R Arnold

𝑎 C Augier

𝑏 A S Barabash

𝑐 A Basharina-Freshville

𝑑 E Birdsall

𝑒 S Blondel

𝑏 M Bongrand

𝑏 D Boursette

𝑏 R Breier

𝑓 V Brudanin

J Busto

𝑖 S Calvez

𝑏 C Cerna

𝑗 J P Cesar

𝑘 M Ceschia

𝑑 A Chapon

𝑙 E Chauveau

𝑗 A Chopra

𝑑 L Dawson

𝑑 S De Capua

𝑒 D Duchesneau

𝑚 D Durand

𝑏,𝑑 𝑙 G Eurin

J J Evans

𝑒 D Filosofov

𝑔 R Flack

𝑑 P Franchini

𝑛 C Girard-Carillo

𝑏 H Gómez

𝑏 B Guillon

𝑙 P Guzowski

𝑒 M Hoballah

𝑏 R Hodák

𝑜 M H Hussain

𝑑 A Jeremie

𝑚 S Jullian

𝑏 J Kaizer

𝑓 A Klimenko

𝑔 O Kochetov

𝑔 S I Konovalov

𝑐 V Kovalenko

𝑔 D Lalanne

𝑏 K Lang

𝑘 Y Lemière

𝑙 T Le Noblet

𝑚 Z Liptak

𝑙 X R Liu

𝑑 P Loaiza

𝑜 𝑏 M Macko

C Macolino

𝑏 C Marquet

𝑗 F Mauger

𝑙 A Minotti

𝑚 Y Mora

𝑜 B Morgan

𝑝 J Mott

𝑑 I Nemchenok

𝑔 M Nomachi

𝑞 F Nova

𝑘 F Nowacki

𝑎 H Ohsumi

𝑟 G Oliviéro

𝑙 R B Pahlka

𝑓 𝑘 V Palušová

𝑗 C Patrick

𝑑 F Perrot

𝑗 A Pin

𝑗 F Piquemal

𝑗 P Povinec

𝑘 𝑓 M Proga

𝑑 W S Quinn

Y A Ramachers

𝑝 A Remoto

𝑚 J L Reyss

𝑠 R Saakyan

𝑑 A Salamatin

𝑔 R Salazar

𝑘 X Sarazin

𝑛 𝑏 J Sedgbeer

𝑔 Yu Shitov

𝑏 𝑛 L Simard

𝑡 F Šimkovic

𝑓 A Smolnikov

𝑔 S Söldner-Rembold

𝑒 I Štekl

𝑢 𝑜 J Suhonen

𝑣 C S Sutton

G Szklarz

𝑏 H Tedjditi

𝑖 J Thomas

𝑑 V Timkin

𝑑 𝑔 S Torre

Vl I Tretyak

𝑤 V I Tretyak

𝑔 V I Umatov

𝑐 C Vilela

𝑑 V Vorobel

𝑥 D Waters

𝑑 𝑑 F Xie

J Žemlička 𝑜

Measurement of the distribution of 207 Bi depositions on calibration sources for SuperNEMO SuperNEMO Collaboration

Keywords: neutrinoless double beta decay, energy calibration, 207 Bi, source distribution, Timepix pixel detector, SuperNEMO

A

: The SuperNEMO experiment will search for neutrinoless double-beta decay (0𝜈𝛽𝛽), and study the Standard-Model double-beta decay process (2𝜈𝛽𝛽). The SuperNEMO technology can measure the energy of each of the electrons produced in a double-beta (𝛽𝛽) decay, and can reconstruct the topology of their individual tracks. The study of the double-beta decay spectrum requires very accurate energy calibration to be carried out periodically. The SuperNEMO Demonstrator Module will be calibrated using 42 calibration sources, each consisting of a droplet of 207 Bi within a frame assembly.

The quality of these sources, which depends upon the entire 207 Bi droplet being contained within the frame, is key for correctly calibrating SuperNEMO's energy response. In this paper, we present a novel method for precisely measuring the exact geometry of the deposition of 207 Bi droplets within the frames, using Timepix pixel detectors. We studied 49 different sources and selected 42 high-quality sources with the most central source positioning.

