Monte Carlo simulation of the n_TOF Total Absorption Calorimeter

Nuclear Instruments and Methods in Physics Research A 671 (2012) 108–117

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Monte Carlo simulation of the n_TOF Total Absorption Calorimeter C. Guerrero a,b,n, D. Cano-Ott a, E. Mendoza a, J.L. Taı´n c, A. Algora c, E. Berthoumieux d, N. Colonna e, h ¨ , C. Lampoudis d, C. Domingo-Pardo c, E. Gonza´lez-Romero a, M. Heil g, D. Jorda´n c, F. Kappeler a f g T. Martı´nez , C. Massimi , R. Plag a

´gicas, Madrid, Spain CIEMAT, Centro de Investigaciones Energe´ticas Medioambientales y Tecnolo CERN, Geneva, Switzerland c Instituto de Fı´sica Corpuscular, CSIC-Universidad de Valencia, Spain d CEA/Saclay - DSM/DAPNIA, Gif-sur-Yvette, France e Istituto Nazionale di Fisica Nucleare, Bari, Italy f Dipartimento di Fisica, Universita di Bologna, and Sezione INFN di Bologna, Italy g GSI Helmholtz Centre for Heavy Ion Research GmbH, Darmstadt, Germany h FZK Forschungszentrum Karlsruhe, Germany b

The n_TOF Collaboration1 a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 September 2011 Received in revised form 28 November 2011 Accepted 5 December 2011 Available online 22 December 2011

The n_TOF Total Absorption Calorimeter (TAC) is a 4p BaF2 segmented detector used at CERN for measuring neutron capture cross-sections of importance for the design of advanced nuclear reactors. This work presents the simulation code that has been developed in GEANT4 for the accurate determination of the detection efficiency of the TAC for neutron capture events. The code allows to calculate the efficiency of the TAC for every neutron capture state, as a function of energy, crystal multiplicity, and counting rate. The code includes all instrumental effects such as the single crystal detection threshold and energy resolution, finite size of the coincidence time window, and signal pile-up. The results from the simulation have been validated with experimental data for a large set of electromagnetic de-excitation patterns: b-decay of well known calibration sources, neutron capture reactions in light nuclei with well known level schemes like natTi, reference samples used in (n, g) measurements like 197Au and experimental data from an actinide sample like 240Pu. The systematic uncertainty in the determination of the detection efficiency has been estimated for all the cases. As a representative example, the accuracy reached for the case of 197Au(n, g) ranges between 0.5% and 2%, depending on the experimental and analysis conditions. Such a value matches the high accuracy required for the nuclear cross-section data needed in advanced reactor design. & 2011 Elsevier B.V. All rights reserved.

Keywords: Monte Carlo simulation Geant4 Neutron cross-sections Time-of-flight Neutron capture

1. Introduction The n_TOF Total Absorption Calorimeter (TAC) [1] is a 4p detector made of 40 BaF2 crystals. Thanks to its large solid angle coverage and its high total absorption efficiency, it is especially well suited for measuring capture cross-sections of low-mass/ radioactive samples. It has been used extensively at the CERN n_TOF facility [2,3] for measuring capture cross-sections relevant to the design of advanced nuclear reactors [4–6], for instance

n Corresponding author at: CIEMAT, Centro de Investigaciones Energe´ticas Medioambientales y Tecnolo´gicas, Madrid, Spain. Tel.: þ 34 913466778; fax: þ 34 913466576. E-mail address: [email protected] (C. Guerrero). 1 http://cern.ch/nTOF.

0168-9002/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2011.12.046

some Minor Actinides (237Np, 240Pu and 241,243Am [7,8]) and uranium isotopes (233,234,235,238U [9–11]). In all these cases, the high accuracy requests for advanced reactor design require the minimization of all the uncertainties associated to the experimental and data analysis techniques. The measurement of capture cross-sections with the TAC is based on the detection of the electromagnetic (EM) cascade following every neutron capture reaction as a function of neutron time-of-flight (TOF). The TAC has a high intrinsic efficiency for fully absorbing the EM cascades from neutron capture, thus facilitating the suppression of low-energy/low-multiplicity background associated to radioactive decays. The optimization of the capture to background ratio is achieved by selecting events with appropriate energy and multiplicity, typical of (n, g) reactions. It can also serve to suppress the high multiplicity and energy

C. Guerrero et al. / Nuclear Instruments and Methods in Physics Research A 671 (2012) 108–117

deposition events characteristic of competing fission channels. This, however, has an impact on the detection efficiency of the TAC which becomes dependent on the characteristics of the EM de-excitation pattern of the nucleus. Under these circumstances, the detection efficiency is best determined by Monte Carlo simulations, which provide the necessary flexibility for investigating its dependence on the particular g-ray energies and multiplicities of each investigated nucleus. We have developed a simulation code of the TAC using GEANT4 [15] and an event reconstruction software that provide the value of the detection efficiency for any isotope and any condition concerning the deposited energy, multiplicity and counting rate. The simulation code and the event reconstruction software are described in Section 3. The validation of the code has been performed with experimental data from b-decay sources with known decay schemes and from neutron capture reactions in natTi, 197Au and 240Pu and is discussed in Sections 4 and 5, respectively. The detection efficiency resulting from the simulations as well as the associated uncertainty are discussed in detail in Section 6. Last, the conclusions are given in Section 7.

