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Demonstration of a transmission nuclear resonance fluorescence measurement for a realistic radioactive waste canister scenario
Nuclear Instruments and Methods in Physics Research B 347 (2015) 11–19
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Demonstration of a transmission nuclear resonance fluorescence measurement for a realistic radioactive waste canister scenario C.T. Angell a,⇑, R. Hajima a, T. Hayakawa a, T. Shizuma a, H.J. Karwowski b,c, J. Silano b,c a
Quantum Beam Science Center, Japan Atomic Energy Agency, Tokai-mura, Ibaraki 319-1195, Japan Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255, USA c Triangle Universities Nuclear Laboratory, Durham, NC 27708-0308, USA b
a r t i c l e
i n f o
Article history: Received 7 August 2014 Received in revised form 21 January 2015 Accepted 24 January 2015
Keywords: Nuclear resonance fluorescence Non-destructive assay Transmission Spent nuclear fuel
a b s t r a c t Transmission nuclear resonance fluorescence (NRF) is a promising method for precision non-destructive assay (NDA) of fissile isotopes—including 239Pu—in spent fuel while inside a storage canister. The assay, however, could be confounded by the presence of overlapping resonances from competing isotopes in the canister. A measurement is needed to demonstrate that transmission NRF is unaffected by the shielding material. To this end, we carried out a transmission NRF measurement using a mono-energetic c-ray beam on a proxy target (Al) and absorbing material simulating a realistic spent fuel storage canister. Similar amounts of material as would be found in a possible spent fuel storage canister were placed upstream: concrete, stainless steel (SS 304), lead (as a proxy for U), and water. An Al absorption target was also used as a reference. These measurements demonstrated that the canister material should not significantly influence the non-destructive assay. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction The non-destructive assay (NDA) of fissile isotopes in spentnuclear fuel (SNF) is an ever-present challenge to safeguards. Being able to assay the SNF inside a storage canister could help mitigate concern of diversion of special nuclear material from easyto-access SNF in long-term storage [1]. Assay of fuel inside shipping canisters could also enhance safety of fuel handling by not requiring invasive entry into canisters for verification. Additionally, the Fukushima meltdown presented a new challenge to the safeguards regime. The triple reactor meltdown and hydrogen explosions damaging the fuel assemblies stored in the spent fuel ponds resulted in a loss of continuity of knowledge [2]. Recovery from a loss of knowledge requires the development of new nondestructive assay techniques [1]. If the fuel debris upon removal is put directly into the final storage canisters—a step that would minimize future possibilities of re-contamination—a method which can precisely assay the fuel when stored inside the shielded canister will be necessary. Nuclear resonance fluorescence [3] (NRF) may be the only method that can be used to perform quantitative assay of such shielded material. NRF is a fundamental process whereby a discrete nuclear state resonantly absorbs a c ray, and then decays ⇑ Corresponding author. E-mail address: [email protected] (C.T. Angell). http://dx.doi.org/10.1016/j.nimb.2015.01.053 0168-583X/Ó 2015 Elsevier B.V. All rights reserved.
by c-ray emission, either to the ground state or an excited state (see Fig. 1). NRF is an active technique, requiring an intense source of high energy c rays. The c-ray energy for absorption is precisely determined from the level energy. The level energy is typically known to about 1 keV. The emitting c-ray energy is similarly known to about 1 keV, though it is slightly less than the absorption energy because of energy that goes into the nuclear recoil. The 10 eV nuclear recoil energy is larger than the resonance width, which excludes the possibility of re-absorption. The intrinsic resonance width, which determines the absorption strength of the resonance, is on the order of a few meV to as much as 1 eV. It is further broadened several eV by Doppler broadening, which conserves the total strength of the resonance. The level energy is uniquely determined by the precise realization of nuclear structure for a given nucleus: a change of even one nucleon will have a dramatic effect on the level properties of the nucleus, changing the energy and strength of each level, as well as the total number of levels excited by NRF. For fissile materials, strongly excited levels exist at around 2–3 MeV [4], incidentally the energy region where c-rays have maximum penetrating power. These resonances exist at this energy because of a structural phenomenon called the ‘‘scissors mode’’ of excitation [5] in which the protons and neutrons in a deformed nucleus oscillate out of plane from each other. Because of the precisely defined characteristic level energy, and the sensitivity to the structure of the nucleus manifested in both the level energy and level strength,
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NRF can provide an isotope-specific signature of almost every nucleus on the periodic table, allowing discernment between neighboring isotopes, including nuclei whose properties as measured by neutrons may otherwise be nearly identical. This is particularly true of the actinide nuclei (as discussed above), but has an exception for light nuclei. The lightest nuclei (particularly lighter than carbon) either have no bound states which can be excited by a c-ray (e.g. hydrogen), or the bound states do not have a strong c decay branch, limiting applicability of NRF in those cases. NRF was first proposed for detection of nuclear material [6], and then for assay of nuclear fuel [7,8], with the difference only being in measurement precision. Assay has significantly higher requirements for precision. Both applications can be done in one of two ways: direct or transmission. The direct measurement method measures c-rays directly emitted from the decay of states excited in the nuclear material. The transmission method measures the development of notches following transmission through the fuel [6,9,10]. When a c-ray beam transits material, notches are left in the beam energy distribution due to the resonant absorption of photons. The energies of these notches are characteristic of the absorbing isotope, the isotope of interest (IOI), and their depth is characteristic of the amount of that isotope. The widths of these notches are the same as those of the Doppler broadened resonances—a few eV wide. These notches can be used to assay the shielded material if the notch depth can be measured. The notch depth induced by the IOI can be determined by measuring the reduction in scattering from a sample of the same isotope placed downstream of the shielded material. The resonances overlap in energy with the induced notches, and as the notch deepens due to increased material amount in the melted fuel, the induced scattering (normalized by the total transmitted flux) also decreases. A transmission measurement’s detector resolution is determined by the width of resonances in the IOI. This is significantly better than the few keV resolution of the best high-purity Germanium detector at these energies, highlighting a significant advantage that a transmission measurement has over a direct measurement. A transmission measurement is isotope specific because isotopes other than the IOI will have their resonances (and induced notches) at different energies. It is insensitive to the shielding material as long as the material does not contain the IOI, but even then a correction can be made by separate measurements on an empty, typical canister. A transmission measurement, however, will lose the property of isotope specificity if resonances from other isotopes randomly overlap with resonances in the IOI to a significant degree [11]. Such overlap will mimic the IOI’s absorption signature. Although the amount of resonance overlap will be significantly smaller because of the higher intrinsic resolution compared to a direct measurement, the effect of resonance overlap will be indistinguishable from absorption due to the IOI. This is unlike a direct measurement where some signature of an additional resonance may be present in the spec-
Fig. 1. Nuclear resonance fluorescence is a process where the nucleus becomes resonantly excited by absorbing a c ray with an energy equal to that of the state Ex . The state then de-excites by the emission of a c ray with energy Ex back to the ground state or energy Ex E1 to an excited state with energy E1 .
trum, such as an overly broad peak. The canister which the fuel will be stored in will present a large source of possibly overlapping resonances which could interfere even with a transmission measurement. Therefore a transmission measurement studying the degree of possible resonance overlap is needed using the same materials as those which would be used in spent fuel storage canisters. The issue of random resonance overlap is particularly problematic for the proposed integral resonance transmission (IRT) method [11]. The IRT method utilizes the resonance absorption of all resonances within the beam width of a quasi-monoenergetic c-ray beam by integrating over all NRF scattering strength. This has the potential to improve measurement efficacy by enabling the use of more efficient and faster scintillator detectors. There is a liability, however, that accompanies the use of lower resolution detectors. Using lower resolution detectors precludes the possibility of detecting random resonance overlap from the disagreement in inferred absorption from two or more resonances that are simultaneously excited. Careful measurements exploring the possibility of random resonance overlap are particularly needed in order to effectively use the IRT method. To study the possible overlap of a single resonance with resonances present in the canister material, we carried out an NRF transmission experiment using materials similar in type and thickness to the TMI-2 debris canister [12] which was used to store the fuel debris generated from the Three Mile Island accident. Even if other storage canisters are used, they will be effectively similar in composition (concrete and steel) as the TMI-2 canister. It should be noted that the TMI-2 canisters (described below) are unique in that they are designed to contain a single fuel assembly, and use low-density concrete for shielding, which facilitates assay of the material stored inside. Vitrified waste would also readily yield to assay using NRF in transmission, including the IRT method, and has a total areal density similar to a loaded TMI-2 canister [13]. The present measurement additionally demonstrates the feasibility of a transmission measurement to assay material stored inside a shielded canister. A quasi-monoenergetic c-ray beam was used in the present measurement as proposed future assay systems will use quasimonoenergetic sources [14]. There are, in practice, only two types of sources available: bremsstrahlung and quasi-monoenergetic sources. Bremsstrahlung c-ray beams are generated when highenergy electrons impinge on a high-Z radiator, producing a broad spectrum of radiation from the incident electron energy on-down, with increasing intensity with decreasing energy. An electron energy is typically chosen to be about 500 keV higher than the state of interest. Such sources produce significant amounts of background radiation resulting in a low signal-to-noise ratio. Particularly problematic is the inelastic background component from intra-target bremsstrahlung from Compton-scattered electrons, but elastic scattering processes (such as Rayleigh scattering and Delbrück scattering) also contribute to the background. Quasimonoenergetic sources generated by inverse-Compton backscattering [15] provide a way to substantially reduce the beam-generated background. When a high-energy electron beam (around 200 MeV) intersects an intense beam of low-energy (a few eV) laser light, a few of the electrons and photons will collide boosting the photon energy to the MeV energy regime. The resultant beam (after collimation) has a near-Gaussian beam profile, with a narrow energy spread. The energy width of the c-ray beam depends on the emittance of the electron beam and laser beam, with the narrowest proposed resolution being about 0.5% at the full-width half-maximum [14]. Because the entire flux of the beam is located at the region of interest, the beam-generated background is substantially reduced at the region of interest by eliminating the contribution from inelastic background processes (which starts at about 0.2 MeV below the highest beam energy), maximizing the signalto-noise ratio.