1 Introduction

The SuperNEMO experiment

SuperNEMO [1,2] is a double-beta (𝛽𝛽) decay experiment, designed to look for the hypothesized lepton-number-violating process of neutrinoless double-beta decay (0𝜈𝛽𝛽). SuperNEMO's trackercalorimeter design, based on the NEMO-3 technology, is also well suited for precision studies of the Standard Model double-beta decay process (2𝜈𝛽𝛽) which is present in all 0𝜈𝛽𝛽 candidate isotopes. Both types of 𝛽𝛽 decay produce two electrons around the MeV energy scale, which SuperNEMO can individually track; the processes can be distinguished by studying the energies of these electrons. The majority of 0𝜈𝛽𝛽 detectors are homogeneous, meaning that the 𝛽𝛽 source also serves as the detection material (for example 76 Ge semiconductor detectors, or bolometers of 𝛽𝛽 isotopeenriched crystals). In SuperNEMO, however, the source is independent of the detector. The basic unit of a SuperNEMO-style detector is a module, as shown in figure 1. The modular design allows the detector size to be increased by adding identical modules to the detector. After the construction of each module, it is possible to verify whether the expected specifications (e.g. energy resolution, background level, etc.) have been met. An initial module, known as the SuperNEMO Demonstrator, is currently undergoing the final stages of installation and commissioning at LSM (the Modane Underground Laboratory, France).

A SuperNEMO module consists of a 𝛽𝛽-decay source in the form of thin, solid foils enriched in a 𝛽𝛽-decaying isotope, sandwiched between two identical detector halves. This opens up the possibility of studying any 𝛽𝛽-decaying candidate isotope that can be produced in the form of thin foils. The SuperNEMO Demonstrator Module has 34 source foils amounting to a total of 6.25 kg of selenium, of which 6.11 kg is the 𝛽𝛽 isotope 82 Se, with an average thickness of 0.286 mm and an average surface density of 50 mg of selenium per cm 2 [4,[START_REF] Jeremie | ICHEP2016[END_REF]. The feasibility of using other isotopes (such as 150 Nd) is also under investigation.

The two electrons emitted in 𝛽𝛽 decays are detected in the SuperNEMO Demonstrator Module by its particle tracker and calorimeter. The source foils are sandwiched between two tracking detectors, which together consist of 2034 drift cells operating in Geiger mode, in a vertical magnetic field [START_REF] Cascella | [END_REF]. The tracker reconstructs charged-particle trajectories, allowing significant background suppression, as well as extracting the angular distribution of the 𝛽𝛽 electrons. The energy of the individual decay electrons is measured by a segmented calorimeter, consisting of plastic scintillator blocks coupled to photomultiplier tubes surrounding the detector on all six sides. Calorimeter modules in the main walls of the detector have an average energy resolution of 7.5% FWHM at 1 MeV. The ability of the calorimeter to distinguish a 0𝜈𝛽𝛽 signal from 2𝜈𝛽𝛽, and to study 2𝜈𝛽𝛽 decay mechanisms that affect the energy spectrum, depends on the correct calibration of its energy response [3].

SuperNEMO calibration system

In order to perform energy calibrations of the SuperNEMO Demonstrator Module, 207 Bi sources are used. K-shell electrons from internal-conversion decays of 207 Bi provide three relevant calibration lines at 482 keV, 976 keV and 1682 keV; lower-intensity lines from L-and M-shell conversions are also included to achieve a good fit of the 207 Bi spectrum. The sources, which were previously used in the NEMO-3 detector [7], were produced at IPHC Strasbourg. For each source, a very thin droplet of 207 Bi solution was deposited on a Mylar foil (12 𝜇m thick) and then covered with another identical foil. Over time, the solvent has dried out, but the droplets of 207 Bi remain stable. Both Mylar foils were sealed by a rectangular frame made of radiopure copper, with internal dimensions 8 mm × 13 mm (figures 2a and 2b). The dimensions of the sources were chosen for compatibility with NEMO-3's calibration tubes, and have been incorporated into the SuperNEMO design. The 42 calibration sources used in the SuperNEMO Demonstrator Module are inserted and guided into gaps between the 82 Se 𝛽𝛽 source foils, using six identical mechanisms (figure 2c). The insertion and removal of the sources will be controlled by an automatic source deployment system developed by the University of Texas at Austin [8]. The calibration procedure will be performed at regular intervals during the data taking; the necessary calibration frequency will be determined experimentally, and is expected to be on the order of one run every few days or weeks. Information about the position of the sources relative to the rest of the detector is used when reconstructing the emitted electron trajectories and the associated energy losses. The deployment system lowers the source envelopes to their predefined locations as shown in figure 2c, with a precision of 60 𝜇m. However, the deposition distribution of the 207 Bi droplet within the copper frame is unknown (figure 2a). Most importantly, one needs to verify that the 207 Bi droplet did not spill in between the copper frame parts during the sealing process. This could cause emitted electrons to lose additional energy, which would result in a distortion of the reconstructed energy lines, and spoil the energy calibration of the SuperNEMO Demonstrator Module.

