Unfolding of sparse high-energy γ -ray spectra from LaBr 3 :Ce detectors
P.-A. Söderström, L. Capponi, V. Iancu, D. Lattuada, A. Pappalardo, G. V. Turturică, E. Açıksöz, D. L. Balabanski, P. Constantin, G. L. Guardo, M. Ilie, S. Ilie, C. Matei, D. Nichita, T. Petruse, A. Spataru
PPrepared for submission to JINST
Unfolding of sparse high-energy γ -ray spectra fromLaBr :Ce detectors P.-A. Söderström, a L. Capponi, a V. Iancu, a D. Lattuada, a , b , c A. Pappalardo, a G. V. Turturică, a , d E. Açıksöz, a D. L. Balabanski, a P. Constantin, a G. L. Guardo, a , c M. Ilie, d , e S. Ilie, a , d C. Matei, a D. Nichita, a , d T. Petruse, a , d and A. Spataru a , d a Extreme Light Infrastructure-Nuclear Physics (ELI-NP), Horia Hulubei National Institute for R&D inPhysics and Nuclear Engineering (IFIN-HH), Reactorului 30, 077125 Bucharest-Măgurele, Romania b Universitá di Enna Kore, Enna 94100, Italy c Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali del Sud, Catania 95125, Italy d Politehnica University of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania e Tandem Accelerators Department (DAT), Horia Hulubei National Institute for R&D in Physics and NuclearEngineering (IFIN-HH), Reactorului 30, 077125 Bucharest-Măgurele, Romania
E-mail: [email protected]
Abstract: Here we report on the characterization of one of the large-volume LaBr :Ce detectorsfor the ELIGANT project at ELI-NP. The main focus of this work is the response function forhigh-energy γ rays of such detectors. In particular, we compare a selection of unfolding methodsto resolve small structures in γ -ray spectra with high-energies. Three methods have been comparedusing γ -ray spectra with energies up to 12 MeV obtained in an experiment at the 3 MV Tandetron™facility at IFIN-HH. The results show that the iterative unfolding approach gives the best qualitativereproduction of the emitted γ -ray spectrum. Furthermore, the correlation fluctuations in high-energy regime from the iterative method are two orders of magnitude smaller than when using thematrix inversion approach with second derivative regularization. In addition, the iterative method iscomputationally faster as it does not contain large matrix inversions. The matrix inversion methoddoes, however, give more consistent results over the full energy range and in the low-statisticslimit. Our conclusion is that the performance of the iterative approach makes it well suitable forsemi-online analysis of experimental data. These results will be important, both for experimentswith the ELIGANT setup, and for on-line diagnostics of the energy spread of the γ -ray beam whichis under implementation at ELI-NP.Keywords: Gamma detectors, Analysis and statistical methods Corresponding author. a r X i v : . [ phy s i c s . i n s - d e t ] O c t ontents The Extreme Light Infrastructure – Nuclear Physics (ELI-NP) [1] facility currently under imple-mentation in Romania will be a unique European laboratory for photonuclear physics. One ofthe projects being constructed under the ELI-NP umbrella is ELI Gamma Above Neutron Thresh-old (ELIGANT). ELIGANT, especially the ELIGANT Gamma Neutron (ELIGANT-GN) [2–4]setup, will focus on competing γ -ray and neutron emission in photonuclear reactions. The goalof ELIGANT-GN is the detailed study of the high-energy photo-excitation response of atomic nu-clei with focus on the giant dipole resonance (GDR), pygmy dipole resonance (PDR), and similarstructures through simultaneous measurements of neutron and γ -ray decay-channels. The narrow-bandwidth nature of the proposed γ -ray beam [5] will provide a unique opportunity to scan theGDR and PDR with a well defined energy, in many cases smaller than the typical energy resolutionof scintillator detectors. This means that the ELIGANT collaboration will be able to, for example,study in detail the decay branching of the GDR fine structure [6] and the PDR to the ground, 0 + ,state and the first excited, 2 + , state for even-even nuclei. The detection of different γ branchesto the first 0 + and 2 + states is straightforward in some doubly magic cases, like Pb, where theexcitation energy of the first excited state is around 4 MeV. However, if we want to explore similartopics in slightly deformed nuclei, the energy difference between the ground state transition andthe transition to excited states will be smaller and the signal of interest may be hidden under theresponse of the γ -ray detector.Another important aspect in the evaluation of future experimental data is the properties of thebeam itself. It was, indeed, noted in a report by the International Atomic Energy Agency (IAEA) [7]that one of the major sources of observed