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For the IOI, since it is impossible in a single study to make measurements of possible random resonance overlap for each IOI separately (235U, 239Pu, 241Pu, etc.), and for each resonance in the IOI, a measurement of a single resonance will be sufficient to give a measure of the possible degree of overlap expected, and demonstrate the feasibility of assay inside of a storage canister for spent nuclear fuel. With this in mind, we chose 27Al as the proxy IOI as it has strong resonances at similar energies to the actinide nuclei [4]. This measurement complements previous transmission measurements on 238U [9,10] by demonstrating that resonance overlap should not be a significant issue when assaying material stored inside a TMI-2, or similar, canister. 2. Experiment The demonstration measurement was carried out using the quasi-monoenergetic c-ray beam at the High Intensity c-ray Source (HIcS) in Durham, NC, USA [16]. The incident flux, without attenuation, was about 108 c-rays/s, with a 3.7% beam width (fullwidth half maximum), and circular polarization. The beam was pulsed, with a spacing of about 180 ns between pulses. Two beam energies were used, Ec ¼ 2:205 MeV and 2.983 MeV (centroid energies), respectively studying the resonance absorption of the 2212 keV and 2982 keV states in 27Al. The 2212 keV state has a ground state integrated cross section of 18.0 ± 0.3 eV b, and the 2982 keV state’s is 32.0 ± 0.7 eV b [17]. The fluorescence of the much weaker 3004 keV state was also observed. The integrated cross section of the 2212 keV and 2982 keV states are comparable to those measured in the actinides, with the largest state in 238U being 80 eV b at 2468 keV [18], and in 235 U, between 13 and 30 eV b at 1733 keV [4,19,20] (though it is confirmed the strongest state, its absolute strength is still disputed), and in 239Pu, 13 eV b at 2143 keV [4]. The experimental setup enabling the measurement of the resonance absorption will be first described, followed by a detailed description of the absorption targets and measurements. The analytical framework for calculating the expected resonance absorption effect and how it relates to the experimental observables will be presented. The absorption of the Al resonances in targets placed upstream of the scattering target is directly proportional to the amount of Al in those targets.
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collimated by a 22 mm diameter Pb collimator that was 20 cm long. There was substantial shielding immediately following the absorption targets and collimators, consisting of two 40 cm-thick Pb walls (with about 30 cm space between them), a 10 cm-thick concrete wall, and then a 20 cm-thick Pb wall. Each wall completely subtended all possible scattering angles from the absorption targets and collimators to the detectors. There was, however, an approximately 4 cm by 4 cm square hole to allow the beam to transport through (in the concrete wall was placed a Pb tube [about 10 cm outer diameter] directly along the path of the beam with a cylindrical 3 cm diameter hole to allow the beam to pass through). In order to prevent small angle scattering from the absorption targets to pass through the beam transport hole and reach the detectors, an additional a 20 cm thick Pb wall with a 3 cm square opening for the beam was placed immediately before the detectors. After passing through the beam transport hole, the beam intersected the scattering target. A scattering target of Al with a thickness of 2.53 cm was used. The scattering target was placed in the middle of four 60% HPGe detectors placed an average of about 12 cm from the target. Additionally, the Al target was inside of a plastic pipe which was pumped to rough vacuum to minimize scattering on the air. The detectors were placed at a scattering angle of h ¼ 120 , with two in the horizontal plane, and two in the vertical plane (see Fig. 2). They were shielded with 2.5 cm Pb on all sides, and Pb (0.55 cm) and Cu (0.4 cm) filters were placed in front of the detectors to reduce the intensity of low energy photons hitting the detector. The detector signal, following amplification, was digitized using a multichannel analyzer (MCA). After the Al scattering target, the beam was incident on a Cu scattering plate 1 mm thick located about 1 m downstream from the scattering target. The Compton scattering from the Cu plate was monitored by a 120% HPGe detector to deduce the c-ray flux for each run [18]. Periodically, the beam energy profile was measured by lowering Cu absorbers into the beam upstream (typically about 20 cm total thickness) and moving the monitor detector into the beam. Small changes in the beam energy profile were compensated for by correlating the shape and position of the Compton-scattered peak with the beam profile peak. That correlation was done using measurements of the Compton scattering peak immediately before or after the beam profile measurements.
2.1. Experimental setup
2.2. Absorption targets and measurements
The beam first traversed the absorption targets (see Fig. 2) which were similar to a fully-loaded TMI-2 canister [12]. Following transmission through the absorbing targets, the beam was then
The absorption targets were chosen to mimic the type and amount of material found in the TMI-2 canister [12] (see Fig. 3). A TMI-2 canister has a cylindrical stainless steel outer shell (a
Fig. 2. The experimental setup, approximately to scale. The beam first traversed the water, concrete, lead, and stainless steel absorption targets. After collimation, the beam then was incident on the Al scattering target. The scattered c rays were measured by four detectors, two in the horizontal, and two in the vertical direction, placed at an angle of 120° from the beam (two detectors out of the image plane are not shown). Finally, the beam intersected the Cu plate, and the Compton scattering from it was monitored to normalize for variations in flux.
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C.T. Angell et al. / Nuclear Instruments and Methods in Physics Research B 347 (2015) 11–19 Table 1 The absorption targets’ thicknesses, densities, and areal densities. The reported density of the concrete is the average of the two pieces (see text for details). The attenuation is that from non-resonant scattering processes, and was evaluated at 2982 keV [23]. The attenuation quoted for the canister scenario is the value for concrete, stainless steel, lead (proxy for uranium), and water multiplied together.
Fig. 3. Schematic of cross section of the TMI-2 canister. The outer cylinder consists of stainless steel (SS) with the stated thickness. The internal sleeve is made of sheets of stainless steel which sandwich a layer of BoralÒ (boron aluminide). The stainless steel was assumed to have the same thickness as that of the outer cylinder. The outer diameter for the cylinder and the internal dimensions for the square sleeve are shown. The filling material between the two was LiCon, a low density concrete. The beam path assumed for evaluating material thicknesses is shown as a dotted line. Not shown is the water or heavy metal that the canister was assumed to be loaded with. See text for details.
14-in. Schedule 10 pipe) with an outer diameter of 35.56 cm and a 0.635 cm wall thickness, and a square, stainless steel internal sleeve at the center of the canister with an internal dimension of 23.178 cm, and an assumed wall thickness of 0.635 cm. The inner sleeve also incorporates sheets of BoralÒ (boron aluminide), which we did not attempt to mimic as it should absorb few photons. 10B has a resonance at 2154 keV which would pose no issue for the present measurement at 2.2 MeV, even if it were included, because of the 58 keV separation from the 2212 keV state in 27Al. In a transmission measurement, only resonances within a few eV could potentially interfere with the measurement. The state in 10B could interfere with a direct measurement if low-resolution detectors are used, such as scintillator detectors [21]. The space between the inner sleeve and the outer cylinder is filled with LiCon, a low density concrete with q = 1 g/cm3 which uses plastic beads as aggregate. At the thickest point, a total of 2.54 cm of stainless steel and 9.84 cm of concrete will be traversed. These values are a sum of twice the wall thicknesses for both the inner and outer sleeves, accounting for both entry into and exit from the canister. Absorption targets of stainless steel and concrete approximating these values were used. For the TMI-2 canister, there was an average loading of heavy metal corresponding to 1.9 cm-thick of Uranium. Pb was used to simulate the attenuation from the heavy metal, using a thickness of 3.25 cm. Though water is not normally apart of the TMI-2 canister, it was included to be complete as water may be used to fill the voids of the material stored in the canister. A plastic container filled with water 15.24 cm thick was used. An aluminum absorber (2.54 cm) was used in a separate measurement as a reference. It was placed in the same position as the stainless steel absorber; no other absorbers were present for that measurement. Each target was a single solid piece of material except for the concrete block. It consisted of two pieces: a masonry block 9.2 cm thick (density: 2.42 g/cm3), and a cast piece of Rockite cement (no aggregate) 1.67 cm thick (density: 1.73 g/cm3). Resonance absorption is also expected in concrete as it contains some Al. The masonry block was assumed to have a typical composition of concrete, which contains 2–3% of Al by weight. The Rockite cement is 98% (by weight) gypsum (calcium sulfate), containing no Al, and 2% Portland cement, presenting a negligible amount of Al in comparison with that in the masonry block. To calculate the Al concentration in the masonry block, an average was used between the typical concentration of Al in ‘‘ordinary’’ concrete
Material
Thickness (cm)
Density (g/cm3)
Areal density (g/cm2)
Attenuation (fraction)
Aluminum Concrete Stainless steel Lead Water Canister
2.5 10.9 2.5 3.2 15.2
2.7 2.3 8.5 11.3 1.0
6.8 25.4 21.6 36.9 15.2
0.78 0.39 0.46 0.21 0.55 0.020
(2.0% Al by weight) and Portland concrete (3.3% Al by weight) [22]. The density for both types of concrete reported in Ref. [22] (2.30 g/cm3) was smaller than what was measured for the masonry block (2.42 g/cm3). The measured density was used. The concrete used here varies significantly from the low-density concrete used in the TMI-2 canister, and represents a more stringent case as it is much denser, and contains higher Z material. The target materials and thicknesses used are listed in Table 1. In addition, the beam attenuation due to non-resonant processes (principally scattering on electrons) is shown, calculated using attenuation coefficients from the NIST XCOM database [23]. The coefficients were evaluated at the energy of the 2982 keV resonance. Beam attenuation was calculated as A ¼ elqt where l is the attenuation coefficient, q is the density, and t the thickness (qt is the areal density). Non-resonant scattering reduces the total flux at all energies, and is a constant effect over the entire width (of a few 100 keV) of the beam, while the resonant absorption discussed in this manuscript is energy-specific, affecting only a few eV wide region of the beam. The attenuation factor quoted for the canister scenario is representative of a TMI-2 canister filled with debris. The sequence of materials used in the measurement, as shown in Fig. 2, was chosen for ease of executing the experiment, and is not reflective of the actual TMI-2 canister as described above. For a transmission measurement, however, the ordering of material is irrelevant as long as the total areal density of material in the path of the beam is the same. This is because for all attenuating processes, the effect is a summation in an exponent (see e.g. Eq. (2), below, for resonant attenuation), which is equivalent to multiplying by the separate attenuation terms. Mathematically, attenuation is represented as em1 þm2 þ where mi is the effect due to material i, and can be rewritten as em1 em2 . . . Because multiplication (or addition) is commutative, every commutation of material will have the same effect. In contrast, a direct measurement is substantially affected by ordering as the effect of entry and exit paths are two separate and distinct terms in an integral over the volume of the object of interest. In that case, the precise distribution of material must be known in order to accurately assay the mass of the isotope of interest. For a transmission measurement, the insensitivity to the precise material arrangement is one of its greatest strengths. Measurements at Ec ¼ 2:983 MeV were done for the following cases: no absorber, Al, concrete, Pb, stainless steel (304), water, and for a canister scenario. In the canister scenario, the materials which simulate the TMI-2 canister (concrete, Pb, stainless steel, and water) were placed in the beam simultaneously. The measurement using an Al absorbing target was done as a reference. Two sets of measurements were taken: without and with a Pb shielding wall in place next to the Cu scattering plate (see Fig. 2) to prevent Compton scattering from the Al target reaching the monitor detector. With the shielding wall in place, only the no absorber, Al absorber, concrete, and canister scenario measurements were