The goal of this work was to establish an experimental method to describe the deposition distribution of 207 Bi droplets within the calibration sources for the SuperNEMO Demonstrator Module. 207 Bi is a complex emitter; along with electrons, it emits both X-rays and gammas. For this analysis, instead of observing the electrons used to calibrate the SuperNEMO Demonstrator Module, the 207 Bi deposition within each source was studied by detecting low-energy X-rays from the 207 Bi source, which produce single-pixel depositions in a silicon pixel detector, allowing us to take advantage of the detector's peak sensitivity, and providing better localisation of signals. As a result, we established a ranking of the measured SuperNEMO calibration sources based on how closely the 207 Bi droplet had been deposited relative to the center of the copper frame. The best 42 sources were chosen to be installed in the calibration setup for the SuperNEMO Demonstrator Module.

Measurement and data analysis 2.1 Timepix Detectors and Calibrations

The droplet positioning measurements were performed using three Timepix silicon pixel detectors provided by IEAP, CTU in Prague (figure 3). Two of the detectors (H04-W0163 and H11-W0163) are 0.3 mm thick, while the third (L05-W0163) is 1 mm thick. Timepix detectors have the ability to measure the energy deposited by an incident particle, and its time of arrival. They were developed by the Medipix collaboration [9]. The sensitive chip is a square with sides 14.08 mm long, divided into 256 × 256 pixels (size of each pixel: 0.055 mm × 0.055 mm).

For the Timepix detectors to be used to measure the distribution of the 207 Bi source droplets, the detectors required a precise spatial calibration, and an approximate energy calibration. Both were carried out at IEAP, CTU in Prague. The energy response of each of the 65536 pixels in each detector was calibrated individually. This calibration consisted of relatively long measurements (several hours) in order to collect enough statistics in each pixel. The calibration was performed using fluorescent foils exposed to X-rays. Three fluorescent foils -Fe (6.398 keV), Cu (8.04 keV) and Cd (23.106 keV) -each provided one energy calibration point. The calibration function has four parameters; the fourth parameter is the result of threshold equalization of the detector. [START_REF] Tureček | IEEE Nuclear Science Symposium Conference Record[END_REF]. This energy calibration allowed the energy-weighted distribution of spatial data from the 207 Bi sources to be generated, and enabled a basic energy cut to select the particles of interest for our 207 Bi measurement. By using low-energy X-rays, we were able to select single-pixel depositions, which give us the best position localization. Higher-energy depositions, like those from 𝛽-decay electrons, activate several pixels, which reduces the ability to identify the spatial coordinates of the decay.

When a Timepix detector is used to monitor the 207 Bi source, the 207 Bi droplet position is only represented in the detector chip coordinates. However, the purpose of the measurement is to represent the position of the 207 Bi droplet with respect to its copper frame. In order to make such spatial calibration possible, we defined a Reference Alignment Point (RAP, figure 3b) for all measurements.

An additional measurement was taken in which a thin metallic square, perforated by holes distributed equidistantly in a grid (figure 4a) laser-cut to few-𝜇m precision, was placed on top of the detector, so that the yellow dot in figure 4a matched the RAP. The distance between the centers of adjacent holes, in both the vertical and horizontal directions, was equal to 1 mm. We irradiated this setup with X-rays. The result of this measurement can be seen in figure 4b. Thanks to this measurement, we were able to extract the position of each pixel in the sensitive area of the detector relative to the RAP. The position of the RAP and the 1-mm spacing of the metal grid were used to convert from the coordinate system of the detector (in pixels) to that of the source frame (in mm).

Measurement protocol

The duration of a measurement sufficient to collect enough data for an individual 207 Bi source was typically around 2-3 hours, due to the relatively low source activity (120-145 Bq) and selection efficiency (approximately 6% for the thinner detectors, and 9% for the thicker, for the data of interest to this study: while the detector's efficiency is close to 100% for X-rays produced by 207 Bi, these values refer to the efficiency of the single-pixel and energy-range cuts imposed to ensure that the position of the droplet corresponds to the activated pixel). This led to an event rate in our region of interest (ROI), as explained in section 2.4, of around 8-10 events per second. To accumulate sufficient statistics to precisely measure the droplet position, we aimed for around 50000 events in the ROI for each source. Due to scheduling constraints, less data was collected for sources 93, 94, and 95; nevertheless, it was sufficient to evaluate these sources. Repeated and extended measurements were taken for a subset of sources, taking advantage of the laboratory schedule to collect larger samples with millions of events and confirm consistency with the lower-statistics measurements. All three pixel detectors were used in parallel, and were connected to one computer. Measurements for the 49 available 207 Bi sources were taken over a period of almost 12 full days, which included short interruptions to exchange the samples.