systematic disagreements in the evaluation of photonucleardata was the differences in photon spectra where the cross-sections were derived by unfolding ofthe data. This triggered a new large-scale experimental campaign for re-measuring several key– 1 –lements [8]. At ELI-NP a large beam diagnostics program is under development with severalinstruments being implemented. For example, one proposed instrument that will measure theabsolute energy as well as the energy spread of the γ -ray beam is a large volume high-puritygermanium (HPGe) or LaBr :Ce detector with anti-Compton shield placed directly in the beam,following an attenuator [5]. In order to have control of the beam properties it is important to quicklyunderstand the underlying beam spectrum from the measured spectrum of the monitoring detector.Another proposed instrument based on a similar principle, but using a Compton scattered beamcomponent instead of the attenuated main beam, has been reported in Reference [9]. In that worka HPGe detector was used for monitoring the beam intensity from comparing experimental data toGeant4 simulations. For both of these types of instruments it can be desirable to have a fast andaccurate evaluation for control of beam parameters.In previous work, the ELIGANT-GN detectors have been thoroughly characterized in the low-energy regime in the context of the ELIGANT Gamma Gamma (ELIGANT-GG) [10] setup forstudies of competitive double- γ decay [11, 12]. In the high-energy regime, the response functionand linearity of larger volume LaBr :Ce detectors were investigated in the energy range 6 −
38 MeVby direct measurements at the NewSUBARU synchrotron radiation facility [13].Here we will report on an experiment for testing the high-energy response of the ELIGANT-GNdetectors with particular focus on different methods of unfolding the experimental spectra to resolvesmall structures.
The experiment was performed at the 3 MV Tandetron™ facility at the Horia Hulubei NationalInstitute of Physics and Nuclear Engineering (IFIN-HH), Măgurele, Romania [14]. The γ rays usedfor this study were obtained from a 1.05 MeV proton beam with an average beam current of 11.6 µ Aimpinging on a composite target of Al and CaF with a mass ratio of 99% and 1%, respectively [15].This produced γ rays in three energy groups, around 2 MeV and 11 MeV from the Al ( p , γ ) Sireaction and around 7 MeV from the F ( p , γα ) O reaction. One ELIGANT-GN detector was usedfor this measurement, which consisted of a 3 × :Ce crystal coupled with a HamamatsuR11973 photomultiplier tube (PMT) and a AS20 voltage divider. The signals from the detectorswere read out by a CAEN v1730 digitizer using a sampling frequency of 500 MS/s and a resolutionof 14 bits.The experiment was performed concurrently to another experiment aiming for effective Z evaluation of an unknown material [15]. Thus, the geometry of the experimental setup, shown inFigure 1, was such that the LaBr :Ce detector was not aligned with the front-face of the detector inthe direction of the reaction target. Instead, the ELIGANT-GN detector was placed at an angle of90 degrees relative to the beam axis at a distance of 40 cm from the target, 20 cm below the beam.This was taken into careful consideration in the Geant4 simulations used to construct the detectorresponse. As a consequence, the single- and double escape peaks in the energy spectrum wereapproximately a factor of 50% larger relative to what is expected when the detector is directly facingthe source, as in the ELIGANT-GN design. The energy spectrum obtained from this experiment isshown in Figure 1. – 2 –
000 4000 6000 8000 10000 12000 14000 (keV) g E10 C oun t s / k e V Figure 1 . (Left) Energy spectrum obtained in the LaBr :Ce detector in the 250 keV to 15 MeV range.(Right) Experimental setup with the measurements for industrial applications [15] shown in blue and themeasurement for high-energy response of the ELIGANT detectors shown in red. As a first step in the calibration of the detector, a linear calibration was carried out only using the511 keV peak from positron annihilation and the 1779 keV peak from the 2 + → + transition in Si from the Al ( p , γ ) Si reaction. The full energy calibration was performed using the strongestpeaks of the known γ -ray transitions following the two reactions: 511 keV, 1779 keV, 6130 keV,6917 keV, 7117 keV, and 10760 keV. In addition, we also used the first and second escape peakof the 6130 keV transition , and the first escape peaks of the 6917 keV, 7117 keV, 10760 keV, and12331 keV transitions. For this purpose, a second-order polynomial was used to correct the linearcalibration.The basic idea behind