2. Neutron capture cross-section measurements with the n_TOF TAC The Neutron Time-of-Flight (n_TOF) facility at CERN [2,3] aims at measuring neutron induced cross-sections as a function of neutron energy using the TOF technique. Neutrons are generated in spallation reactions by a pulsed 20 GeV proton beam impinging on a lead block, which is surrounded by 5 cm of water serving both as coolant and neutron moderator. The resulting white neutron beam ranges from thermal energies to over 1 GeV, with a nearly 1/E isolethargic flux dependence up to 100 keV. The neutrons reach the experimental area at 185 m from the spallation target through an evacuated beam line. The measurement of neutron capture cross-sections with a calorimeter is based on the detection of the complete prompt g-ray cascade emitted in each reaction. The use of a high efficiency calorimeter allows one to detect the complete g-ray cascade, minimizing the dependence of its response with the particular de-excitation pattern (energy and multiplicity) of the excited compound nucleus formed in the capture reaction. The n_TOF TAC is made of 40 BaF2 crystals, 12 pentagonal and 28 hexagonal, each coupled to a 5 inch Photonis XP4508 photomultiplier. The crystals form a hollow sphere with inner and outer radii of 10.6 cm and 25.6 cm, respectively. Two opposite channels are left open for the entrance and exit of the neutron beam line. The samples are placed at the geometrical center of the sphere and are usually disks 10–30 mm in diameter. Two types of spherical neutron shielding [12] are used in the inner hole of the TAC for reducing the background caused by neutrons scattered at the sample: one based on a highly enriched 6Li and 1 H salt and one based on 10B enriched polyethylene. This background is further reduced by the use of 10B enriched carbon fiber capsules for each crystal. The results presented in this work correspond to measurements with the 6Li based neutron absorber. Fig. 1 presents a view of the open TAC with the neutron beam line, the neutron absorber around the sample, and the encapsulated hexagonal and pentagonal BaF2 crystals. The signals from each module are digitized on Acqiris-DC270 8 bit flash-ADCs operating at 500 MSamples/s [13]. The digital pulses are analyzed offline [14] by fitting a Maxwellian and an exponential function to the two BaF2 scintillation components, with decay times tshort ¼ 0:7 ns and tlong ¼ 630 ns, respectively. The individual signals are grouped into events by setting an

109

Fig. 1. One of the hemispheres of the TAC with the neutron absorber placed in the center and the neutron beam line passing through the detector assembly.

adequate coincidence window. Each event is characterized by its time-of-flight TOF (which determines the neutron energy En), the number mcr of hit crystals (referred to as crystal multiplicity), the energy Eicr deposited in each crystal (i¼1,mcr), and the total P i energy Esum deposited in the TAC (Esum ¼ Ecr ). The cross-section is obtained from the capture yield, which is calculated from the experimental counting rate by taking into account the detection efficiency and other experimental quantities. If not minimized properly, the uncertainty of the efficiency can become one of the largest contributions to the overall uncertainty of the final crosssection. The quantities mcr, Eicr and Esum serve to discriminate between different types of reactions. For instance, the background from the sample activity (or other decays) appears at deposited energies below a few MeV and is characterized by a low crystal multiplicity. On the contrary, EM cascades from capture reactions produce events with larger multiplicities and the deposited energy is as large as the neutron separation energy of the compound nucleus (Sn  5210 MeVÞ. Thus, the selection of a subset of events within the appropriate range of mcr and Esum values results in the optimization of the capture to background ratio. This is indeed one of the main advantages of the TAC with respect to other alternatives.

3. Monte Carlo simulation of the TAC The reliability of the results from the Monte Carlo simulation depends on (i) the accurate modeling of the physical processes governing the transport of particles through the detector, (ii) the implementation of the detailed detector geometry, (iii) the accurate modeling for the generation of primary events and (iv) the design of an event reconstruction algorithm capable of reproducing all the experimental effects that may affect the measured distributions.

3.1. Simulation code and physics model The Monte Carlo simulation code of the TAC has been programmed using the GEANT4 simulation package [15]. The reasons for choosing GEANT4 are its versatility in the modeling of volumes, the availability of extensive physics models for the transport of particles trough matter, its powerful tracking capabilities, and the direct technical support by CERN combined with a large set of debugging and validation references. The physics processes for this work, which deals with the transport and detection of g-rays, were modeled using the GEANT4 Standard Electromagnetic Package [16].

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3.2. Detector geometry The geometry of the detector has been modeled with the highest possible (and reasonable) fidelity, as it can be appreciated in Fig. 2, which shows one hemisphere of the detector. The dimensions were taken from direct measurements of the real geometry and also the CAD design drawings. The simulated geometry includes the 40 modules, each consisting of a BaF2 crystal enclosed in a 10B enriched carbon fiber capsule and coupled to a photomultiplier with aluminum housing. The sample holder in the center of the TAC, the aluminum vacuum tubes, the 6 Li enriched neutron moderator/absorber and the aluminum honey-comb structure that holds the complete assembly have been also included in the simulation. There are two parameters of the geometry that could not be determined with the necessary accuracy from a direct measurement: the distances of each individual module from the centre of TAC, which may vary within 1 mm from module to module, and the density of the neutron absorber, which consists of a lithium salt foam with air bubbles (formed during the solidification process), encapsulated in aluminum. These two parameters have been determined with the help of dedicated measurements and simulations as discussed in Section 4. Although this work is focused in the detector response to EM cascades, all materials have been defined including the information on their known isotopic composition, which is of importance for the correct simulation of neutron interactions [17].