Structure of measured data

As mentioned above, each of the Timepix pixel detectors used in the study has a square chip with a size of 14.08 mm × 14.08 mm divided into 256 × 256 pixels. Raw data obtained from a detector has a simple format of three columns, storing the 𝑥 and 𝑦 coordinates of each pixel and the energy deposited in the pixel, respectively. Each file contains information about the total energy per individual pixel over a specified time period known as a "time slice". The dead time between two time slices is typically around 200 ms, regardless of the length of the time slice. A time slice of 1 second was chosen, as this allowed individual particles to be isolated, while minimizing the relative fraction of dead time. In figure 5, data recorded in a single 1-second time slice is visualized as an example.

The software used, Pixelman [START_REF] Tureček | [END_REF] (developed at IEAP, CTU in Prague), provides a user interface for the Timepix detectors. While the software can be used to extract the previously-described raw data, Pixelman also provides a pre-analyzed 'clustered output' [12] format, which enables the identification and energy measurement of individual particles. The algorithm that transforms the raw data into clustered output first groups the triggered pixels from one time slice into clusters, based on their spatial adjacency. It then extracts the energy of each cluster (representing one particle, which might have triggered several pixels) and its position. The sum of the energy deposited in all the individual pixels of a cluster represents the energy deposited by the particle in the detector. The cluster position is defined as the average position of the individual pixels in the cluster, weighted by the energy deposited in each pixel. The clustered output also reports a 'cluster size', corresponding to the number of pixels in each cluster, which is related to the particle type: single-pixel isolated energy deposits are typically produced by photons and Auger electrons, while high-energy electrons generate multi-pixel clusters. The analysis described in the following sections was performed on this clustered output.

Data analysis method

The main goal of this study was to develop an experimental method that could evaluate the quality of a source based on the position of 207 Bi within its source frame assembly. In practice, this can prevent the use of any sources with unwanted contamination caused by 207 Bi droplet leakage into the region of the copper source frame. The study also has the potential to reduce systematic uncertainties related to the calibration source positions within the SuperNEMO Demonstrator Module. Precise knowledge of source positions can enable us to evaluate our tracker's vertex resolution capabilities, and to ensure that electron track lengths are correctly reconstructed.

The positions of the clusters measured for a single source (integrated over all the time slices) can be represented by a two-dimensional histogram. Each cluster is weighted by its energy in order to obtain an energy distribution. This histogram shows a wide peak corresponding to the region of the source frame where the 207 Bi has been deposited (figure 6). The 𝑥 and 𝑦 directions are aligned with the 8-mm and 13-mm axes of the source frame, respectively.

High-energy electrons activate several pixels; the location of the earliest hit, likely to correspond to the electron's source position in the 207 Bi droplet, is unknown. The best source localization of the 207 Bi droplet was therefore achieved by selecting only the clusters corresponding to a single pixel, and with a reconstructed energy between 3 keV and 30 keV, reducing the uncertainty on the measurement of the cluster position (figure 6b). This energy region consists of X-rays and Auger electrons from electron capture on 207 Bi, and contains the majority of these single-pixel events The black points represent the position of the calculated weighted center (𝑥 0 , 𝑦 0 ). The blue circles represent the contour lines where the fitting function reaches half of the maximal value (thus, the radius of the circle is the half width at half maximum, HWHM). a) Energy distribution for all clusters with an energy in the range 3-1300 keV (no cluster size cut). The distribution includes all types of particle produced in 207 Bi decays (X-rays, gammas and electrons). b) Energy distribution for single-pixel clusters with an energy in the range 3-30 keV, corresponding to Auger electrons and X-rays. Note differing scale on color axis.

(figure 7). This selection made a negligible difference to the best-fitted position coordinates of the droplets' centers, with an average difference between the pre-cut and post-cut position of 0.054 mm, comparable to the size of a single detector pixel. This energy range and single-pixel cut will henceforth define our region of interest (ROI). It should be noted that, during measurement, there is a small gap (1.5-3 mm, depending on the individual source) between the 207 Bi source and the Timepix detector. As particles are emitted from the source at varying angles, even when a single pixel is triggered, the corresponding particle may not have been emitted immediately above that pixel.