the unfolding of experimental data is that if there is a histogram of anemitted spectrum, (cid:174) x , separated into n bins, this spectrum can be measured by a detector with an n × m response matrix, A , resulting in a measured spectrum, (cid:174) y , in a histogram consisting of m bins,as (cid:174) y = A (cid:174) x . (3.1)If the detector response is linear, as it can be approximated in the low-energy regime, the interpre-tation of (cid:174) y is straightforward as each bin directly corresponds to an emitted energy given a finitedetector resolution. If this data is non-linear, as is the case in the high-energy regime, (cid:174) y contains alarge contribution from physics processes such as Compton scattering and electron/positron escapein addition to the full energy deposition. In these cases, the response A has to be properly charac-terized to understand the data. For this work, we used Geant4 simulations [16] (version 10.05) toobtain A via the dedicated Geant4 and ROOT Object-Oriented Toolkit (GROOT) software devel-oped for ELI-NP [17]. For this purpose a desktop computer with 7.7 GB of memory and an Intel®Xeon® Processor E5-1620 with a clock frequency of 3.7 GHz, running Ubuntu 18.04.2 was used.This is the same hardware and software that was used in Reference [10] where detector efficiencieswere well reproduced up to an energy of 1.4 MeV. Due to the small amount of material present inthe experimental area, see Figure 1, we simplified the setup by only considering the active detectorvolume in the previously described geometry. The simulations were performed in steps of 5 keV,between 250 keV and 15 MeV, with 100 000 γ -rays emitted in the detector direction for each energy– 3 –or a total of 295 . · events and, approximately, seven days of computer time. The energy of thedetected γ rays were randomly shifted in energy based on a Gaussian distribution with the measuredenergy resolution for each event. The energy resolution was obtained from the experimental datausing the same transitions as for the energy resolution and interpolated as σ E γ E γ = (cid:115) E γ N phe ( + (cid:15) PMT ) + σ , (3.2)based on the discussion in Reference [18], with fitted parameters N phe = . − , (cid:15) PMT = . σ noise = . N phe ), the variance of the PMT ( (cid:15) PMT ), anda generic noise term ( σ noise ) originating from electronics and similar. Note that these values arejust fitted to interpolate the energy resolution of the detector, and should not be considered reliablemeasurements of the physical quantities. They are, however, similar in magnitude to what we expectthem to be in a dedicated evaluation. Finally, the spectrum of detected γ -rays were normalized toone for each emitted energy, to maintain the number of events in the spectrum after unfolding.
400 600 800 1000 1200 (keV) g Detected E00.010.020.030.040.050.060.07 R e s pon s e =1000 keV g Emitted E 2000 4000 6000 (keV) g Detected E00.0010.0020.0030.0040.0050.006 R e s pon s e = 7000 keV g Emitted E 5000 10000 (keV) g Detected E00.00050.0010.00150.002 R e s pon s e = 14000 keV g Emitted E
Figure 2 . Projection of the response matrix for emitted γ -ray energies of 1000 keV (left), 7000 keV (middle),and 14000 keV (right). The projections of the response matrix at three selected energies are shown in Figure 2. Asexpected the full-energy peak is dominating the response matrix at low energies. At a few MeV γ -ray energy a significant part of the energy deposition is starting to go into the single escapepeak and the Compton edge, while remaining distinguishable features. Above a γ -ray energy ofapproximately 10 MeV the energy deposition in the full-energy peak is strongly reduced and themeasured spectrum is dominated by Compton scattering with a minor fine structure coming from theescape peaks. Besides these features the projection of the spectra are rather smooth and featureless.This is due to the simplified geometry used in this work, motivated by the small amount of materialthat could induce secondary scattering in this setup. Another motivation for this simplification wasthat the low-energy thresholds in the data acquisition was at 200 keV, and the lower edge of thehistograms used for the analysis at 250 keV. These are the energies where structures originatingfrom, for example, backscattering typically appear. Thus, this simplification is expected to onlyhave minor influence at the low-energy edge of the acquired and subsequently unfolded histograms.– 4 – The matrix inversion method