3.3. Generation of primary events Two types of EM cascades have been measured with the TAC and simulated correspondingly: 1. EM cascades following the b-decay of well known sources. The measurement of simple EM cascades of known pattern offers a valuable set of data for benchmarking the geometry and physics of the simulation. In addition these measurement provide the energy and time resolution of each TAC module [1]. 2. EM cascades following neutron capture reactions. The simulation of known de-excitation pattern from neutron capture reactions allows to validate the simulation for high-energy and high-multiplicity events. The simulation of capture cascades from any given nucleus yields the detection efficiency

Fig. 2. The Total Absorption Calorimeter (only one hemisphere) as it is implemented in the simulation code.

for such reactions, which is the main result for the analysis of cross-section measurements. These two event generators are discussed in Sections 4 and 5, respectively. 3.4. Event reconstruction algorithm The simulation starts with the generation of a given number of events emitted at the sample position: an extended source of 1 cm in diameter at the center of the TAC. Each event, an EM cascade from b decay or a neutron capture reaction, contains the information on the number of emitted g-rays and electrons (b-particles and conversion electrons CE) together with their associated energy and emission angle. Each event is tagged with a TOF stamp selected in such a way that the time distribution of the simulated events is analog to the real one (see details in Section 3.5). The particles emitted in each event are transported and tracked through the detector assembly until they are absorbed or escape the TAC. The energy and time of each interaction inside the BaF2 crystals are recorded at each step of particle tracking. The information from individual interactions (time from the start, deposited energy and reference number of the crystal hit) is combined by means of a coincidence analysis of the 40 modules using a coincidence window of 20 ns. When the time distance between two consecutive events is shorter than the coincidence window they are considered as a single detected event, as it occurs under experimental conditions. The result is a list of detected events with a given TOF, mcr, Eicr P i (i¼ 1,mcr) and Esum ¼ Ecr (these variables are defined in Section 2). In the experiment, the observed deposited energy and energy resolution result not only from the actual energy released in the detector but also from the light production by scintillation, the optical transport of light within the detector and the multiplication process in the PMT. Thus, in order to be compare the simulated with experimental data, the energy deposited in the simulation (Eicr ) is folded with a Gaussian-like energy resolution with an energy dependent width, which was determined from the experimental data for each individual BaF2 module [1]. Last, a detection threshold of Eicr 4 100 keV is applied to each crystal in both experimental and simulated data. 3.5. Modeling of the signal pile-up The long tail of the BaF2 signals (of several ms) hinders the identification and subsequent pulse shape analysis of individual signals appearing close in time at high counting rates. It has been found empirically that there is a minimum separation time tdt between two consecutive signals which guarantees a correct identification and pulse shape analysis. The tdt depends on the energy of the first (E1) and second (E2) signals. A maximum value for tdt ðE1 ,E2 Þ of 3 ms was verified for the extreme case, when E1 is in the MeV and E2 in the hundreds of keV. It has been also observed that the amplitude (i.e. energy) E1 provided by the analysis routine is overestimated when the second signal is not identified. This problem, which becomes important only at high counting rates ( 4 300 kHzÞ, has been investigated in detail by quantifying the performance of the analysis routine for artificially generated pile-up events with pairs of isolated signals of known amplitude. In this way, the probability for losing pile-up signals and the subsequent distortion in the reconstructed amplitudes has been modeled as a function of E1 and E2 as well as of the counting rate, and is included in the event reconstruction of Monte Carlo simulated data.

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The real situation is even more complex because of the resonant structure of sðn, gÞ cross-sections. Rapid variations in the crosssection as a function of energy lead to rapid variations of the counting rate as a function of the time of flight. When the length of the signals is comparable to the width of a resonance, expressed in time of flight, the time-dependence of the counting rate needs to be taken into account. As typical values at n_TOF, cross-sections resonances at a few eV, tens of eV and hundreds of eV exhibit a TOF spread of  100 ms, few ms and less than 1 ms, respectively. The pileup probability follows the resonant structure of the cross-section and can not be approximated analytically. For this reason, we have developed a method which consists in the sorting of the primary events of our simulation according to the real TOF distribution of the true cross-section. Then, the time sequence of signals occurring inside each crystal is analyzed. Each signal is flagged as identified or missed, depending on its amplitude Ei þ 1 and time separation tdt ðEi þ 1 ,Ei Þ to the previous signal. If needed, the energy Ei þ 1 of the signal is also modified according to a model, which emulates the pulse shape analysis routine. Last, the time coincidence between all the TAC crystals is verified and the sum energy is computed. In this way, the pile-up effect could be described for each specific cross-section measurement as function of the TOF and the analysis conditions in Esum and mcr. A more detailed discussion of the influence of signal pile-up in the cross-section measurements with the TAC and the validation of the algorithm presented in this section is given in Ref. [18]. In the following and for the sake of clarity, the results discussed in this paper correspond to measurements with constant (or slowly varying) counting rates, always below 300 kHz.