The comparison of energy distributions with and without these cuts is shown in figure 6. After applying the cuts (figure 6b), the radius of the half-width-at-half-maximum (HWHM) contour is reduced by approximately 20% with respect to the full sample (figure 6a). A plot similar to figure 6b was obtained for each measured source and fitted with a two-dimensional function.

𝑓 (𝑥, 𝑦) = 𝐴 (𝑥 -𝑥 0 ) 2 + (𝑦 -𝑦 0 ) 2 + 𝛾 . (2.1)
Here,the 𝑥 0 and 𝑦 0 coordinates represent the measured center of the source (in pixels), 𝛾 is proportional to the square of the width of the peak, and 𝐴 is a scale factor. A visual representation of the quantities extracted from the fit can be found in figure 8. The blue circles in figures 6 and 8 represent the border where the fitting function drops to half of its peak value (i.e. 𝐴/2𝛾). The radius of the blue circle represents a two-dimensional equivalent of the HWHM of the distribution.

For the purpose of this study, we considered this contour as a measured effective size of the 207 Bi droplet. The fitting function was chosen for its simple form that contains all necessary degrees of freedom. All of the droplets were confirmed visually to be circular in shape, apart from two; both sources with non-circular drops also failed subsequent selection criteria, and were not installed in the SuperNEMO Demonstrator Module. The position of the source extracted from the fit is given relative to the sensitive detector chip. Since the aim of the study was to extract the relative position of the source droplet with respect to the source frame, a spatial calibration, described in section 2.1, was used to provide the relative position of the center of the source frame (𝐶 𝑥 , 𝐶 𝑦 ) with respect to the chip. Information about the center of the frame allows us to define the position, ì 𝑟, of the 207 Bi droplet relative to the center of the source frame. It can be calculated as follows:

ì 𝑟 = (𝑟 𝑥 , 𝑟 𝑦 ) = (𝑥 0 -𝐶 𝑥 , 𝑦 0 -𝐶 𝑦 ).
(2.

2)

The vector ì 𝑟 can be seen in figure 8.

Results

Categorization of sources based on droplet position

For this study, we collected data from 49 different source samples in 52 measurements. As explained previously, the standard acquisition time to collect sufficient statistics was 2-3 hours. Supplementary high-statistics measurements on sources 126, 132 and 139, for periods of up to a few days, aimed to improve precision and better estimate systematic uncertainties, as explained in section 3.2. A sample of some of these measurements is shown in table 1; a complete list is in tables A1 and A2 of [13]. 1.0 46.0 4.0×10 6 2.0×10 6 49.5 11.9

As previously discussed, the aim of this study was to estimate the position of the 207 Bi droplet in each source relative to the center of its frame of (inner) dimensions 8 mm × 13 mm, where the 𝑥 direction corresponds to the shorter axis of the frame. This droplet position is described by the length of the vector 𝑟 = |ì 𝑟 | defined in subsection 2.4. According to the magnitude of 𝑟 we defined three source categories:

• very good sources (𝑟 < 0.5 mm), represented by green triangles;

• good sources (0.5 mm ≤ 𝑟 < 1.0 mm), represented by yellow circles;

• unacceptable sources (𝑟 ≥ 1.0 mm), represented by red squares.

The computed values of ì 𝑟, colored according to their category, are shown in table 2 for a subset of measurements, and in figure 9 for all measurements (the full list is also included in tables A3 and A4 of [13]). The positions of the 49 source droplets, and their radii, are summarized in figure 10. We identified 5 sources where the center of the droplet had been deposited more than 1 mm away from the center of the source frame center (red squares), which were rejected. The centers of the remaining 44 droplets were within 1 mm of the centers of the frames (green triangles or yellow circles).

Estimation of the uncertainty on the droplet position

Before each of the measurements, the measured source was aligned to the RAP manually. In figure 3b one can notice that in the shorter, horizontal direction (𝑥) the source touched the black plastic chip holder; however, in the longer, vertical direction (𝑦), the source could move freely and the human factor could introduce an extra source of uncertainty in this direction. An indication of this comes from the distribution of the measured droplet centers in 9, where it can be clearly seen that the measured 𝑦 positions of the centers tend to be higher than the centers of their respected source frames, as calculated from the RAP of the calibration grid (as in 4). As there is no asymmetry to the frames, and because the foils were produced with the intention of placing droplets in the center of the frames, it is reasonable to assume that the mean position of the full set of droplets should be central with respect to the frame. The offset of this mean position from our measured central point should therefore provide an estimation of the uncertainty on the measured values of the droplet position ì 𝑟. This mean position, indicated by the black cross in figure 11 has an offset of magnitude 0.02 mm in the 𝑥 direction, and 0.39 mm in the 𝑦 direction. It can be noted that, were this position to be taken as our central point, only two of our sources would be categorized as 'unacceptable', with a droplet position more than 1 mm from this new center (outside the yellow circle in figure 11). Both of these sources are already rejected by the original methodology.