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repeated. Measurement at Ec ¼ 2:205 MeV was done only for using the Al absorbing target as a second reference measurement, with the shielding wall in place. Each measurement lasted about 1 h, except for the canister scenario which was done for 7 h with the shielding wall in place (or 10 h for no wall), and the Pb measurement was done for two and a half hours (no wall). The final number of counts in the peak of interest ranged from 3700 counts to 19,600 counts. 2.3. Absorption ratio The absorption for each scenario was measured relative to the no absorber case by normalizing the NRF count rate by the monitor count rate. The absorption ratio is inversely proportional to the amount of mass in the absorption target. This can be seen by considering the definition of the absorption ratio in terms of the measured NRF counts. The measured number of NRF counts is defined in Ref. [3], but we include here an addition for pileup correction and include in the definition of the integrated cross section the affect of absorption: 0
CðN a Þ ¼ Uere na /ðEr Þ
1 LTp pff Nt bIcs ðna Þ; ð1 þ pp Þ
ð1Þ
where CðN a Þ is the counts in the NRF peak, U is the total c-ray flux before the absorption target, which is followed by a correction term for the reduction in the flux due to atomic scattering in the absorption target, with re being the atomic scattering cross section and n0a being the areal density of electrons in the absorption target. Continuing on, /ðEr Þ is the fractional flux at the resonance energy (Er ), pp is the pileup amount of the primary (NRF) detectors, LTp is the detector livetime, pff is the detector efficiency, N t is the scattering target areal density, and b is the branching ratio for the observed de-excitation transition. Ics ðna Þ is the integrated cross section for absorption by the NRF resonance (neglecting decay branching ratios):
Ics ðna Þ ¼
Z
rD ðEc ;C0 Þna
e
rD ðEc ; C0 ÞdEc ;
ð2Þ
where na is the areal density of the IOI in the absorption target, rD is the resonance cross section including Doppler broadening (a Breit– Wigner line shape), Ec is the excitation energy of the resonance, and C0 is the ground state width. When no absorber is present (na ¼ 0), this equation reduces to the typical form for the integrated cross section for excitation (again, neglecting the branching ratio) [3]:
phc
C0 ;
Ec
1 Ics
Nm ð1 þ pm Þ
0
Uere na ¼
Cu re N0 t LTm m ff N t e
rCompton
;
ð5Þ
where Uere na is the flux at the scattering target, Nm is the number of counts in the monitor detector, pm is the pileup amount of the monitor detector, LT m is the livetime of the monitor detector, m ff 0
is the efficiency, NCu is the areal density of the Cu scatterer, and t rCompton is the cross section for Compton scattering. The term ere Nt , where N 0t is the areal density of electrons in the scattering target, is included to correct for attenuation in the scattering target due to atomic scattering. The correction in the Cu plate is negligible as the Cu is generally thin (on order of 1 mm). If the generated beam flux is kept constant, the ratio of the flux between the two measurements is proportional to the absorption due to coherent processes in the absorption target. Rðna Þ is experimentally defined taking the ratio of the count rates for when an absorber is present to when no absorber is present (see Eq. (1)), and substituting in Eq. (5) for U:
ð3Þ Rðna Þ ¼
where g is the statistical spin factor: g ¼ ð2Jf þ 1Þ=ð2Ji þ 1Þ, with Jf being the spin of the excited state and Ji the spin of the ground state. The absorption ratio, Rðna Þ, is theoretically defined as the ratio of the integrated cross section when an absorber is present with areal density na (Eq. (2)) to that when no absorber is present (Eq. (3)):
Rðna Þ ¼
In practice, a correction is needed for the difference in total flux incident on the scattering target between the measurement with and without an absorbing target for determining Rðna Þ experimentally. The flux after the absorption target is determined by measuring the Compton scattering from a Cu plate using a monitor detector [18]:
0
1
1
Ics ¼ g
Fig. 4. The 2982 keV state’s calculated (solid line) and measured (filled circles) absorption amounts displayed as 1 Rðna Þ. This metric is positively correlated with increasing thickness (areal density).
Z
1
erD ðEc ;C0 Þna rD ðEc ; C0 ÞdEc :
ð4Þ
1
The more material present in the beam, the smaller the absorption ratio. The absorption ratio can be readily calculated given the resonance properties and the absorber areal density. We have done this for the case of the 2982 keV resonance for varying absorber areal density as shown in Fig. 4. This equation can be further modified for including the marginal effect from correcting for the scattering target thickness [10]. We attempted this, but found that it did not change the absorption ratio calculation over the range of the presently considered Al thicknesses.
p p m m CðNa Þ Nm 0 ð1 þ pa Þ ð1 þ p0 Þ LT 0 LT a /0 ðEr Þ : m p p m Cð0Þ Na ð1 þ p0 Þ ð1 þ pa Þ LT a LT m 0 /a ðEr Þ
ð6Þ
The subscript 0 refers to the no-absorber case, and the subscript a refers to the absorber case. Defining Rðna Þ as a ratio in this way cancels out, in Eq. (1), the efficiency and the scattering target mass. For the flux component, Eq. (5), the monitor detector efficiency, the Cu scatterer areal density, the Compton scattering cross section, and the correction for absorption due to atomic elastic processes cancel out. This assumes that the beam energy does not drift sufficiently to significantly change the efficiency or Compton cross section. Only those terms that could vary between runs remain, being the respective number of measured counts, the pileup amounts and the livetimes, for both the primary and monitor detectors. In an assay situation, comparing the experimental Rðna Þ with the theoretically calculated curve will determine the amount of material in the absorption target. In the present case, because we control for the areal density, na , we can test whether or not there are overlapping resonances present, and demonstrate that a transmission assay can be done for shielded material.
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2.4. Determining experimental quantities The NRF peak areas were determined by fitting each peak with a Gaussian. The spectra from the four detectors were summed into a single spectrum. The summed peak areas ranged from 8500 counts for the canister scenario to 36,700 counts for the no-absorber measurement. The pileup amount was estimated from the count rate [24] using the known properties of the spectroscopic amplifier [25] (a shaping time of 4 ls was used), and ranged between 0% and 5%. Given the small amount of pileup, a simple relationship between the livetime ratio (LTR) and pileup amount (p) was found: p ¼ 0:42ð1 LTRÞ. The livetime reported by the MCA was used. The livetime ratio is the amount of time the detector is live (waiting to process an event) to the real (total) time of the measurement. The livetime ratio for the primary detectors averaged 0.94 (equivalently 6% deadtime). This relationship was used only for determining pileup in the primary detectors. 2.4.1. The monitor detector The number of counts in the monitor detector during a flux measurement was determined by first subtracting the pileup component of the spectrum, then the background, and then de-convolving the spectrum, removing the detector response. The livetime ratio for the monitor detector averaged 0.87 (equivalently 13% deadtime), and ranged as low as 0.67 and as high as 0.98. The pileup component of the spectrum was calculated using the proscription of Cano-Ott et al. [26]. The pileup amount (the integral of the pileup component of the spectrum, divided by the total counts of the spectrum) was determined by scaling the counts in the pileup component until it matched the counts in the spectrum above the signal induced by either the beam or naturally occurring background, whichever was at higher energy. The pileup amount determined this way was larger than the pileup inferred from the count rate by about 10–20% for pileup above about 3%, but lower for pileup below 1%. In one case (the measurement using the Al absorber, without shielding next to the Cu scatterer), the pileup determined from fitting was 50% higher than that expected from the count rate. The cause for this discrepancy is not known. De-convolving of the spectrum was done in order to prevent the non-full-energy-absorption component of the detector response from interfering with determining the properties of the incident beam peak. If a fit to the peak is done directly without removing the detector response, then the resultant fitted peak will be broader than the real beam width. The area will also be larger, and the magnitude of the effect will depend on the width of the beam. De-convolving the spectrum removes these two effects, enabling reliable extraction of the beam properties. The detector response matrix (for de-convolving) was constructed using the semi-empirical detector response model [27] and was calibrated using a 56Co spectrum measured by placing the source on the Cu plate (see Fig. 5). The resulting peak was fit with a Gaussian (see Fig. 6). A sizable low-energy tail is present, but its presence may be partially explained by a failure of the model. The excess is well correlated with the location of the single scatter Compton continuum, and with the Compton continuum of annihilation photons (see Ref. [27] for definitions and explanations), two components of the model that are difficult to constrain using only a 56Co spectrum. Inaccurate knowledge of these components, fortunately, will not interfere with accurately extracting a peak area because they only affect the detector response at energies more than 250 keV below the incident energy. This is more than the width of the present beam. The alternative, that flux is actually present at those energies, is supported by the observation of the decay of the 2212 keV state, but not at the level expected from the present attempt at de-convolving the spectrum. The flux at 2212 keV as a ratio to that at the
Fig. 5. The 56Co spectrum as determined using the constructed detector response model (line), compared with that measured for the monitor detector using a 56Co source (points).