4. TAC response to b-decay The Monte Carlo simulations have been validated first with measurements of the response of the TAC to b-decay sources with well known de-excitation patterns. Four calibration sources (137Cs, 60Co, 88Y and 24Na) have been measured in two geometric configurations of the TAC: without and with the neutron absorber shell described in Section 2. While 137Cs emits a single g-ray, the other sources emit two-step g-ray cascades with individual energies from 898 keV (88Y) up to 4.1 MeV (24Na). Their b-decay schemes have been retrieved from ENSDF [19], which provides the complete information on the feeding probabilities, level

111

scheme, branching ratios and conversion coefficients. In the case of two-step g-ray cascades the angular correlation between the successive g-rays has been calculated with the expression: WðyÞ ¼ 1 þ

‘ X

ai cos2i y,

ð1Þ

1

where 2‘ is the order of the lowest multipole transition in the cascade and the coefficients ai are those given by Hamilton [20] and tested for these particular b-decay sources in Refs. [21,22]. The simulation of the known sources have served to improve the accuracy of the geometry parameters mentioned in Section 3.2: the effective radial distance RTAC of all the BaF2 modules to the center of the TAC, and the effective density rabs of the 6Li compound used as neutron absorber. A value RTAC ¼10.67 cm was determined for the configuration without neutron absorber, from the best overall agreement for all calibration sources between the experimental data and simulations. Correspondingly, a density rabs ¼ 0:77 g=cm3 was obtained for the configuration with absorber. An example of the excellent agreement between the experimental and simulated responses in both configurations is shown in Fig. 3 where, for the particular case of 88Y, the experimental data are reproduced for any condition in crystal multiplicity mcr. The electronic noise, observed below  300 keV, is significant only when no conditions in mcr are applied. The different contribution of the partial and total absorption peaks is very sensitive to the geometric efficiency of the detector and to absorption in the structural materials surrounding each crystal. Thus the accurate reproduction of all experimental data sets serves as validation of the geometry implemented in the simulation and warrants the high accuracy of the results in this respect. The large sum peak in Fig. 3 at a total deposited energy of 2.7 MeV is a consequence of the high total absorption efficiency of the TAC. As a reference, Fig. 4 shows the total absorption and detection efficiencies for individual g-rays from 100 keV to 8 MeV. The detection probability is larger than 80% in the entire energy range, which results in a nearly 100% efficiency for detecting at least one of the g-rays emitted in a capture cascade with multiplicity three or higher.

5. TAC response to neutron capture events Three data sets have been used for validating of the Monte Carlo simulated response of the TAC to EM cascades from 14

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2

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1 1.5 2 2.5 Deposited energy (MeV)

3

3.5

0

0

0.5

1 1.5 2 2.5 Deposited energy (MeV)

3

3.5

Fig. 3. Experimental (solid line) and simulated (markers) responses of the TAC to the 88Y source (g-ray energies of 898 and 1836 keV) measured without (left) and with (right) neutron absorber. The data are shown for different conditions in crystal multiplicity (mcr). The low energy peak observed only in the experimental data for mcr 40 is related to low energy (Esum o 200 keVÞ and low multiplicity ðmcr ¼ 1Þ background.

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1

S +E

Efficiency

0.8

Statistical region

Detection efficiency (with absorber)

Levels from LD models Transitions from PSF

0.9

Detection efficiency

0.7 0.6 Total absorption efficiency

0.5

E 0.4

0

1

2

3 4 5 6 γ-ray energy (MeV)

7

8

Fig. 4. Detection and total absorption efficiency of the TAC to mono-energetic g-rays (with and without neutron absorber). A low energy threshold of 100 keV has been applied in all cases.

neutron capture events: natTi, 197Au and 240Pu. The three cases are complementary and cover the wide range of situations that are encountered when measuring neutron capture cross-sections of light (Ti), medium (Au) or heavy (Pu) nuclei. The case of nat Ti represents a chain of light nuclei with low level density and a known level and decay scheme up to Sn, with individual g-ray energies up to  7 MeV. The case of 197Au corresponds to a medium mass nucleus that emits higher multiplicity cascades, and for which the nuclear levels are known only at low excitation energies, thus requiring a description based on statistical models of the de-excitation mechanisms at high excitation energies. The case of 240Pu corresponds to a heavy nucleus with a very high level density, for which the extreme statistical model applies.