As an additional check of this method of estimating the uncertainty on the droplet position, we considered the higher-statistics repeated measurements of droplet position and radius for three sources (126, 132 and 139), as shown in table 2. Only clusters from the ROI (energy range 3-30 keV 8, for repeated measurements on an unacceptable (red), good (yellow), and very good (green) source (see section 3.1). Asterisks denote a second measurement on a source, taken under the same conditions as the first. In the 𝑥 direction, where source positioning was constrained by the plastic holder, the repeatedmeasurement method yielded a larger variation in values than was indicated by the mean position offset (0.04 mm vs. 0.02 mm). Conversely, in the 𝑦 direction, where manual alignment was required, the consideration of mean droplet position yielded a larger offset than the repeated measurements would indicate (0.39 mm vs. 0.22 mm). In order to be conservative, we consider that a source should be deemed unacceptable if the radius of the droplet comes within a distance Δ𝑥 = 0.04 mm or Δ𝑦 = 0.39 mm of the source frame. It should be noted that, in both cases, these uncertainty estimates are small relative to the typical effective radius of the 207 Bi droplet which, at around 2 mm (see section 3.1), can be understood as a very conservative estimate of the uncertainty on the source position.

Droplet containment within the source frames

As explained in section 2.4, one goal of this study was to ensure that sources selected for the SuperNEMO Demonstrator Module did not suffer leakage of the 207 Bi droplet into the region of the copper frame. To confirm this was the case for our selected sources, the profiles of each droplet in the 𝑥 and 𝑦 directions were plotted relative to the source frame (figure 12).

To produce the projected profiles in figure 12, each droplet is assumed to be circular, centered at its measured best-fit point, with a radius corresponding to the fitted HWHM. The projection of each droplet is shown relative to the position of the copper frame, at ±4 mm in the 𝑥 direction, and ±6.5 mm in the 𝑦 direction (the frame extends beyond the plot, but only its inner dimension is relevant). Gray bars inside the source frame represent the uncertainty on position measurements in each dimension (Δ𝑥 = 0.04 mm and Δ𝑦 = 0.39 mm) as estimated in section 3.2. Sources colored green were categorized as very good, yellow as good, and red as unacceptable, based on the positions of the droplets' centers, as explained in section 3.1. The mean HWHM value for all measurements, including the rejected sources and repeated measurements on individual sources, is 2.03 ± 0.21 mm. It can be seen that none of the selected (green and yellow) sources show any overlap between the droplet and the source frame, and furthermore, that the distance between the droplet and frame is greater than the uncertainty on the droplet's position. We therefore conclude that there is no danger of leakage under the copper frame from our selected sources. The selected sources have a mean HWHM of 2.01 ± 0.19 mm.

Conclusions

In this paper, we describe a method for measuring the position of 207 Bi droplets in the SuperNEMO calibration sources within their frames, using Timepix detectors. We successfully applied this method to 49 207 Bi calibration sources developed for the SuperNEMO experiment, and evaluated their quality. All 49 sources of 207 Bi were proven to be eligible for calibration of the SuperNEMO Demonstrator Module, as none of them presented leaks towards the copper frame. The 42 sources whose 207 Bi droplets were closest to the center of the copper source frames (out of 44 that passed our stricter quality criteria) were chosen and installed in the SuperNEMO Demonstrator Module. These measurements also allow better characterization of the source deposition distributions, ensuring that knowledge of the 207 Bi source positions does not limit the energy and vertex reconstruction of the SuperNEMO Demonstrator Module.

Figure 1 :

 1 Figure 1: Overview of the SuperNEMO Demonstrator Module. Figure by C. Bourgeois [3].

Figure 2 :

 2 Figure 2: a) Photograph of 207 Bi source number 139. b) Diagram of the envelope which fixes the source within the deployment system. c) Simplified diagram of the 207 Bi deployment system. Orange rectangles represent source envelopes (not to scale). Six columns, each comprising seven 207 Bi sources, are vertically deployed into gaps between the 82 Se 𝛽𝛽 source foils by an automatic system above the SuperNEMO Demonstrator Module.