Fig. 6. The Compton scattered spectrum at Ec ¼ 2:983 MeV with pileup and background subtracted (upper solid line). Signal was de-convolved, removing detector response (lower solid line). The Compton peak was fit with a Gaussian (dashed line), and used to determine the number of measured Compton scattered events.
beam peak, 2983 keV, would be expected to be about 5% from the above de-convolved spectrum. The same ratio as determined from the observed 2212 keV c-ray intensity (subtracting the contribution from the decay of the 3004 keV state with a known 12% branching ratio) ranged between 0.1% and 7% (max and min, including uncertainties), with a median value of 1%. While there is flux at lower energies, further refinements to the present detector response model are needed in order to accurately determine it from the Compton scatter spectrum. An alternative to the above method is possible because a ratio was taken, which cancels out the efficiency. An integral of counts above a threshold could be taken for equal effect as any measure of the number of counts in the spectrum can be used as long as that measure is directly proportional to the incident flux. Care would be needed, however, because if the beam energy shifts between measurements then it will no longer be true that the measurement efficiency is the same for each measurement. Monitoring the energy of the Compton scattering peak could be done to compensate for such changes in beam energy. We tested using the integral of counts, following pileup and background subtraction, over the interval of 2 MeV to just above the Compton peak. This resulted in an average deviation of 1% between the two methods, within the systematic uncertainty related with the number of counts in the monitor detector (see below). The Compton scattered spectrum was also used to measure the beam profile. The position and width of the Compton scattered
C.T. Angell et al. / Nuclear Instruments and Methods in Physics Research B 347 (2015) 11–19
peak are correlated with the position and width of the beam profile. The properties of the Compton scatter peak were determined by de-convolving the spectrum (as described above). The correlation of those parameters to those of the incident beam was calibrated by comparing the position and width of the directly measured beam profile with that of the Compton scattered peak measured in close succession to the beam profile measurement. Having the calibration measurement in close proximity reduces the likelihood that the beam profile changed between the two measurements. This calibration was done at both beam energies. See Ref. [28] for more details. 2.4.2. Statistical and systematic uncertainties The uncertainties for absorption ratio included both statistical and systematic sources of uncertainty. The statistical uncertainty for absorption was due to the uncertainty in the measured counts in the NRF peak. The uncertainty from a fit using a Gaussian peak and a flat background was used. For the largest peaks (>104 counts), the fit under-reported the uncertainty, so the square root of counts was used instead. The systematic uncertainty included that from the variation in the beam energy profile and from pileup in the number of counts in the monitor detector. The beam energy profile systematic uncertainty was due to variation in its mean energy and width, and was determined by comparing the variation in the ratio of the 2982 keV peak to the 3004 keV peak intensity. It was on order of 3%. The systematic uncertainty of the number of counts in the monitor detector was dominated by pileup subtraction. The systematic uncertainty induced in a spectrum by pileup subtraction was determined to be maximally 20% of the pileup amount. This was determined from the variance in the spectrum sum over the region of the Compton peak when the pileup amount was allowed to vary by 7%. This variance in the pileup amount was taken as the average difference between determining it by fitting compared with determining it from the detector rate [29]. The above maximal uncertainty was used for all cases to be consistent. The final systematic uncertainty in the number of counts in the monitor detector ranged from 0% to 4%. 3. Results We compared the experimental absorption amount (1 Rðna Þ) determined using Eq. (6) with that expected theoretically from Eq. (4) using the known resonance parameters [17] and the inserted Al absorption areal density (see Table 2 and Figs. 7 and 8). This showed that for each measurement (except Pb) the mea-
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sured absorption values are consistent with expectation. This is reinforced in Fig. 4, which plots the calculated increase in absorption, 1 Rðna Þ, for the 2982 keV state as a function of Al thickness, along with the experimentally measured values. At Ec ¼ 2982 keV, the absorption ratios for SS and water are consistent with no absorber present. The Pb measurement is slightly outside expectation even when systematic uncertainty is included. The experimental absorption ratio for absorbing materials where measurements without and with a Pb shielding wall existed (Al, concrete, and canister scenario) were weighted to determine a single absorption ratio for that material. The statistical and systematic uncertainties were separately determined using a weighted mean. No absorption ratios are reported for the 3004 keV state because of the small width (e.g. integrated cross section) of the state. The absorption ratio depends jointly on the mass of the Al in the absorbing target and the width of the state (see Eq. (2)). A resonance with a small width will be significantly less absorbing than a resonance with a large width. The 3004 keV state has a width (i.e. integrated cross section) that is an order of magnitude smaller than that of the 2982 keV state (see Fig. 7). There was a discrepancy between the integrated cross section of the 3004 keV state in the literature and that measured here in ratio to the 2982 keV state; the results of that analysis were published in Ref. [28]. The signature of resonance overlap—an absorption ratio smaller than expected—was not seen in the present experiment. This places an upper limit of about 4% absorption (the maximum combined uncertainty) on a possible contribution of overlapping resonances for the present combination of materials. Given that resonance overlap occurs randomly, this present result would be expected to apply, on average, to other combinations of materials as well, particularly for the IRT method, which uses the sum of many resonances. Nevertheless, in an application setting, calibration measurements constraining the contribution of resonance overlap in an absorption measurement will be needed for each combination of IOI and absorbing materials. The present measurement of Al absorption in concrete is symbolic of measuring the resonance absorption due to the fissile content in spent nuclear fuel, and demonstrates that it is, in principle, possible to do so. The Al in the concrete is mixed through out the material, and is a relatively small fraction of the total by weight (3%). The fissile content, 239Pu for example, is similarly mixed through out the spent fuel, and is a small fraction of the total amount of material in the spent fuel (1%). There was about
Table 2 Expected and measured absorption amounts (1 Rðna Þ) of the 2212 keV and 2982 keV resonances in 27Al for the several measured samples. Absorption in the concrete was calculated assuming the typical 2% concentration by weight. A larger absorption amount (smaller absorption ratio, Rðna Þ) indicates a greater concentration of Al. The canister absorption value is the same as that of the concrete as it used the same sample. Statistical and systematic uncertainties are given for each value. Expected absorption amounts of ‘0’ are stated for cases where no Al was in the absorbing target. Material
Aluminum
2212 keV
2982 keV
Expected
Measured
0.282 ± 0.004
0:310:01 0:03
stat sys
Expected
Measured
0.345 ± 0.006
stat sys 0:01 stat 0:050:02 sys stat 0:010:01 0:05 sys 0:01 stat 0:080:06 sys stat 0:020:01 0:05 sys stat 0:010:01 0:03 sys
Concrete
0.04 ± 0.01
SS (304)
0
Lead
0
Water
0
Canister
0.04 ± 0.01
0:3580:005 0:020
Fig. 7. The NRF scattering peaks observed for a beam energy of Ec ¼ 2:983 MeV for no absorber (N/A), Al absorber, concrete, and absorbers representing the canister (concrete, stainless steel, Pb, and water). The spectra were normalized for the same amount of incident flux. Only significant absorption was seen when using the Al absorber, as expected.
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mentary measurements of the resonances at Er ¼ 2212 keV and 2982 keV using an Al absorber verified the resonance absorption calculations. The present results suggest that resonance overlap will not be a significant issue for using a transmission NRF measurement to assay, for example, long-stored SNF in a storage canister, or the Fukushima melted fuel debris in its final deposition canister. It also demonstrates the practicality of using NRF to assay material inside of a storage canister designed for radioactive material. Further work is needed for developing the IRT method more fully, particularly for calculating the average sensitivity to resonance overlap when using the method. This measurement also highlighted the need to significantly reduce the systematic uncertainties of an NRF measurement so that a transmission measurement of the 239Pu in fuel debris stored inside a TMI-2 canister will be feasible. Fig. 8. The same as Fig. 7 for Ec ¼ 2:205 MeV, and for no absorber and Al absorber cases.
1 1022 atoms/cm2 of 27Al in the concrete. In contrast, there would be about 1 1021 atoms/cm2 of 239Pu in a TMI-2 canister loaded with fuel debris [12], assuming the heavy metal content is 1% 239 Pu, by weight. The corresponding resonant absorption ratio for the 13 eV b resonance at 2143 keV would be 0.995 (or 1 Rðna Þ ¼ 0:005). An assay measurement of Pu would have the added difficulty that the atomic elastic scattering contribution to the scattering target would be substantially larger, interfering with the NRF signature. The atomic elastic scattering cross section scales by Z 2 , becoming sizable for actinide elements. For U, it reaches 50 lb/sr for 2.1 MeV c rays at 120° [30]. The primary effect will be to decrease the signal to noise ratio, resulting in even longer measurement times than would be otherwise expected [7]. If the absorption measurement due to such a small concentration of 239Pu were to be attempted, significant reduction in the presently measured uncertainties would be needed. The statistical uncertainty measured in the present experiment could be significantly suppressed from the current ±0.01 value if the proposed next generation c-ray sources were available. A source based on a compact energy recovery linac and using a Fabre–Pérot cavity for the primary laser is expected to generate a c-ray beam 4 orders-of-magnitude brighter than the presently used source [14]. The systematic uncertainty due to pileup correction could be eliminated by eliminating the need for such corrections. Using fast scintillator detectors with waveform digitizing electronics would achieve this [21]. The uncertainty associated with determining the beam profile of a quasi-monoenergetic source is more difficult to suppress. The beam profile could be directly determined, however, from the properties of the electron beam and laser beam. Determining the beam profile directly from those properties, rather than through a secondary measurement of Compton scattering, could significantly reduce the uncertainty related with determining the beam profile. Additionally, taking a ratio of resonances simultaneously excited by the beam would reduce the systematic uncertainties associated with determining the beam profile (see e.g. Ref. [28], which demonstrates this idea using the present data for the 2982 keV and 3004 keV resonances). If two nearby resonances are not available in a single isotope, an additional isotope could be added to the transmission measurement station to add a second resonance near the resonance of interest for such a comparison.
4. Summary In summary, no resonance overlap for the 2982 keV Al resonance in the simulated canister scenario was observed. Comple-
Acknowledgments We would like to acknowledge the excellent service and beams provided by the staff at the High Intensity c-ray Source, and M. Emamian for help with target preparation. This study was supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan.