Exp.known levels

0.3

En

Total absorption efficiency (with absorber)

E E

E E Ground State (

Z)

Fig. 5. Nuclear level scheme used in the generator model of the DECAYGEN code. (Color version online) Red and green arrows correspond to transitions starting from statistical or experimental levels, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The generation of each capture cascade starts at the known resonance (i.e. nuclear level) and proceeds until the ground (or a sufficiently long lived metastable) state is reached. The algorithm can be described as follows:

5.1. Generation of capture cascades The generation of EM cascades following neutron capture has been performed with the DECAYGEN [23] code. DECAYGEN relies on experimental information such as nuclear levels and transition probabilities, as well as a parametrization of the nuclear level density (LD) and of the photon strength functions (PSF). Full details of the code are given in Ref. [23] and examples of its use can be found in Refs. [24,25]. DECAYGEN separates the description of the nuclear level scheme and transition probabilities below the capture level at Sn þ En (note that the recoil energy is neglected in the case of heavy nuclei) in two different energy ranges (see Fig. 5):

 The region at lower excitation energies (En o Ecut ), where the



nuclear levels and EM transition branching ratios are supposed to be known experimentally. The data describing this region were retrieved from the Evaluated Nuclear Structure Data File (ENSDF) [19]. The electron conversion process is also calculated for the K,L- and M-shells from tabulated binding energies, fluorescence yields and internal conversion coefficients. The region at higher excitation energies (En 4 Ecut ), for which the nuclear levels are calculated by sampling the LD distribution. The EM branching ratio matrices are computed for E1, M1 and E2 transitions from the relative ratios of the corresponding PSFXL(Eg ), where X represents the character of the transition (E or M) and L the multipolarity (1,2).

1. A large number of levels is generated between Ecut and Sn þ En by sampling the level density distribution. 2. The branching ratio matrix for E1, M1 and E2 transitions from the present level to all lower, statistical or experimental, is calculated. 3. The transition to a new level is sorted randomly according to the probabilities given by the branching ratio matrix. 4. If the new level is in the statistical energy range (En 4Ecut ) the loop returns to Step 2, otherwise the branching ratio is known and thus the loop returns to Step 3. DECAYGEN is used for producing a list of EM cascades, each one characterized by the number, energy, time-of-flight and emission angle of the g-rays of the cascade. The emission angle of each g-ray is sorted randomly according to an isotropic distribution, which is a good approximation for the neutron energy region and the type of resonances (s-wave) of interest in this work. The time-of-flight for all the g-rays in each cascade follows the real, and thus variable, reaction rate distribution as mentioned in Section 3.5 and discussed in detail in Ref. [18]. 5.2. TAC response to cascades from

nat

Ti(n, g) reactions

The EM cascades from neutron capture reactions in natTi are an excellent validation tool for the simulation code and the cascade generator for two reasons. First, the capture cascades in natTi have

C. Guerrero et al. / Nuclear Instruments and Methods in Physics Research A 671 (2012) 108–117

-4

Counts (arb. units)

10

>0) >1) >2) >3) >4)

MC (m MC (m MC (m MC (m MC (m

Photon Strength Function (MeV-3)

Exp. Exp. Exp. Exp. Exp.

-5

10

113

MC(a) MC(b) MC(c)

10-7

-8

10

-9

10

-10

10

1 0

2

4 6 8 Deposited energy (MeV)

10

Fig. 6. Simulated (markers) and experimental (solid-lines) TAC response to nat Ti(n, g) for different conditions in crystal multiplicity. The experimental data correspond to neutron energies between 1 eV and 10 eV, where neutron capture is the dominant reaction.

total energies higher than 8 MeV with individual g-rays energies up to 6.7 MeV, thus extending the energy range covered with standard g-ray sources (see Section 4). Second, because the dominant ( 4 75%) reaction in the eV region is 48Ti(n, g), for which the branching ratio matrix from its capture to its ground state is known from previous experiments [19,26]. A 386.4 mg and 15 mm diameter disk-like sample of natural titanium was irradiated at n_TOF and measured with the TAC in the configuration with the neutron absorber. The measurement has been simulated [17] with a total of 107 capture cascades, and the comparison of the Monte Carlo (markers) and experimental (solid lines) deposited energy spectra in the TAC are displayed in Fig. 6 for several conditions in crystal multiplicity. An excellent agreement is observed at all energies and for all multiplicities, this being a remarkable result considering that we used the decay scheme from literature without varying any parameter of the TAC geometry. The dominant structure in Fig. 6 around 8.1 MeV corresponds to the total absorption of the capture cascade from 48Ti, and the structures at 6.7 MeV and 1.4 MeV correspond to the escape peaks of the two step cascade from the capture to the ground state through the first excited level at 1.4 MeV. The small peak at 2.2 MeV observed at low multiplicities corresponds to the background due to neutrons scattered in the sample and then captured in the hydrogen of the neutron absorber. The low energy (Esum o1 MeVÞ contribution observed in the low multiplicity spectra are due to electronic noise. These effects were not included in the simulation and therefore are not reproduced. 197

Au(n, g) reactions

We have irradiated a gold disk with a mass of 185.4 mg and 10 mm in diameter and measured the capture reactions with the TAC in the configuration with the neutron absorber. The results shown in this section correspond to neutron energies in the low energy tail of the resonance at 4.9 eV, where the counting rate remains below 300 kHz and thus pile-up effects are negligible. The EM decay from the capture level at En ¼ Sn þEn ¼ 6:51 MeVðJ p ¼ 2 þ Þ [27] in 198Au to the ground state (J p0 ¼ 2 Þ is more complex to model than in the case of natTi since the level scheme of 198Au is reasonably well known only below 1.5 MeV and the level density is larger below Sn. A total of 136 levels and