The most straightforward way to obtain the true spectrum, (cid:174) x , given a measured spectrum, (cid:174) y , and aresponse matrix A is by the matrix inversion method [19, 20], (cid:174) x = A − (cid:174) y , (4.1)where we define the relation between covariance matrices V x , y as V x = A − V y (cid:16) A − (cid:17) T . (4.2)In the following discussion, V y is assumed to be the identity matrix. While this method is, inprinciple, perfect, the mathematical nature of inverse matrices will introduce large alternatingpositive and negative values in A − due to very strong negative correlations in V x . Thus, whilethe unfolded spectrum, shown in the top section of Figure 3, from a statistical point of viewis completely correct it is not very useful for evaluation of the experimental data. While not atopic within the scope of this report, note that these large negative and positive values, althoughunphysical, contain important correlations in the covariance matrix and need to be kept for anypropagation of uncertainties to be correct, for the methods evaluated here. g E40 - - · C oun t s / k e V Matrix raw g E1000 - · C oun t s / k e V Matrix L1 g E1000 - · C oun t s / k e V Matrix L2
Figure 3 . (Top) Unfolded energy spectrum using the matrix inversion method without regularization.(Bottom left) Same as the top spectrum but with Thikhonov-Phillips regularization of strength τ = − .(Bottom right) Same as the top spectrum but with second derivative regularization of strength τ = − – 5 –ne common solution to this is to make the solution less perfect by introducing a regularizationparameter, τ , that smooths out A − and reduces the correlations of V x [21]. There are severalmethods to do this, but in this work we will look at two simple cases. The first is the Thikhonov-Phillips regularization [22, 23] where τ is introduced as a constant to the identity matrix, , as A T V − y (cid:174) y = (cid:16) A T V − y A + τ (cid:17) (cid:174) x . (4.3)This will smooth the solution with respect to (cid:174) x , as shown in the bottom left of Figure 3. We willrefer to this method as Matrix L1 hereafter. The other approach is to smooth the solution withrespect to the second derivative of (cid:174) x [21] using the matrix L of size n × m + A T V − y (cid:174) y = (cid:16) A T V − y A + τ L T L (cid:17) (cid:174) x . (4.4)In this case L is constructed so that for each row (cid:174) L n = ( , . . . , L n , m = , L n , m + = − , L n , m + = , , . . . ) . Applying equation (4.4) to A and (cid:174) y from Figure 1, with τ = − , produces the emissionspectrum, (cid:174) x , shown in the bottom right of Figure 3. We will refer to this method as Matrix L2hereafter. Two major drawbacks of the matrix inversion procedure are the need for regularization, and thevery computationally intense processes of large matrix inversion. To avoid these issues the iterativeunfolding procedure [24, 25] has been implemented within the framework of the Oslo method forexperiments on level densities and γ strength functions [26–28]. A detailed discussion about thepossible systematic errors in the Oslo method can be found in Reference [28]. This method hastypically been used successfully for unfolding of high γ -ray density spectra with γ -ray energiesup to 7 MeV [29–31] with some examples up to 10 MeV [32]. In Reference [27] the method isevaluated for discrete γ -ray spectra following the decay of Eu up to γ -ray energies of 1.4 MeV.The iterative unfolding procedure is based on successive refolding of a starting guess spectrum.We call the unfolded spectrum in an iteration i , (cid:174) x (cid:48) i and a refolded spectrum (cid:174) y (cid:48) i . For a starting guess,usually (cid:174) x (cid:48) = (cid:174) y can be used. This gives the first step of the procedure as (cid:174) y (cid:48) = A (cid:174) x (cid:48) = A (cid:174) y . (5.1)In the next iteration the starting guess is modified as (cid:174) x (cid:48) = (cid:174) x (cid:48) + (cid:0) (cid:174) y − (cid:174) y (cid:48) (cid:1) , (5.2)and the procedure is repeated for each iteration i (cid:174) x (cid:48) i = (cid:174) x (cid:48) i − + (cid:0) (cid:174) y − (cid:174) y (cid:48) i − (cid:1) , (cid:174) y (cid:48) i = A (cid:174) x (cid:48) i , (5.3)until convergence. Typically the iterative process is repeated tens of times before it converges. Inthis work, however, since we are mainly interested in the high-energy response, a larger number of– 6 –