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Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Demonstration of a transmission nuclear resonance fluorescence measurement for a realistic radioactive waste canister scenario C.T. Angell a,⇑, R. Hajima a, T. Hayakawa a, T. Shizuma a, H.J. Karwowski b,c, J. Silano b,c a
Quantum Beam Science Center, Japan Atomic Energy Agency, Tokai-mura, Ibaraki 319-1195, Japan Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255, USA c Triangle Universities Nuclear Laboratory, Durham, NC 27708-0308, USA b
a r t i c l e
i n f o
Article history: Received 7 August 2014 Received in revised form 21 January 2015 Accepted 24 January 2015
Keywords: Nuclear resonance fluorescence Non-destructive assay Transmission Spent nuclear fuel
a b s t r a c t Transmission nuclear resonance fluorescence (NRF) is a promising method for precision non-destructive assay (NDA) of fissile isotopes—including 239Pu—in spent fuel while inside a storage canister. The assay, however, could be confounded by the presence of overlapping resonances from competing isotopes in the canister. A measurement is needed to demonstrate that transmission NRF is unaffected by the shielding material. To this end, we carried out a transmission NRF measurement using a mono-energetic c-ray beam on a proxy target (Al) and absorbing material simulating a realistic spent fuel storage canister. Similar amounts of material as would be found in a possible spent fuel storage canister were placed upstream: concrete, stainless steel (SS 304), lead (as a proxy for U), and water. An Al absorption target was also used as a reference. These measurements demonstrated that the canister material should not significantly influence the non-destructive assay. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction The non-destructive assay (NDA) of fissile isotopes in spentnuclear fuel (SNF) is an ever-present challenge to safeguards. Being able to assay the SNF inside a storage canister could help mitigate concern of diversion of special nuclear material from easyto-access SNF in long-term storage [1]. Assay of fuel inside shipping canisters could also enhance safety of fuel handling by not requiring invasive entry into canisters for verification. Additionally, the Fukushima meltdown presented a new challenge to the safeguards regime. The triple reactor meltdown and hydrogen explosions damaging the fuel assemblies stored in the spent fuel ponds resulted in a loss of continuity of knowledge [2]. Recovery from a loss of knowledge requires the development of new nondestructive assay techniques [1]. If the fuel debris upon removal is put directly into the final storage canisters—a step that would minimize future possibilities of re-contamination—a method which can precisely assay the fuel when stored inside the shielded canister will be necessary. Nuclear resonance fluorescence [3] (NRF) may be the only method that can be used to perform quantitative assay of such shielded material. NRF is a fundamental process whereby a discrete nuclear state resonantly absorbs a c ray, and then decays ⇑ Corresponding author. E-mail address: [email protected] (C.T. Angell). http://dx.doi.org/10.1016/j.nimb.2015.01.053 0168-583X/Ó 2015 Elsevier B.V. All rights reserved.
by c-ray emission, either to the ground state or an excited state (see Fig. 1). NRF is an active technique, requiring an intense source of high energy c rays. The c-ray energy for absorption is precisely determined from the level energy. The level energy is typically known to about 1 keV. The emitting c-ray energy is similarly known to about 1 keV, though it is slightly less than the absorption energy because of energy that goes into the nuclear recoil. The 10 eV nuclear recoil energy is larger than the resonance width, which excludes the possibility of re-absorption. The intrinsic resonance width, which determines the absorption strength of the resonance, is on the order of a few meV to as much as 1 eV. It is further broadened several eV by Doppler broadening, which conserves the total strength of the resonance. The level energy is uniquely determined by the precise realization of nuclear structure for a given nucleus: a change of even one nucleon will have a dramatic effect on the level properties of the nucleus, changing the energy and strength of each level, as well as the total number of levels excited by NRF. For fissile materials, strongly excited levels exist at around 2–3 MeV [4], incidentally the energy region where c-rays have maximum penetrating power. These resonances exist at this energy because of a structural phenomenon called the ‘‘scissors mode’’ of excitation [5] in which the protons and neutrons in a deformed nucleus oscillate out of plane from each other. Because of the precisely defined characteristic level energy, and the sensitivity to the structure of the nucleus manifested in both the level energy and level strength,
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NRF can provide an isotope-specific signature of almost every nucleus on the periodic table, allowing discernment between neighboring isotopes, including nuclei whose properties as measured by neutrons may otherwise be nearly identical. This is particularly true of the actinide nuclei (as discussed above), but has an exception for light nuclei. The lightest nuclei (particularly lighter than carbon) either have no bound states which can be excited by a c-ray (e.g. hydrogen), or the bound states do not have a strong c decay branch, limiting applicability of NRF in those cases. NRF was first proposed for detection of nuclear material [6], and then for assay of nuclear fuel [7,8], with the difference only being in measurement precision. Assay has significantly higher requirements for precision. Both applications can be done in one of two ways: direct or transmission. The direct measurement method measures c-rays directly emitted from the decay of states excited in the nuclear material. The transmission method measures the development of notches following transmission through the fuel [6,9,10]. When a c-ray beam transits material, notches are left in the beam energy distribution due to the resonant absorption of photons. The energies of these notches are characteristic of the absorbing isotope, the isotope of interest (IOI), and their depth is characteristic of the amount of that isotope. The widths of these notches are the same as those of the Doppler broadened resonances—a few eV wide. These notches can be used to assay the shielded material if the notch depth can be measured. The notch depth induced by the IOI can be determined by measuring the reduction in scattering from a sample of the same isotope placed downstream of the shielded material. The resonances overlap in energy with the induced notches, and as the notch deepens due to increased material amount in the melted fuel, the induced scattering (normalized by the total transmitted flux) also decreases. A transmission measurement’s detector resolution is determined by the width of resonances in the IOI. This is significantly better than the few keV resolution of the best high-purity Germanium detector at these energies, highlighting a significant advantage that a transmission measurement has over a direct measurement. A transmission measurement is isotope specific because isotopes other than the IOI will have their resonances (and induced notches) at different energies. It is insensitive to the shielding material as long as the material does not contain the IOI, but even then a correction can be made by separate measurements on an empty, typical canister. A transmission measurement, however, will lose the property of isotope specificity if resonances from other isotopes randomly overlap with resonances in the IOI to a significant degree [11]. Such overlap will mimic the IOI’s absorption signature. Although the amount of resonance overlap will be significantly smaller because of the higher intrinsic resolution compared to a direct measurement, the effect of resonance overlap will be indistinguishable from absorption due to the IOI. This is unlike a direct measurement where some signature of an additional resonance may be present in the spec-
Fig. 1. Nuclear resonance fluorescence is a process where the nucleus becomes resonantly excited by absorbing a c ray with an energy equal to that of the state Ex . The state then de-excites by the emission of a c ray with energy Ex back to the ground state or energy Ex E1 to an excited state with energy E1 .
trum, such as an overly broad peak. The canister which the fuel will be stored in will present a large source of possibly overlapping resonances which could interfere even with a transmission measurement. Therefore a transmission measurement studying the degree of possible resonance overlap is needed using the same materials as those which would be used in spent fuel storage canisters. The issue of random resonance overlap is particularly problematic for the proposed integral resonance transmission (IRT) method [11]. The IRT method utilizes the resonance absorption of all resonances within the beam width of a quasi-monoenergetic c-ray beam by integrating over all NRF scattering strength. This has the potential to improve measurement efficacy by enabling the use of more efficient and faster scintillator detectors. There is a liability, however, that accompanies the use of lower resolution detectors. Using lower resolution detectors precludes the possibility of detecting random resonance overlap from the disagreement in inferred absorption from two or more resonances that are simultaneously excited. Careful measurements exploring the possibility of random resonance overlap are particularly needed in order to effectively use the IRT method. To study the possible overlap of a single resonance with resonances present in the canister material, we carried out an NRF transmission experiment using materials similar in type and thickness to the TMI-2 debris canister [12] which was used to store the fuel debris generated from the Three Mile Island accident. Even if other storage canisters are used, they will be effectively similar in composition (concrete and steel) as the TMI-2 canister. It should be noted that the TMI-2 canisters (described below) are unique in that they are designed to contain a single fuel assembly, and use low-density concrete for shielding, which facilitates assay of the material stored inside. Vitrified waste would also readily yield to assay using NRF in transmission, including the IRT method, and has a total areal density similar to a loaded TMI-2 canister [13]. The present measurement additionally demonstrates the feasibility of a transmission measurement to assay material stored inside a shielded canister. A quasi-monoenergetic c-ray beam was used in the present measurement as proposed future assay systems will use quasimonoenergetic sources [14]. There are, in practice, only two types of sources available: bremsstrahlung and quasi-monoenergetic sources. Bremsstrahlung c-ray beams are generated when highenergy electrons impinge on a high-Z radiator, producing a broad spectrum of radiation from the incident electron energy on-down, with increasing intensity with decreasing energy. An electron energy is typically chosen to be about 500 keV higher than the state of interest. Such sources produce significant amounts of background radiation resulting in a low signal-to-noise ratio. Particularly problematic is the inelastic background component from intra-target bremsstrahlung from Compton-scattered electrons, but elastic scattering processes (such as Rayleigh scattering and Delbrück scattering) also contribute to the background. Quasimonoenergetic sources generated by inverse-Compton backscattering [15] provide a way to substantially reduce the beam-generated background. When a high-energy electron beam (around 200 MeV) intersects an intense beam of low-energy (a few eV) laser light, a few of the electrons and photons will collide boosting the photon energy to the MeV energy regime. The resultant beam (after collimation) has a near-Gaussian beam profile, with a narrow energy spread. The energy width of the c-ray beam depends on the emittance of the electron beam and laser beam, with the narrowest proposed resolution being about 0.5% at the full-width half-maximum [14]. Because the entire flux of the beam is located at the region of interest, the beam-generated background is substantially reduced at the region of interest by eliminating the contribution from inelastic background processes (which starts at about 0.2 MeV below the highest beam energy), maximizing the signalto-noise ratio.