6

Fig. 7. Photon Strength Functions (PSF) used for 198Au (see Fig. 8) above the neutron separation energy. MC(d) is not shown because it corresponds to a combination of MCðcÞ with the known primary transition going from the capture level to the low excitation energy known levels (see text for details).

the associated branching ratio matrices are known experimentally below this energy. The description of the high excitation energy region relies on the LD models and PSF found in literature. In this particular case, the nuclear levels are computed from the Back Shifted Fermi Gas model (BSFG) with the parameters from RIPL-2 [28,29]. Regarding the PSF, the situation is complex because the energy shape and intensity of the PSF found in RIPL-2 [29] are the result of systematic investigations at transition energies only around the GDR ðEn 4 10 MeVÞ and tuned so that average resonance parameters around the neutron separation energy are reproduced. Both cases are well above our region of interest ðEn o Sn C 6:5 MeVÞ. In addition, a recent work [30] has confirmed the previously observed anomalous behavior of the PSF in 198Au. In this work we have investigated the response of the TAC to 197 Au(n, g) cascades under different assumptions on the associated PSF (see Fig. 7), although a detailed discussion and an investigation of the PSF of 198Au are out of the scope of this paper. The results are summarized in Fig. 8, which displays the experimental and simulated multiplicity and deposited energy spectra in the TAC. The four simulations correspond to:

 MCðaÞ the PSF with EGLO shape as given in RIPL-2.  MCðbÞ the PSF with EGLO shape as given in RIPL-2 with a

 

5.3. TAC response to cascades from

5 3 2 4 Transition energy (MeV)

modification that allows reproducing the experimental data by adding a soft structure at 6.8 MeV for E1 and a very small one at 5.5 MeV for M1 transitions. MCðcÞ the PSF with SLO shape as given in RIPL-2 where the E1 is modified below 5.8 MeV by a scaling factor q ranging between 0.2 and 1 (as suggested in Ref. [30]). MCðdÞ a modification of MC(c) but using the energies and intensities given in CapGam [26] for the high energy (Eg 44:9 MeVÞ primary transitions from the capture level to the known part of the level scheme.

The results displayed in Fig. 8 show that, except for MC(a), all these PSF parameterizations reproduce the data well, indicating that the EGLO shape from RIPL-2 as such can not reproduce the experimental data. It is observed as well that, as a consequence of the high intrinsic efficiency of the TAC and given the complexity of the cascades, there are different PSF that allow reproducing the data. It appears that, as one would expect, the inclusion of the experimentally known high energy primary transitions (case

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E sum >2 MeV

Mult=1 5

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1

2

3

4

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7

Deposited energy (MeV)

0

1

2

3

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Deposited energy (MeV)

Fig. 8. Experimental and simulated (see text for details) TAC response to 197Au(n, g) in terms of crystal multiplicity (top-left) and deposited energy for different conditions in crystal multiplicity.

MC(d)) helps to reproduce better the low multiplicity deposited energy distributions. It is important to note that the calculation of the detection efficiency is not significantly affected by the PSF, but depends mainly on how well the detector response to 197Au(n, g) reactions is reproduced. As discussed in detail in Section 6, the simulated detection efficiencies for cases MCðbÞ, MCðcÞ and MCðdÞ differ by less than 1% for a wide range of values for Esum and mcr. 5.4. TAC response to cascades from

240

Pu(n, g) reactions

We have irradiated a disk-shaped 240Pu sample 45 mg in mass and 10 mm in diameter encapsulated in titanium and measured the capture reactions with the TAC in the configuration with neutron absorber. The results shown in this section correspond to the de-excitation of the 20.5 eV resonance, where the counting rate was always below 300 kHz. For the simulations, only the first 26 levels in 241Pu up to 560 keV have been adopted. Above that energy, the discrete level scheme of 241Pu was assumed to be incomplete and instead described statistically with the RIPL-2 parameters for the BSFG formula up to the neutron separation energy. Because there are no experimental data for the PSF of 240Pu, the parametrization in RIPL-2 corresponds only to systematic trends in lighter nuclei.

The comparison of the experimental data and simulations in Fig. 9 shows two Monte Carlo calculations. MC(a) stands for simulations made using the PSF from RIPL-2 and does not reproduce the experimental data, clearly indicating a lack of transitions with energies around 2.3 MeV. In order to reproduce the experimental data and to investigate the existence of structures in the tail of the PSF around that energy, the effect of the E1 and M1 PSF was empirically investigated. A Gaussian-shaped structure with an energy between 1 and 5 MeV and width between 0.1 and 3 MeV was added to the RIPL-2 E1 and M1 PSF, and the corresponding Monte Carlo simulations compared to the experimental data. The best reproduction found is shown by full circles in Fig. 9, which corresponds to MC(b), calculated with a E1 PSF including a Gaussian structure at Ep ¼2.3 MeV and a width of Gp ¼ 0:75 MeV. In fact, the sensitivity of the Monte Carlo simulations on the different PSF shows that the data measured with the TAC can as well serve for a detailed investigation of the PSF of heavy isotopes, which can be described within the extreme statistical model. The conclusions on the calculation of the detection efficiency as a function of the Esum and mcr parameters are the same as for the case of the 197Au(n, g) cascades discussed in Section 5.3. Provided that the Monte Carlo simulations reproduce reasonably well the experimental data, the value of the detection efficiency is stable.

