 1097.168 0.019 0.6906 0.0049 416.8728 0.004 0.3306 0.0028 2112.073 0.031 0.1798 0.0017 818.625 0.019 0.1457 0.0013 1507.492 0.005 0.1168 0.0010 138.316 0.015 0.0419 0.0005 1752.344 0.012 0.0280 0.0004 355.4113 0.015 0.0086 0.0002 463.1978 0.007 0.0089 0.0002 972.5003 0.024 0.0057 0.0002
Energy (kev) Unc (kev) Ratio Unc. 834.074 0.009 1 0.0008 2201.529 0.038 0.2840 0.0006 629.955 0.008 0.2741 0.0017 2507.605 0.045 0.14035 0.00031 894.25 0.01 0.10594 0.00031 2490.929 0.044 0.08178 0.00019 1050.694 0.013 0.07273 0.00009 600.91 0.008 0.06155 0.00038 1860.98 0.03 0.05693 0.00013 1596.756 0.024 0.04544 0.00009 1463.994 0.021 0.03768 0.00007 786.427 0.008 0.03531 0.00003 810.255 0.009 0.02204 0.00006 1276.773 0.017 0.01666 0.00004 1230.901 0.016 0.01501 0.00003 1260.094 0.017 0.01224 0.00003 970.672 0.011 0.01153 0.00002 2109.331 0.036 0.01136 0.00004 1680.72 0.026 0.00962 0.00004 1571.618 0.024 0.00883 0.00003 1215.098 0.016 0.00850 0.00003 999.893 0.012 0.00847 0.00002 1710.846 0.027 0.00464 0.00002 2844.018 0.053 0.00458 0.00003 2514.72 0.046 0.00326 0.00003 2214.001 0.039 0.00241 0.00002 1877.688 0.037 0.00232 0.00002 1837.102 0.031 0.00227 0.00002 1568.163 0.027 0.00181 0.00003 1920.227 0.034 0.00179 0.00002 2621.113 0.049 0.001519 0.000010 2981.292 0.058 0.000629 0.000008 3035.44 0.064 0.000249 0.000005 3094.232 0.067 0.000175 0.000004 2939.855 0.074 0.000146 0.000004 3324.869 0.099 0.000097 0.000004 3337.854 0.162 0.000047 0.000003 3067.405 0.111 0.000039 0.000003 2943.755 0.234 0.000019 0.000003 Ga-72 J.A.G. Medeiros et al. / Applied Radiation and Isotopes 54 (2001) 245-259
Extended energy efficiency curve at a large distance with D5 of the NAA lab 2 MeV 3 MeV
Kayzero representation of the Hyperlab s efficiency curve 22
Efficiency at closer distances, real sample geometry Transfer this calibration to closer geometries by SOLCOI or Monte Carlo SOLCOI Efficiency-transfer 1 0 500 1000 1500 2000 2500 3000 0.1 0.01 0.001 0.0001 0cm 5cm 10cm 20cm 30cm 23
Conclusions PGAA can help out NAA in high-energy calibration, might even harmonize a few discrepancies Our NAA counting stations are now well calibrated within the entire required energy range Mathematics and uncertainty budget are clarified for the entire computation Validation is still in progress, but looks promising 24
Thank you for your attention!