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For the IOI, since it is impossible in a single study to make measurements of possible random resonance overlap for each IOI separately (235U, 239Pu, 241Pu, etc.), and for each resonance in the IOI, a measurement of a single resonance will be sufficient to give a measure of the possible degree of overlap expected, and demonstrate the feasibility of assay inside of a storage canister for spent nuclear fuel. With this in mind, we chose 27Al as the proxy IOI as it has strong resonances at similar energies to the actinide nuclei [4]. This measurement complements previous transmission measurements on 238U [9,10] by demonstrating that resonance overlap should not be a significant issue when assaying material stored inside a TMI-2, or similar, canister. 2. Experiment The demonstration measurement was carried out using the quasi-monoenergetic c-ray beam at the High Intensity c-ray Source (HIcS) in Durham, NC, USA [16]. The incident flux, without attenuation, was about 108 c-rays/s, with a 3.7% beam width (fullwidth half maximum), and circular polarization. The beam was pulsed, with a spacing of about 180 ns between pulses. Two beam energies were used, Ec ¼ 2:205 MeV and 2.983 MeV (centroid energies), respectively studying the resonance absorption of the 2212 keV and 2982 keV states in 27Al. The 2212 keV state has a ground state integrated cross section of 18.0 ± 0.3 eV b, and the 2982 keV state’s is 32.0 ± 0.7 eV b [17]. The fluorescence of the much weaker 3004 keV state was also observed. The integrated cross section of the 2212 keV and 2982 keV states are comparable to those measured in the actinides, with the largest state in 238U being 80 eV b at 2468 keV [18], and in 235 U, between 13 and 30 eV b at 1733 keV [4,19,20] (though it is confirmed the strongest state, its absolute strength is still disputed), and in 239Pu, 13 eV b at 2143 keV [4]. The experimental setup enabling the measurement of the resonance absorption will be first described, followed by a detailed description of the absorption targets and measurements. The analytical framework for calculating the expected resonance absorption effect and how it relates to the experimental observables will be presented. The absorption of the Al resonances in targets placed upstream of the scattering target is directly proportional to the amount of Al in those targets.
13
collimated by a 22 mm diameter Pb collimator that was 20 cm long. There was substantial shielding immediately following the absorption targets and collimators, consisting of two 40 cm-thick Pb walls (with about 30 cm space between them), a 10 cm-thick concrete wall, and then a 20 cm-thick Pb wall. Each wall completely subtended all possible scattering angles from the absorption targets and collimators to the detectors. There was, however, an approximately 4 cm by 4 cm square hole to allow the beam to transport through (in the concrete wall was placed a Pb tube [about 10 cm outer diameter] directly along the path of the beam with a cylindrical 3 cm diameter hole to allow the beam to pass through). In order to prevent small angle scattering from the absorption targets to pass through the beam transport hole and reach the detectors, an additional a 20 cm thick Pb wall with a 3 cm square opening for the beam was placed immediately before the detectors. After passing through the beam transport hole, the beam intersected the scattering target. A scattering target of Al with a thickness of 2.53 cm was used. The scattering target was placed in the middle of four 60% HPGe detectors placed an average of about 12 cm from the target. Additionally, the Al target was inside of a plastic pipe which was pumped to rough vacuum to minimize scattering on the air. The detectors were placed at a scattering angle of h ¼ 120 , with two in the horizontal plane, and two in the vertical plane (see Fig. 2). They were shielded with 2.5 cm Pb on all sides, and Pb (0.55 cm) and Cu (0.4 cm) filters were placed in front of the detectors to reduce the intensity of low energy photons hitting the detector. The detector signal, following amplification, was digitized using a multichannel analyzer (MCA). After the Al scattering target, the beam was incident on a Cu scattering plate 1 mm thick located about 1 m downstream from the scattering target. The Compton scattering from the Cu plate was monitored by a 120% HPGe detector to deduce the c-ray flux for each run [18]. Periodically, the beam energy profile was measured by lowering Cu absorbers into the beam upstream (typically about 20 cm total thickness) and moving the monitor detector into the beam. Small changes in the beam energy profile were compensated for by correlating the shape and position of the Compton-scattered peak with the beam profile peak. That correlation was done using measurements of the Compton scattering peak immediately before or after the beam profile measurements.
2.1. Experimental setup
2.2. Absorption targets and measurements
The beam first traversed the absorption targets (see Fig. 2) which were similar to a fully-loaded TMI-2 canister [12]. Following transmission through the absorbing targets, the beam was then
The absorption targets were chosen to mimic the type and amount of material found in the TMI-2 canister [12] (see Fig. 3). A TMI-2 canister has a cylindrical stainless steel outer shell (a
Fig. 2. The experimental setup, approximately to scale. The beam first traversed the water, concrete, lead, and stainless steel absorption targets. After collimation, the beam then was incident on the Al scattering target. The scattered c rays were measured by four detectors, two in the horizontal, and two in the vertical direction, placed at an angle of 120° from the beam (two detectors out of the image plane are not shown). Finally, the beam intersected the Cu plate, and the Compton scattering from it was monitored to normalize for variations in flux.
14
C.T. Angell et al. / Nuclear Instruments and Methods in Physics Research B 347 (2015) 11–19 Table 1 The absorption targets’ thicknesses, densities, and areal densities. The reported density of the concrete is the average of the two pieces (see text for details). The attenuation is that from non-resonant scattering processes, and was evaluated at 2982 keV [23]. The attenuation quoted for the canister scenario is the value for concrete, stainless steel, lead (proxy for uranium), and water multiplied together.
Fig. 3. Schematic of cross section of the TMI-2 canister. The outer cylinder consists of stainless steel (SS) with the stated thickness. The internal sleeve is made of sheets of stainless steel which sandwich a layer of BoralÒ (boron aluminide). The stainless steel was assumed to have the same thickness as that of the outer cylinder. The outer diameter for the cylinder and the internal dimensions for the square sleeve are shown. The filling material between the two was LiCon, a low density concrete. The beam path assumed for evaluating material thicknesses is shown as a dotted line. Not shown is the water or heavy metal that the canister was assumed to be loaded with. See text for details.
14-in. Schedule 10 pipe) with an outer diameter of 35.56 cm and a 0.635 cm wall thickness, and a square, stainless steel internal sleeve at the center of the canister with an internal dimension of 23.178 cm, and an assumed wall thickness of 0.635 cm. The inner sleeve also incorporates sheets of BoralÒ (boron aluminide), which we did not attempt to mimic as it should absorb few photons. 10B has a resonance at 2154 keV which would pose no issue for the present measurement at 2.2 MeV, even if it were included, because of the 58 keV separation from the 2212 keV state in 27Al. In a transmission measurement, only resonances within a few eV could potentially interfere with the measurement. The state in 10B could interfere with a direct measurement if low-resolution detectors are used, such as scintillator detectors [21]. The space between the inner sleeve and the outer cylinder is filled with LiCon, a low density concrete with q = 1 g/cm3 which uses plastic beads as aggregate. At the thickest point, a total of 2.54 cm of stainless steel and 9.84 cm of concrete will be traversed. These values are a sum of twice the wall thicknesses for both the inner and outer sleeves, accounting for both entry into and exit from the canister. Absorption targets of stainless steel and concrete approximating these values were used. For the TMI-2 canister, there was an average loading of heavy metal corresponding to 1.9 cm-thick of Uranium. Pb was used to simulate the attenuation from the heavy metal, using a thickness of 3.25 cm. Though water is not normally apart of the TMI-2 canister, it was included to be complete as water may be used to fill the voids of the material stored in the canister. A plastic container filled with water 15.24 cm thick was used. An aluminum absorber (2.54 cm) was used in a separate measurement as a reference. It was placed in the same position as the stainless steel absorber; no other absorbers were present for that measurement. Each target was a single solid piece of material except for the concrete block. It consisted of two pieces: a masonry block 9.2 cm thick (density: 2.42 g/cm3), and a cast piece of Rockite cement (no aggregate) 1.67 cm thick (density: 1.73 g/cm3). Resonance absorption is also expected in concrete as it contains some Al. The masonry block was assumed to have a typical composition of concrete, which contains 2–3% of Al by weight. The Rockite cement is 98% (by weight) gypsum (calcium sulfate), containing no Al, and 2% Portland cement, presenting a negligible amount of Al in comparison with that in the masonry block. To calculate the Al concentration in the masonry block, an average was used between the typical concentration of Al in ‘‘ordinary’’ concrete
Material
Thickness (cm)
Density (g/cm3)
Areal density (g/cm2)
Attenuation (fraction)
Aluminum Concrete Stainless steel Lead Water Canister
2.5 10.9 2.5 3.2 15.2
2.7 2.3 8.5 11.3 1.0
6.8 25.4 21.6 36.9 15.2
0.78 0.39 0.46 0.21 0.55 0.020
(2.0% Al by weight) and Portland concrete (3.3% Al by weight) [22]. The density for both types of concrete reported in Ref. [22] (2.30 g/cm3) was smaller than what was measured for the masonry block (2.42 g/cm3). The measured density was used. The concrete used here varies significantly from the low-density concrete used in the TMI-2 canister, and represents a more stringent case as it is much denser, and contains higher Z material. The target materials and thicknesses used are listed in Table 1. In addition, the beam attenuation due to non-resonant processes (principally scattering on electrons) is shown, calculated using attenuation coefficients from the NIST XCOM database [23]. The coefficients were evaluated at the energy of the 2982 keV resonance. Beam attenuation was calculated as A ¼ elqt where l is the attenuation coefficient, q is the density, and t the thickness (qt is the areal density). Non-resonant scattering reduces the total flux at all energies, and is a constant effect over the entire width (of a few 100 keV) of the beam, while the resonant absorption discussed in this manuscript is energy-specific, affecting only a few eV wide region of the beam. The attenuation factor quoted for the canister scenario is representative of a TMI-2 canister filled with debris. The sequence of materials used in the measurement, as shown in Fig. 2, was chosen for ease of executing the experiment, and is not reflective of the actual TMI-2 canister as described above. For a transmission measurement, however, the ordering of material is irrelevant as long as the total areal density of material in the path of the beam is the same. This is because for all attenuating processes, the effect is a summation in an exponent (see e.g. Eq. (2), below, for resonant attenuation), which is equivalent to multiplying by the separate attenuation terms. Mathematically, attenuation is represented as em1 þm2 þ where mi is the effect due to material i, and can be rewritten as em1 em2 . . . Because multiplication (or addition) is commutative, every commutation of material will have the same effect. In contrast, a direct measurement is substantially affected by ordering as the effect of entry and exit paths are two separate and distinct terms in an integral over the volume of the object of interest. In that case, the precise distribution of material must be known in order to accurately assay the mass of the isotope of interest. For a transmission measurement, the insensitivity to the precise material arrangement is one of its greatest strengths. Measurements at Ec ¼ 2:983 MeV were done for the following cases: no absorber, Al, concrete, Pb, stainless steel (304), water, and for a canister scenario. In the canister scenario, the materials which simulate the TMI-2 canister (concrete, Pb, stainless steel, and water) were placed in the beam simultaneously. The measurement using an Al absorbing target was done as a reference. Two sets of measurements were taken: without and with a Pb shielding wall in place next to the Cu scattering plate (see Fig. 2) to prevent Compton scattering from the Al target reaching the monitor detector. With the shielding wall in place, only the no absorber, Al absorber, concrete, and canister scenario measurements were