Figure 3 :

 3 Figure 3: a) Photograph of one of the Timepix pixel detectors used in this work, H04-W0163, which has a 0.3 mm-thick silicon sensor. b) Photograph of the source position during each measurement. The two yellow arrows point to the Reference Alignment Point (RAP).

Figure 4 :

 4 Figure 4: a) Photograph of the calibration grid. The yellow circle denotes the corner corresponding to the RAP during the spatial calibration measurements. b) The grid as seen in the detector after the exposure to X-rays. Neither the first two rows nor the first column are visible in the dataset; nor is the yellow reference point shown in the left-hand figure, as these lie outside the sensitive area of the detector. In order to identify individual holes in the dataset, we covered one of the holes with a piece of metal.

Figure 5 :

 5 Figure 5: Visualization of the data collected from a sample 207 Bi source in a one-second time slice. A typical photon and electron candidate are marked.

Figure 6 :

 6 Figure 6: Energy distributions measured for source number 133, with different selections applied.The black points represent the position of the calculated weighted center (𝑥 0 , 𝑦 0 ). The blue circles represent the contour lines where the fitting function reaches half of the maximal value (thus, the radius of the circle is the half width at half maximum, HWHM). a) Energy distribution for all clusters with an energy in the range 3-1300 keV (no cluster size cut). The distribution includes all types of particle produced in207 Bi decays (X-rays, gammas and electrons). b) Energy distribution for single-pixel clusters with an energy in the range 3-30 keV, corresponding to Auger electrons and X-rays. Note differing scale on color axis.

Figure 7 :

 7 Figure 7: Measured energy spectrum for source number 126, including a) all clusters in the energy range 3-1300 keV (no cluster size cut) and b) single-pixel clusters in the range 3-30 keV.

Figure 8 :

 8 Figure 8: Graphical representation of quantities extracted from the fit to equation 2.1: the blue circle represents the HWHM contour; the black dot denotes the center of the 207 Bi deposition (𝑥 0 , 𝑦 0 ); the red dot, the center of the frame (𝐶 𝑥 , 𝐶 𝑦 ); and the green arrow, the vector ì 𝑟 of the droplet's position with respect to the frame's center.

Figure 9 :

 9 Figure 9: Position of the center of the 207 Bi droplet for each of the measured sources, relative to the center of the source frame. Source quality rankings of very good (green triangle), good (yellow circle) and unacceptable (red square), are explained in section 3.1. Uncertainties are not shown, for the purpose of clarity. Note that the position of one source fell outside the range of this plot.

Figure 10 :

 10 Figure 10: Summary histograms showing the positions of the droplets' centers, relative to the center of the source frame, for very good (green), good (yellow) and unacceptable (red) sources. Histograms a) and b) summarize the displacements along the short (𝑥) and long (𝑦) axes of the source frame respectively; c) shows the magnitudes of source droplet displacements; and d) shows the radii of the droplets. For sources where multiple measurements were taken, average values are plotted.

Figure 11 :

 11 Figure 11: Position of the center of the 207 Bi droplet for each of the measured sources, relative to the center of the source frame, as in figure 9. Markers denote quality rankings as in the original figure. The black cross denotes the mean position of the droplet centers at (-0.02 mm, 0.39 mm).Green and yellow rings denote a 0.5 mm and 1.0 mm offset respectively from this mean position.

Figure 12 :

 12 Figure 12: Projections of the 𝑥 (top) and 𝑦 (bottom) positions of the droplet in each source. The center of each bar indicates the fitted position of the droplet 𝑟 𝑥 or 𝑟 𝑦 ; the bar height is twice the HWHM; and the label indicates source ID number. Colors indicate quality categories (see section 3.1). The brown horizontal bars indicate the position of the copper frame position; the adjoining gray bars show the uncertainty on position measurements.

Table 1 :

 1 Statistics of a sample set of measurements, including standard measurements of 2-3 hours and extended measurements of 2 days or more. The first column shows the ID number of the measured source, with an asterisk (*) denoting measurements repeated under the same experimental conditions. The second and third columns indicate the Timepix detector and its thickness (𝑑 DET ). The table also contains the active exposure time (not including dead time) (𝑡 live ), total statistics collected (𝑁 TOT ), number (𝑁 ROI ) and fraction of events in the ROI, and detection rate. The ROI included all single-pixel clusters in the energy range 3-30 keV. The full data set (TOT) contains all 3-1300 keV clusters of 1 to 100 pixels. Note the improved detection rate and fraction in the ROI for the thicker (1 mm) detector.