000 4000 6000 8000 10000 12000 14000 keV g E1000 - · C oun t s / k e V Iterative g E0500010000150002000025000 C oun t s / k e V Figure 4 . (Left) Unfolded energy spectrum using the iterative approach. (Right) Measured raw spectrumin the high-energy regime (red) and decomposed into the full-energy component (solid black), Comptoncomponent (dotted black), single-escape events (blue) and double-escape events (green). Three peaks havebeen identified in this spectrum marked with 1, 2, and 3, respectively. iterations was necessary before convergence of the high-energy part. Thus, a Kolmogorov-Smirnovtest [33, 34] with a cut-off at a Kolmogorov similarity of α = . σ , betweenthe original and unfolded-refolded spectra was employed to define convergence. Using A and (cid:174) y from Figure 1, the result after 197 iterations is shown in Figure 4.The existence of two peak-like structures around 10 MeV can clearly be seen in the unfoldedspectrum. In Figure 4 we show the spectrum in this region with a decomposition into the full-energypeak, the single- and double-escape peaks, and the Compton continuum. We see that the secondpeak is hidden under the distribution from the larger peak at slightly higher energy in the rawspectrum, clearly identified in the decomposed distributions. To qualitatively estimate the performance of the different unfolding algorithms, the same decom-position as in Figure 4 into different components was performed for all three unfolding methods.To verify that the observed hidden structure is not only an artifact from the unfolding algorithms,or imperfections in the energy calibration of the experimental data, we compare the results to dataobtained by a HPGe detector under the same experimental conditions. The results from these de-compositions are shown in Figure 5. It is clear from the HPGe spectrum that there are, indeed, twominor structures from other silicon resonances, close in energy with a similar intensity as obtainedby the LaBr :Ce spectrum at this energy.Comparing the three different methods qualitatively we note from Figure 5 that all of themidentify the small structure at lower energies. However, we also note that the Thikhonov-Phillipsregularization scheme underestimates the height of the peaks while giving a broader distribution.This is not unexpected as the regularization is performed by smoothing (cid:174) x directly. The second-derivative regularization more accurately reproduces the width and the height of the main peak.Both of these schemes, however, significantly overestimate the size of the hidden lower-energystructure compared to what was obtained from the HPGe data, as well as dropping below zero– 7 – g E050001000015000 C oun t s / k e V Matrix L1 -5 =10 t -4 =10 t -3 =10 t g E050001000015000 C oun t s / k e V -3 =10 t -4 =10 t -5 =10 t Matrix L2 10000 10200 10400 10600 10800 (keV) g E050001000015000 C oun t s / k e V Iterative10000 10200 10400 10600 10800 (keV) g E050001000015000 C oun t s / k e V Matrix L1 -5 =10 t -4 =10 t -3 =10 t g E050001000015000 C oun t s / k e V -3 =10 t -4 =10 t -5 =10 t Matrix L2 10000 10200 10400 10600 10800 (keV) g E050001000015000 C oun t s / k e V Iterative
Figure 5 . Raw energy (red), full-energy deposition (black), and single-escape (blue) spectra in the highenergy regime for the Thikhonov-Phillips matrix regularization (Matrix L1, left), the second derivativeregularization (Matrix L2, middle) and the iterative unfolding procedure (right). The purple spectrum showsHPGe data obtained in similar experimental conditions. The bottom row is the same as the top row, but herethe full-energy peaks in the HPGe spectrum have been refolded with the LaBr :Ce full-energy peak responseand renormalized to the same intensity. at the tails of the distributions. Aside from not reproducing the expected slight shift of the peaktowards lower energies, something that both matrix inversion methods do, the best qualitativeagreement between the HPGe and the LaBr :Ce data is given by the iterative approach. Here thehidden features are well reproduced in magnitude, although giving a slightly too prominent peak,something that is also observed in the second-derivative regularization. Furthermore, there is asensitivity in the results from the matrix algorithms with respect to the choice of τ , in particular forthe Thikhonov-Phillips regularization, that is not present in the parameter-free iterative approach.A more quantitative comparison of the quality between the different unfolding methods canbe obtained by examining the size of the positive-negative fluctuations in the spectra originatingfrom the negative correlations in the unfolding procedure. This comparison is done using theroot-mean-square (RMS) of the unfolded spectrum in the intermediate energy ranges where we donot expect any significant peaks. The RMS values for all three methods are listed in Table 1. Forthis particular type of spectrum, the fluctuations are more evenly distributed in the matrix unfoldingapproach, while in the iterative approach the fluctuations are pushed towards lower energies. Thesize