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C.T. Angell et al. / Nuclear Instruments and Methods in Physics Research B 347 (2015) 11–19
repeated. Measurement at Ec ¼ 2:205 MeV was done only for using the Al absorbing target as a second reference measurement, with the shielding wall in place. Each measurement lasted about 1 h, except for the canister scenario which was done for 7 h with the shielding wall in place (or 10 h for no wall), and the Pb measurement was done for two and a half hours (no wall). The final number of counts in the peak of interest ranged from 3700 counts to 19,600 counts. 2.3. Absorption ratio The absorption for each scenario was measured relative to the no absorber case by normalizing the NRF count rate by the monitor count rate. The absorption ratio is inversely proportional to the amount of mass in the absorption target. This can be seen by considering the definition of the absorption ratio in terms of the measured NRF counts. The measured number of NRF counts is defined in Ref. [3], but we include here an addition for pileup correction and include in the definition of the integrated cross section the affect of absorption: 0
CðN a Þ ¼ Uere na /ðEr Þ
1 LTp pff Nt bIcs ðna Þ; ð1 þ pp Þ
ð1Þ
where CðN a Þ is the counts in the NRF peak, U is the total c-ray flux before the absorption target, which is followed by a correction term for the reduction in the flux due to atomic scattering in the absorption target, with re being the atomic scattering cross section and n0a being the areal density of electrons in the absorption target. Continuing on, /ðEr Þ is the fractional flux at the resonance energy (Er ), pp is the pileup amount of the primary (NRF) detectors, LTp is the detector livetime, pff is the detector efficiency, N t is the scattering target areal density, and b is the branching ratio for the observed de-excitation transition. Ics ðna Þ is the integrated cross section for absorption by the NRF resonance (neglecting decay branching ratios):
Ics ðna Þ ¼
Z
rD ðEc ;C0 Þna
e
rD ðEc ; C0 ÞdEc ;
ð2Þ
where na is the areal density of the IOI in the absorption target, rD is the resonance cross section including Doppler broadening (a Breit– Wigner line shape), Ec is the excitation energy of the resonance, and C0 is the ground state width. When no absorber is present (na ¼ 0), this equation reduces to the typical form for the integrated cross section for excitation (again, neglecting the branching ratio) [3]:
phc
C0 ;
Ec
1 Ics
Nm ð1 þ pm Þ
0
Uere na ¼
Cu re N0 t LTm m ff N t e
rCompton
;
ð5Þ
where Uere na is the flux at the scattering target, Nm is the number of counts in the monitor detector, pm is the pileup amount of the monitor detector, LT m is the livetime of the monitor detector, m ff 0
is the efficiency, NCu is the areal density of the Cu scatterer, and t rCompton is the cross section for Compton scattering. The term ere Nt , where N 0t is the areal density of electrons in the scattering target, is included to correct for attenuation in the scattering target due to atomic scattering. The correction in the Cu plate is negligible as the Cu is generally thin (on order of 1 mm). If the generated beam flux is kept constant, the ratio of the flux between the two measurements is proportional to the absorption due to coherent processes in the absorption target. Rðna Þ is experimentally defined taking the ratio of the count rates for when an absorber is present to when no absorber is present (see Eq. (1)), and substituting in Eq. (5) for U:
ð3Þ Rðna Þ ¼
where g is the statistical spin factor: g ¼ ð2Jf þ 1Þ=ð2Ji þ 1Þ, with Jf being the spin of the excited state and Ji the spin of the ground state. The absorption ratio, Rðna Þ, is theoretically defined as the ratio of the integrated cross section when an absorber is present with areal density na (Eq. (2)) to that when no absorber is present (Eq. (3)):
Rðna Þ ¼
In practice, a correction is needed for the difference in total flux incident on the scattering target between the measurement with and without an absorbing target for determining Rðna Þ experimentally. The flux after the absorption target is determined by measuring the Compton scattering from a Cu plate using a monitor detector [18]:
0
1
1
Ics ¼ g
Fig. 4. The 2982 keV state’s calculated (solid line) and measured (filled circles) absorption amounts displayed as 1 Rðna Þ. This metric is positively correlated with increasing thickness (areal density).
Z
1
erD ðEc ;C0 Þna rD ðEc ; C0 ÞdEc :
ð4Þ
1
The more material present in the beam, the smaller the absorption ratio. The absorption ratio can be readily calculated given the resonance properties and the absorber areal density. We have done this for the case of the 2982 keV resonance for varying absorber areal density as shown in Fig. 4. This equation can be further modified for including the marginal effect from correcting for the scattering target thickness [10]. We attempted this, but found that it did not change the absorption ratio calculation over the range of the presently considered Al thicknesses.
p p m m CðNa Þ Nm 0 ð1 þ pa Þ ð1 þ p0 Þ LT 0 LT a /0 ðEr Þ : m p p m Cð0Þ Na ð1 þ p0 Þ ð1 þ pa Þ LT a LT m 0 /a ðEr Þ
ð6Þ
The subscript 0 refers to the no-absorber case, and the subscript a refers to the absorber case. Defining Rðna Þ as a ratio in this way cancels out, in Eq. (1), the efficiency and the scattering target mass. For the flux component, Eq. (5), the monitor detector efficiency, the Cu scatterer areal density, the Compton scattering cross section, and the correction for absorption due to atomic elastic processes cancel out. This assumes that the beam energy does not drift sufficiently to significantly change the efficiency or Compton cross section. Only those terms that could vary between runs remain, being the respective number of measured counts, the pileup amounts and the livetimes, for both the primary and monitor detectors. In an assay situation, comparing the experimental Rðna Þ with the theoretically calculated curve will determine the amount of material in the absorption target. In the present case, because we control for the areal density, na , we can test whether or not there are overlapping resonances present, and demonstrate that a transmission assay can be done for shielded material.
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C.T. Angell et al. / Nuclear Instruments and Methods in Physics Research B 347 (2015) 11–19
2.4. Determining experimental quantities The NRF peak areas were determined by fitting each peak with a Gaussian. The spectra from the four detectors were summed into a single spectrum. The summed peak areas ranged from 8500 counts for the canister scenario to 36,700 counts for the no-absorber measurement. The pileup amount was estimated from the count rate [24] using the known properties of the spectroscopic amplifier [25] (a shaping time of 4 ls was used), and ranged between 0% and 5%. Given the small amount of pileup, a simple relationship between the livetime ratio (LTR) and pileup amount (p) was found: p ¼ 0:42ð1 LTRÞ. The livetime reported by the MCA was used. The livetime ratio is the amount of time the detector is live (waiting to process an event) to the real (total) time of the measurement. The livetime ratio for the primary detectors averaged 0.94 (equivalently 6% deadtime). This relationship was used only for determining pileup in the primary detectors. 2.4.1. The monitor detector The number of counts in the monitor detector during a flux measurement was determined by first subtracting the pileup component of the spectrum, then the background, and then de-convolving the spectrum, removing the detector response. The livetime ratio for the monitor detector averaged 0.87 (equivalently 13% deadtime), and ranged as low as 0.67 and as high as 0.98. The pileup component of the spectrum was calculated using the proscription of Cano-Ott et al. [26]. The pileup amount (the integral of the pileup component of the spectrum, divided by the total counts of the spectrum) was determined by scaling the counts in the pileup component until it matched the counts in the spectrum above the signal induced by either the beam or naturally occurring background, whichever was at higher energy. The pileup amount determined this way was larger than the pileup inferred from the count rate by about 10–20% for pileup above about 3%, but lower for pileup below 1%. In one case (the measurement using the Al absorber, without shielding next to the Cu scatterer), the pileup determined from fitting was 50% higher than that expected from the count rate. The cause for this discrepancy is not known. De-convolving of the spectrum was done in order to prevent the non-full-energy-absorption component of the detector response from interfering with determining the properties of the incident beam peak. If a fit to the peak is done directly without removing the detector response, then the resultant fitted peak will be broader than the real beam width. The area will also be larger, and the magnitude of the effect will depend on the width of the beam. De-convolving the spectrum removes these two effects, enabling reliable extraction of the beam properties. The detector response matrix (for de-convolving) was constructed using the semi-empirical detector response model [27] and was calibrated using a 56Co spectrum measured by placing the source on the Cu plate (see Fig. 5). The resulting peak was fit with a Gaussian (see Fig. 6). A sizable low-energy tail is present, but its presence may be partially explained by a failure of the model. The excess is well correlated with the location of the single scatter Compton continuum, and with the Compton continuum of annihilation photons (see Ref. [27] for definitions and explanations), two components of the model that are difficult to constrain using only a 56Co spectrum. Inaccurate knowledge of these components, fortunately, will not interfere with accurately extracting a peak area because they only affect the detector response at energies more than 250 keV below the incident energy. This is more than the width of the present beam. The alternative, that flux is actually present at those energies, is supported by the observation of the decay of the 2212 keV state, but not at the level expected from the present attempt at de-convolving the spectrum. The flux at 2212 keV as a ratio to that at the
Fig. 5. The 56Co spectrum as determined using the constructed detector response model (line), compared with that measured for the monitor detector using a 56Co source (points).