C. Guerrero et al. / Nuclear Instruments and Methods in Physics Research A 671 (2012) 108–117

Esum>2 MeV

Mult=1

35

4.5 Exp

30

Exp

4

MC(a)

MC(a)

3.5

MC(b)

25

Counts (arb. units)

Contribution (%)

115

20 15 10

MC(b)

3 2.5 2 1.5 1

5 0

0.5 0

1

2

3 4 5 6 Crystal multiplicity

7

0

8

1

2 3 4 5 Deposited energy (MeV)

Mult=2

6

Mult>2

8 Exp MC(a)

6

MC(b)

5 4 3 2

MC(a) MC(b)

25 20 15 10 5

1 0

Exp

30 Counts (arb. units)

Counts (arb. units)

7

1

2 3 4 5 Deposited energy (MeV)

Fig. 9. Experimental and simulated (see text for details) TAC response to multiplicities.

6

240

0

1

2 3 4 5 Deposited energy (MeV)

6

Pu(n, g) in terms of crystal multiplicity (top-left) and deposited energy for different crystal

6. Estimation uncertainties of the detection efficiency The main goal of this work is the accurate determination of the efficiency of the TAC for detecting capture cascades under any conditions on Esum and mcr. The efficiency is obtained by Monte Carlo simulation from the ratio of detected events to the total number of events simulated, as a function of the conditions on Esum and mcr. The Monte Carlo cascades are also sorted with the correct time of flight distribution and a model of signal pileup is applied to them. Therefore, the detection efficiency calculated does take into account signal losses due to pile-up. The discussion that follows applies to the case of 197Au, which is used as reference in all the neutron capture measurements at n_TOF. A similar work is needed for each specific measurement, case by case. The detection efficiencies resulting from the simulations for 197 Au(n, g) at a counting rate of 300 kHz are listed in Table 1 for several combinations of conditions on Esum and mcr. It can be noticed that even for no condition, the maximum efficiency of the TAC (97.4%) is slightly below 100%, mainly due to the 100 keV detection threshold of each module and the incompleteness of the 4p solid angle coverage. It is observed as well that the detection efficiency decreases progressively when more restrictive analysis conditions are applied. Therefore, the optimal analysis conditions are chosen for each individual experiment, as the best

Table 1 Detection efficiency of the TAC for detecting 197Au(n, g) reactions at low counting rate under different conditions in Esum and mcr.

Esum 40 MeV Esum 41 MeV Esum 42 MeV Esum 43 MeV Esum 44 MeV

mcr 40

mcr 4 1

mcr 4 2

mcr 43

0.974 0.912 0.833 0.743 0.640

0.872 0.843 0.777 0.695 0.399

0.664 0.656 0.619 0.559 0.483

0.407 0.406 0.392 0.361 0.314

compromise between the enhancement of the capture to background ratio and the reduction of efficiency. There are several sources of uncertainty in the calculation of eðEsum ,mcr Þ and all of them have been taken into account for determining the overall accuracy of the results. Regarding the GEANT4 simulation code, the physics models in the GEANT4 Standard Electromagnetic Package and the detector geometry are well validated and thus are not considered a source of uncertainty. This has been confirmed indirectly by comparing the results obtained with GEANT4 with MCNPX [17] for simplified geometries, which led to negligible differences. The only source of uncertainty associated to the detection set-up implemented in the geometry class of the GEANT4 simulation is coming from the two parameters of the TAC geometry RTAC and rabs that have been

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Table 2 Detection efficiency and associated uncertainty for 197Au reactions with a threshold of 100 keV in each crystal and at a counting rate of 0:3 ms1 . Analysis conditions mcr

Esum (MeV) code

4 0 4 0:1 4 2 4 2:5

eðDeÞ

Partial uncertainties (Dei )