of the fluctuations for the low-energy part of the spectra using the iterative approach are aboutfour and two times the size of the fluctuations from the Thikhonov-Phillips matrix regularizationand the second-derivative regularization, respectively. In the intermediate energy range all thethree methods give fluctuations of similar magnitude. For the high-energy range the fluctuations– 8 – able 1 . Kolmogorov similarity (KS) and root-mean-square (RMS) values in the energy ranges 3-5 MeV,8-10 MeV, and 13-15 MeV for the three different unfolding methods evaluated in this work. Method KS RMS 3-5 RMS 8-10 RMS 13-15Unregularized 820000 240000 26000Matrix L1 τ = − τ = − τ = − τ = − τ = − τ = − τ = − τ = − τ , both ofthe regularization schemes give very high Kolmogorov similarity. Thus, while the Kolmogorovsimilarity is a good indicator of the general quality of the result, it does not guarantee that detailsof the underlying spectra are well reproduced, as shown in Figure 5. g E20 - C oun t s / k e V -2 · g E5 - C oun t s / k e V -3 · g E05 C oun t s / k e V -4 · Figure 6 . Performance of the unfolding algorithms with a subset of the data corresponding to a reduction ofa factor of 10 − (left), 10 − (middle), and 10 − (right) in statistics. The black line correspond to the iterativemethod, red line correspond to Matrix L1, and blue line correspond to Matrix L2. The purple spectrumshows HPGe data obtained in similar experimental conditions, refolded with the LaBr :Ce full-energy peakresponse and renormalized to the same intensity. To investigate the effects of statistical fluctuations on the performance of the different algorithmswe have repeated the unfolding processes for three different sub-sets of the data. These three sub-sets were selected to contain a factor of 10 − , 10 − , and 10 − of the events. This correspond to apeak height for the full-energy peak of 100 counts, ten counts, and one count with bin sizes of 5 keV,respectively. The results of these procedures are shown in Figure 6, where the spectra have been– 9 –e-binned for clarity. For the first case the performance of the three methods is similar to the casewith full statistics. In all three cases the iterative method generally follow the trend of the re-foldedHPGe spectrum. However, with a data reduction of 10 − large-scale oscillations start to appearfor the second-derivative regularization and the iterative method. All three methods overestimatethe size of the peak in the extreme case with a 10 − reduction of the data. As a general trend, theThikhonov-Phillips regularization appears as the most stable method in the low-statistics limit. We have performed a qualitative and quantitative comparison between three different unfoldingschemes for γ -ray spectra from LaBr :Ce detectors in the high-energy regime. The results showthat, for γ -rays around 10 MeV the iterative approach gives more reliable reconstruction of hiddenfine-structures in the emission spectrum as well as smaller correlated fluctuations of the data relatedto the unfolding process. The results of the unfolding, with emphasis on the identification of hiddenstructures, is furthermore parameter free in the iterative approach and does, thus, not depend onthe somewhat arbitrary choice of a regularization parameter. In addition, this approach has theadvantage of being computationally relatively fast, making it suitable for fast evaluation of semion-line data for physics experiments and diagnostics of a γ -ray beam.Finally we would like to add a general note of caution that the choices of type of regularization,as well as the strength of the regularization, depends on the type of data and analysis that isperformed. All three cases presented here will introduce a bias to the unfolded data, especially ifover-regularized, or if the iterative procedure is stopped too early. This report has discussed theunfolding strategies in terms of sparse high-energy spectra from LaBr :Ce detectors. For practicalimplementation in other setups, for example providing spectra with very narrow peaks and sharpstructures or smooth low-resolution spectra with high γ -ray densities, it is important that the chosenmethod is evaluated for the intended application. Acknowledgments
The authors would like to acknowledge the support from the Extreme Light Infrastructure NuclearPhysics (ELI-NP) Phase II, a project co-financed by the Romanian Government and the EuropeanUnion through the European Regional Development Fund - the Competitiveness Operational Pro-gramme (1/07.07.2016, COP, ID 1334). We acknowledge A. Imreh from the Technical Division atELI-NP for the CAD drawings of the detector system used for Figure 1.