Fig. 6. The Compton scattered spectrum at Ec ¼ 2:983 MeV with pileup and background subtracted (upper solid line). Signal was de-convolved, removing detector response (lower solid line). The Compton peak was fit with a Gaussian (dashed line), and used to determine the number of measured Compton scattered events.
beam peak, 2983 keV, would be expected to be about 5% from the above de-convolved spectrum. The same ratio as determined from the observed 2212 keV c-ray intensity (subtracting the contribution from the decay of the 3004 keV state with a known 12% branching ratio) ranged between 0.1% and 7% (max and min, including uncertainties), with a median value of 1%. While there is flux at lower energies, further refinements to the present detector response model are needed in order to accurately determine it from the Compton scatter spectrum. An alternative to the above method is possible because a ratio was taken, which cancels out the efficiency. An integral of counts above a threshold could be taken for equal effect as any measure of the number of counts in the spectrum can be used as long as that measure is directly proportional to the incident flux. Care would be needed, however, because if the beam energy shifts between measurements then it will no longer be true that the measurement efficiency is the same for each measurement. Monitoring the energy of the Compton scattering peak could be done to compensate for such changes in beam energy. We tested using the integral of counts, following pileup and background subtraction, over the interval of 2 MeV to just above the Compton peak. This resulted in an average deviation of 1% between the two methods, within the systematic uncertainty related with the number of counts in the monitor detector (see below). The Compton scattered spectrum was also used to measure the beam profile. The position and width of the Compton scattered
C.T. Angell et al. / Nuclear Instruments and Methods in Physics Research B 347 (2015) 11–19
peak are correlated with the position and width of the beam profile. The properties of the Compton scatter peak were determined by de-convolving the spectrum (as described above). The correlation of those parameters to those of the incident beam was calibrated by comparing the position and width of the directly measured beam profile with that of the Compton scattered peak measured in close succession to the beam profile measurement. Having the calibration measurement in close proximity reduces the likelihood that the beam profile changed between the two measurements. This calibration was done at both beam energies. See Ref. [28] for more details. 2.4.2. Statistical and systematic uncertainties The uncertainties for absorption ratio included both statistical and systematic sources of uncertainty. The statistical uncertainty for absorption was due to the uncertainty in the measured counts in the NRF peak. The uncertainty from a fit using a Gaussian peak and a flat background was used. For the largest peaks (>104 counts), the fit under-reported the uncertainty, so the square root of counts was used instead. The systematic uncertainty included that from the variation in the beam energy profile and from pileup in the number of counts in the monitor detector. The beam energy profile systematic uncertainty was due to variation in its mean energy and width, and was determined by comparing the variation in the ratio of the 2982 keV peak to the 3004 keV peak intensity. It was on order of 3%. The systematic uncertainty of the number of counts in the monitor detector was dominated by pileup subtraction. The systematic uncertainty induced in a spectrum by pileup subtraction was determined to be maximally 20% of the pileup amount. This was determined from the variance in the spectrum sum over the region of the Compton peak when the pileup amount was allowed to vary by 7%. This variance in the pileup amount was taken as the average difference between determining it by fitting compared with determining it from the detector rate [29]. The above maximal uncertainty was used for all cases to be consistent. The final systematic uncertainty in the number of counts in the monitor detector ranged from 0% to 4%. 3. Results We compared the experimental absorption amount (1 Rðna Þ) determined using Eq. (6) with that expected theoretically from Eq. (4) using the known resonance parameters [17] and the inserted Al absorption areal density (see Table 2 and Figs. 7 and 8). This showed that for each measurement (except Pb) the mea-
17
sured absorption values are consistent with expectation. This is reinforced in Fig. 4, which plots the calculated increase in absorption, 1 Rðna Þ, for the 2982 keV state as a function of Al thickness, along with the experimentally measured values. At Ec ¼ 2982 keV, the absorption ratios for SS and water are consistent with no absorber present. The Pb measurement is slightly outside expectation even when systematic uncertainty is included. The experimental absorption ratio for absorbing materials where measurements without and with a Pb shielding wall existed (Al, concrete, and canister scenario) were weighted to determine a single absorption ratio for that material. The statistical and systematic uncertainties were separately determined using a weighted mean. No absorption ratios are reported for the 3004 keV state because of the small width (e.g. integrated cross section) of the state. The absorption ratio depends jointly on the mass of the Al in the absorbing target and the width of the state (see Eq. (2)). A resonance with a small width will be significantly less absorbing than a resonance with a large width. The 3004 keV state has a width (i.e. integrated cross section) that is an order of magnitude smaller than that of the 2982 keV state (see Fig. 7). There was a discrepancy between the integrated cross section of the 3004 keV state in the literature and that measured here in ratio to the 2982 keV state; the results of that analysis were published in Ref. [28]. The signature of resonance overlap—an absorption ratio smaller than expected—was not seen in the present experiment. This places an upper limit of about 4% absorption (the maximum combined uncertainty) on a possible contribution of overlapping resonances for the present combination of materials. Given that resonance overlap occurs randomly, this present result would be expected to apply, on average, to other combinations of materials as well, particularly for the IRT method, which uses the sum of many resonances. Nevertheless, in an application setting, calibration measurements constraining the contribution of resonance overlap in an absorption measurement will be needed for each combination of IOI and absorbing materials. The present measurement of Al absorption in concrete is symbolic of measuring the resonance absorption due to the fissile content in spent nuclear fuel, and demonstrates that it is, in principle, possible to do so. The Al in the concrete is mixed through out the material, and is a relatively small fraction of the total by weight (3%). The fissile content, 239Pu for example, is similarly mixed through out the spent fuel, and is a small fraction of the total amount of material in the spent fuel (1%). There was about
Table 2 Expected and measured absorption amounts (1 Rðna Þ) of the 2212 keV and 2982 keV resonances in 27Al for the several measured samples. Absorption in the concrete was calculated assuming the typical 2% concentration by weight. A larger absorption amount (smaller absorption ratio, Rðna Þ) indicates a greater concentration of Al. The canister absorption value is the same as that of the concrete as it used the same sample. Statistical and systematic uncertainties are given for each value. Expected absorption amounts of ‘0’ are stated for cases where no Al was in the absorbing target. Material
Aluminum
2212 keV
2982 keV
Expected
Measured
0.282 ± 0.004
0:310:01 0:03
stat sys
Expected
Measured
0.345 ± 0.006
stat sys 0:01 stat 0:050:02 sys stat 0:010:01 0:05 sys 0:01 stat 0:080:06 sys stat 0:020:01 0:05 sys stat 0:010:01 0:03 sys
Concrete
0.04 ± 0.01
SS (304)
0
Lead
0
Water
0
Canister
0.04 ± 0.01
0:3580:005 0:020
Fig. 7. The NRF scattering peaks observed for a beam energy of Ec ¼ 2:983 MeV for no absorber (N/A), Al absorber, concrete, and absorbers representing the canister (concrete, stainless steel, Pb, and water). The spectra were normalized for the same amount of incident flux. Only significant absorption was seen when using the Al absorber, as expected.
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C.T. Angell et al. / Nuclear Instruments and Methods in Physics Research B 347 (2015) 11–19
mentary measurements of the resonances at Er ¼ 2212 keV and 2982 keV using an Al absorber verified the resonance absorption calculations. The present results suggest that resonance overlap will not be a significant issue for using a transmission NRF measurement to assay, for example, long-stored SNF in a storage canister, or the Fukushima melted fuel debris in its final deposition canister. It also demonstrates the practicality of using NRF to assay material inside of a storage canister designed for radioactive material. Further work is needed for developing the IRT method more fully, particularly for calculating the average sensitivity to resonance overlap when using the method. This measurement also highlighted the need to significantly reduce the systematic uncertainties of an NRF measurement so that a transmission measurement of the 239Pu in fuel debris stored inside a TMI-2 canister will be feasible. Fig. 8. The same as Fig. 7 for Ec ¼ 2:205 MeV, and for no absorber and Al absorber cases.
1 1022 atoms/cm2 of 27Al in the concrete. In contrast, there would be about 1 1021 atoms/cm2 of 239Pu in a TMI-2 canister loaded with fuel debris [12], assuming the heavy metal content is 1% 239 Pu, by weight. The corresponding resonant absorption ratio for the 13 eV b resonance at 2143 keV would be 0.995 (or 1 Rðna Þ ¼ 0:005). An assay measurement of Pu would have the added difficulty that the atomic elastic scattering contribution to the scattering target would be substantially larger, interfering with the NRF signature. The atomic elastic scattering cross section scales by Z 2 , becoming sizable for actinide elements. For U, it reaches 50 lb/sr for 2.1 MeV c rays at 120° [30]. The primary effect will be to decrease the signal to noise ratio, resulting in even longer measurement times than would be otherwise expected [7]. If the absorption measurement due to such a small concentration of 239Pu were to be attempted, significant reduction in the presently measured uncertainties would be needed. The statistical uncertainty measured in the present experiment could be significantly suppressed from the current ±0.01 value if the proposed next generation c-ray sources were available. A source based on a compact energy recovery linac and using a Fabre–Pérot cavity for the primary laser is expected to generate a c-ray beam 4 orders-of-magnitude brighter than the presently used source [14]. The systematic uncertainty due to pileup correction could be eliminated by eliminating the need for such corrections. Using fast scintillator detectors with waveform digitizing electronics would achieve this [21]. The uncertainty associated with determining the beam profile of a quasi-monoenergetic source is more difficult to suppress. The beam profile could be directly determined, however, from the properties of the electron beam and laser beam. Determining the beam profile directly from those properties, rather than through a secondary measurement of Compton scattering, could significantly reduce the uncertainty related with determining the beam profile. Additionally, taking a ratio of resonances simultaneously excited by the beam would reduce the systematic uncertainties associated with determining the beam profile (see e.g. Ref. [28], which demonstrates this idea using the present data for the 2982 keV and 3004 keV resonances). If two nearby resonances are not available in a single isotope, an additional isotope could be added to the transmission measurement station to add a second resonance near the resonance of interest for such a comparison.
4. Summary In summary, no resonance overlap for the 2982 keV Al resonance in the simulated canister scenario was observed. Comple-
Acknowledgments We would like to acknowledge the excellent service and beams provided by the staff at the High Intensity c-ray Source, and M. Emamian for help with target preparation. This study was supported by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan.
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