Monte Carlo 0.974(4) 0.002 0.584(13) 0.011

Generation of (n, g) cascades

Dead-time correction

0.003 0.006

0.001 0.003

adjusted empirically from the comparison of the Monte Carlo results and experimental data from b-decay sources. RTAC and rabs have been varied beyond the range that provides a good reproduction of the experimental data, and the uncertainty in the detection efficiency was computed from the standard deviation of the resulting detection efficiency values. The unknowns in the generation of capture cascades are the parameters for the LD and the PSF. The variation of the LD, i.e. using BSFG or other parametrization and models found as well in RIPL-2, do not show a significant impact on the TAC response, and thus only the dependence on the variation of the PSF has been considered. The uncertainty related to the adjustment of the PSF parameters has been estimated from the standard deviation of the detection efficiency values resulting from simulations with different sets of PSF, not necessarily reproducing the experimental data too precisely. The final results are approximately as much as the standard deviation of the efficiencies computed from MC(b),MC(c) and MC(d) in Section 5.3. Last, a careful investigation of the effects of signal pile-up has shown that the effect can be neglected for counting rates below  300 kHz. At higher counting rates, the distortions in the TAC response due to the performance of the pulse shape analysis for pile-up signals may become significant. In such cases, the corresponding uncertainty in e has been parametrized as a function of the counting rate used for the TOF distribution of events in the simulation, and the minimum time difference tdt ðE1 ,E2 Þ between two consecutive signals of amplitudes E1 and E2 used by the event reconstruction algorithm. Further details are given in Ref. [18]. In any case, most of the measurements performed do not reach counting rates above 300 kHz, in particular in the case of low mass actinide samples. Table 2 contains the partial and total uncertainties in the detection efficiency calculated for the reference case of 197Au(n, g) at a counting rate of  300 kHz. Two extreme cases are considered: no analysis conditions in Esum and mcr, and very restrictive conditions Esum 4 2:5 MeV and mcr 42. The accuracies reached in each case are small and amount to 0.5% and 2%, respectively. The advantages of the calculation of the detection efficiency by Monte Carlo simulations are clear: (i) Monte Carlo simulations eliminate the need for using saturated resonances, which are not always available, or of reference cross-sections to determine the detection efficiency experimentally. (ii) The method allows one to consider the effects due to the detection thresholds, conditions on Esum and mcr, or pile-up events in a rigorous and separate way. The method allows to determine the detection efficiency of the TAC for any nucleus and under any conditions, and has been applied already to the analysis of several actinides (n, g) cross-sections.

7. Summary and conclusions We have developed a detailed GEANT4 Monte Carlo simulation code of the Total Absorption Calorimeter (TAC) used for neutron capture cross-section measurements at the CERN n_TOF facility.

The code allows to calculate with high accuracy the efficiency of the TAC for detecting (n, g) reactions as function of the counting rate and of the thresholds in energy and multiplicity. The geometry of the detector has been modeled in great detail and has been fine-tuned by comparison of the simulated results with experimental data from standard b-decay sources. Two event generators, corresponding to b-decay and neutron capture events, have been implemented and validated with experimental data. We have designed an event reconstruction algorithm to take all experimental effects concerning the measured energy and multiplicity distributions into account, including the energy resolution and threshold in the single modules, the length of the time coincidence window, the selection of conditions on Esum and mcr, and the effect of signal pile-up. The results from the simulations of neutron capture in light (natTi), medium (197Au) and heavy (240Pu) nuclei are in excellent agreement with the experimental data for several combinations of conditions on the deposited energy and the crystal multiplicity. The quality of the results confirm the accurate determination of the TAC efficiency for capture reactions. The uncertainty analysis has been made in detail for the 197Au(n, g) cross-section, which is commonly used as reference at n_TOF. The uncertainty in the detection efficiency has been estimated from the partial uncertainties associated to the Monte Carlo code, the generation of capture cascades and the reconstruction of pile-up signals. An accuracy better than 2% has been reached for all conditions on Esum and mcr of interest for the analysis cross-section data. The code is also a powerful tool for the optimization and analysis of the measurements with the TAC. As an example, it has been used for the design of an upgraded experimental set-up with 10 to 100 times better capture to background ratios [12] and is now being used for the systematic investigations of Photon Strength Functions of actinides isotopes [25].

Acknowledgments This work was partially supported by the Spanish Ministry of Science and Innovation FPA2008-06419-C02-01 and CSD-200700042 grants, by ENRESA under the CIEMAT-ENRESA agreement on Transmutation of high level radioactive waste, by the European Commission 6th Framework Program project IP-EUROTRANS (FI6W-CT-2004-516520) and the European Commission trans-national access program EFNUDAT. References [1] C. Guerrero, et al., Nuclear Instrumentation and Methods in Physics Research Section A 608 (2009) 424. [2] The n_TOF Collaboration, CERN n_TOF Facility: Performance Report, CERN/ INTC-O-011, INTC-2002-037 CERN-SL-2002-053 ECT, 2006. [3] F. Gunsing, et al., Nuclear Instrumentation and Methods in Physics Research Section A 261 (2007) 925. [4] NEA Nuclear Data High Priority Request List /http://www.nea.fr/dbdata/ hprl/index.htmlS. [5] A.J. Koning , J. Blomgren, R. Jacqmin, A.J.M. Plompen, R. Mills, G. Rimpault, E. Bauge, D. Cano-Ott, S. Czifrus, K. Dahlbacka, I. Goncalves, H. Henriksson, D. Lecarpentier, E. Malambu-Mbala, V. Stary, C. Trakas, C. Zimmerman, CANDIDE: Nuclear data for sustainable nuclear energy, EUR 23977 EN-2009. [6] Working Party on International Evaluation Co-operation of the NEA Nuclear Science Committee, Uncertainty and Target Accuracy Assessment for Innovative Systems Using Recent Covariance Data Evaluations, ISBN 978-92-64-99053-1, 2008. [7] D. Cano-Ott, et al., AIP Conference Proceedings 819 (2006) 318. [8] C. Guerrero, et al., Am-241 Neutron Capture Measurement at n_TOF, Final Scientific EFNUDAT Workshop, Geneva, Switzerland, 30 August–2 September 2010. [9] E. Berthoumieux, et al., Simultaneous measurement of the neutron capture and fission yields of 233U, in: Proceedings of International Conference on Nuclear Data for Science and Technology, April 22–27, 2007, Nice, France ND2007, 2007, p. 152.

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