References [1] S. Gales, K. A. Tanaka, D. L. Balabanski, F. Negoita, D. Stutman, O. Tesileanu et al.,
The extremelight infrastructure–nuclear physics (ELI-NP) facility: new horizons in physics with 10 PWultra-intense lasers and 20 MeV brilliant gamma beams , Rep. Prog. Phys. (2018) 094301.[2] F. Camera, H. Utsunomiya, V. Varlamov, D. Filipescu, V. Baran, A. Bracco et al., Gamma above theneutron threshold experiments at ELI-NP , Rom. Rep. Phys. (2016) S539. – 10 –
3] M. Krzysiek, F. Camera, D. M. Filipescu, H. Utsunomiya, G. Colò, I. Gheorghe et al.,
Simulation ofthe ELIGANT-GN array performances at ELI-NP for gamma beam energies larger than neutronthreshold , Nucl. Instrum. Meth. Phys. Res.
A916 (2019) 257.[4] M. Krzysiek, E. Açıksöz, D. L. Balabanski, F. Camera, L. Capponi, G. Ciocan et al.,
Photoneutronmeasurements in the GDR region at ELI-NP , AIP Conf. Proc. (2019) 040004.[5] H. R. Weller, C. A. Ur, C. Matei, J. M. Mueller, M. H. Sikora, G. Suliman et al.,
Gamma BeamDelivery and Diagnostics , Rom. Rep. Phys. (2016) S447.[6] A. Tamii, I. Poltoratska, P. von Neumann-Cosel, Y. Fujita, T. Adachi, C. A. Bertulani et al., CompleteElectric Dipole Response and the Neutron Skin in
Pb,
Phys. Rev. Lett. (2011) 062502.[7]
Handbook on Photonuclear Data for Applications: Cross-sections and Spectra, Final report of aco-ordinated research project 1996 - 1999, IAEA-TECDOC-1178 , 2000.[8] T. Kawano, Y. S. Cho, P. Dimitriou, D. Filipescu, N. Iwamoto, V. Plujko et al.,
IAEA PhotonuclearData Library 2019 , 2019. arXiv:1908.00471 [nucl-th] [9] G. Turturica, C. Matei, A. Pappalardo, D. Balabanski, S. Chesnevskaya, V. Iancu et al.,
Investigationof Compton scattering for gamma beam intensity measurements and perspectives at ELI-NP , Nucl.Instrum. Meth. Phys. Res.
A921 (2019) 27.[10] P.-A. Söderström, L. Capponi, E. Açıksöz, D. L. Balabanski, G. L. Guardo, D. Lattuada et al.,
Sourcecommissioning of the ELIGANT-GG setup for γ -ray coincidence measurements at ELI-NP , Rom. Rep.Phys. (2019) 206.[11] M. Göppert-Mayer, Über elementarakte mit zwei quantensprüngen , Ann. Phys (1931) 273.[12] C. Walz, H. Scheit, N. Pietralla, T. Aumann, R. Lefol and V. Y. Ponomarev, Observation of thecompetitive double-gamma nuclear decay , Nature (2015) 526.[13] G. Gosta, N. Blasi, F. Camera, B. Million, A. Giaz, O. Wieland et al.,
Response function and linearityfor high energy γ -rays in large volume LaBr :Ce detectors , Nucl. Instrum. Meth. Phys. Res.
A879 (2018) 92.[14] I. Burducea, M. Straticiuc, D. G. Ghit , ă, D.V.Mos , u, C. I. Călinescu, N. C. Podaru et al., A new ionbeam facility based on a 3 MV Tandetron at IFIN-HH, Romania , Nucl. Instrum. Meth. Phys. Res.
B359 (2015) 12.[15] G. V. Turturica, V. Iancu, A. Pappalardo, P.-A. Söderström, L. Guardo, D. Lattuada et al., “Effective Z evaluation using proton induced monoenergetic gamma rays and neural networks.” In manuscript.[16] S. Agostinelli, J. Allison, K. Amako, J. Apostolakis, H. Araujo, P. Arce et al., Geant4 –a simulationtoolkit , Nucl. Instrum. Meth. Phys. Res.
A506 (2003) 250.[17] D. Lattuada, D. L. Balabanski, S. Chesnevskaya, M. Costa, V. Crucillà, G. L. Guardo et al.,
A fast andcomplete GEANT4 and ROOT Object-Oriented Toolkit: GROOT , EPJ Web Conf. (2017) 01034.[18] M. Moszyński, A. Syntfeld-Każuch, L. Swiderski, M. Grodzicka, J. Iwanowska, P. Sibczyński andT .Szcz ˛eśniak,
Energy resolution of scintillation detectors , Nucl. Instrum. Meth. Phys. Res.
A805 (2016) 25.[19] N. Starfelt and H. W. Koch,
Differential Cross-Section Measurements of Thin-Target BremsstrahlungProduced by 2.7- to 9.7-MeV Electrons , Phys. Rev. (1956) 1598.[20] P. C. Fisher and L. B. Engle,
Delayed Gammas from Fast-Neutron Fission of Th , U , U , U ,and Pu , Phys. Rev. (1964) B796. – 11 –
21] V. Blobel,
Unfolding Methods in Particle Physics , in
Proceedings of the PHYSTAT 2011 Workshop onStatistical Issues Related to Discovery Claims in Search Experiments and Unfolding (H. B. Prosperand L. Lynons, eds.), vol. CERN-2011-006, p. 240, CERN, Geneva, Switzerland, 2011.[22] A. N. Tikhonov,
Solution of incorrectly formulated problems and the regularization method , SovietMath. Dokl. (1963) 1035.[23] D. L. Phillips, A technique for the numerical solution of certain integral equations of the first kind , J.Assoc. Comput. Mach. (1962) 84.[24] J. F. Mollenauer, Gamma-Ray Emission from Compound Nucleus Reactions of Helium and CarbonIons , Phys. Rev. (1962) 867.[25] D. Sam, L. R. Bunney and D. C. Heater,
Gamma-ray pulse-height spectra: Formation of a responsematrix for iterative unfolding , Nucl. Instrum. Meth. Phys. Res. (1968) 148.[26] M. Guttormsen, T. Ramsøy and J. Rekstad, The first generation of γ -rays from hot nuclei , Nucl.Instrum. Meth. Phys. Res.
A255 (1987) 518.[27] M. Guttormsen, T. S. Tveter, L. Bergholt, F. Ingebretsen and J. Rekstad,
The unfolding of continuum γ -ray spectra , Nucl. Instrum. Meth. Phys. Res.
A374 (1996) 371.[28] A. C. Larsen, M. Guttormsen, M. Krtička, E. Běták, A. Bürger, A. Görgen et al.,
Analysis of possiblesystematic errors in the Oslo method , Phys. Rev. C (2011) 034315.[29] A. C. Larsen, R. Chankova, M. Guttormsen, F. Ingebretsen, S. Messelt, J. Rekstad et al., Microcanonical entropies and radiative strength functions of , V, Phys. Rev. C (2006) 064301.[30] A. C. Larsen, M. Guttormsen, R. Chankova, F. Ingebretsen, T. Lönnroth, S. Messelt et al., Nuclearlevel densities and γ -ray strength functions in , Sc,
Phys. Rev. C (2007) 044303.[31] N. U. H. Syed, M. Guttormsen, F. Ingebretsen, A. C. Larsen, T. Lönnroth, J. Rekstad et al., Leveldensity and γ -decay properties of closed shell Pb nuclei , Phys. Rev. C (2009) 024316.[32] M. Guttormsen, A. C. Larsen, A. Bürger, A. Görgen, S. Harissopulos, M. Kmiecik et al., Fermi’sgolden rule applied to the γ decay in the quasicontinuum of Ti,
Phys. Rev. C (2011) 014312.[33] A. Kolmogorov, Sulla determinazione empirica di una legge di distribuzione , G. Ist. Ital. Attuari. (1933) 83.[34] N. Smirnov, Table for estimating the goodness of fit of empirical distributions , Ann. Math. Stat. (1948) 279.(1948) 279.