	Source Detector ID	𝑑 DET 𝑡 live [mm] [h]	𝑁 TOT [cnts]	𝑁 ROI [cnts]	𝑁 ROI 𝑁 TOT [%] [𝑠 -1 ] 𝑁 ROI 𝑡 live
	73	H04-W0163	0.3	1.7 1.1×10 5 5.0×10 4 43.3	8.3
	74	H11-W0163	0.3	1.8 1.2×10 5 5.4×10 4 43.4	8.4
	111	H11-W0163	0.3	3.8 2.9×10 5 1.3×10 5 43.3	9.1
	120	L05-W0163	1.0	12.7 1.1×10 6 5.5×10 5 50.4 12.1
	126	H04-W0163	0.3	55.5 3.4×10 6 1.5×10 6 43.0	7.4
	126*	H04-W0163	0.3	46.2 3.0×10 6 1.3×10 6 42.5	7.8
	132	H11-W0163	0.3	54.8 4.0×10 6 1.7×10 6 43.5	8.7
	132*	H11-W0163	0.3	46.0 3.3×10 6 1.4×10 6 43.3	8.7
	139	L05-W0163	1.0	54.8 4.7×10 6 2.3×10 6 49.6 11.9
	139*	L05-W0163

Table 2 :

 2 Summary of the quantities defined in figure

  𝑟 𝑥 and 𝑟 𝑦 , between two repeated measurements, we can (very roughly) estimate their uncertainty. The relative difference on the 𝑟 𝑥 component for two different measurements of source 132 is 0.04 mm. Since this value is smaller for sources 126 and 132, we considered 0.04 mm as the uncertainty in the 𝑟 𝑥 component, i.e. Δ𝑥 = 0.04 mm. By applying the same logic for 𝑟 𝑦 , we obtain a value of Δ𝑦 = 0.22 mm from the comparison of the two measurements for source 126.

	Source Droplet radius Droplet displacement
	ID	HWHM	𝑟 𝑥	𝑟 𝑦	𝑟
		[mm]	[mm] [mm] [mm]
	126	2.44	-1.22 0.11	1.23
	126*	2.14	-1.24 0.33	1.28
	132	1.96	-0.25 0.57	0.62
	132*	1.95	-0.29 0.74	0.79
	139	1.61	-0.02 -0.07	0.07
	139*	1.62	-0.05 0.08	0.10
	and cluster size of one pixel) were taken into account. By comparing the droplet position vector
	components,

Acknowledgments

We thank the staff of the Modane Underground Laboratory for their technical assistance in running the experiment. We acknowledge support by the grant agencies of the Czech Republic, CNRS/IN2P3 in France, RFBR in Russia (NCNIL No19-52-16002), APVV in Slovakia (Project No. 15-0576), the Science and Technology Facilities Council, part of U.K. Research and Innovation, and the NSF in the U.S. This work is supported by the Ministry of Education, Youth and Sports of the Czech Republic under the Contract Number LM2018107.


S Bagchi
email: s.bagchi@gsi.de

H Akimune

J Gibelin

M N Harakeh

N Kalantar-Nayestanaki

N L Achouri

B Bastin

K Boretzky

H Bouzomita

M Caamaño

L Càceres

S Damoy

F Delaunay

B Fernández-Domínguez

M Fujiwara

U Garg

G F Grinyer

O Kamalou

E Khan

A Krasznahorkay

G Lhoutellier

J F Libin

S Lukyanov

K Mazurek

M A Najafi

J Pancin

Y Penionzkhevich

L Perrot

R Raabe

C Rigollet

T Roger

S Sambi

H Savajols

M Senoville

C Stodel

L Suen

J C Thomas

M Vandebrouck

J Van De Walle

Signature of a possible α-cluster state in N = Z doubly-magic 56 Ni

An inelastic α-scattering experiment on the unstable N = Z, doubly-magic 56 Ni nucleus was performed in inverse kinematics at an incident energy of 50 A.MeV at GANIL. High multiplicity for αparticle emission was observed within the limited phase-space of the experimental setup. This observation cannot be explained by means of the statistical-decay model. The ideal classical gas model at kT = 0.4 MeV reproduces fairly well the experimental momentum distribution and the observed multiplicity of α particles corresponds to an excitation energy around 96 MeV. The method of distributed mα-decay ensembles is in agreement with the experimental results if we assume that the α-gas state in 56 Ni exists at around 113 +15 -17 MeV. These results suggest that there may exist an exotic state consisting of many α particles at the excitation energy of 113 +15 -17 MeV.

Introduction

The study of α clusters in nuclei is a very interesting field of research in nuclear physics. The main highlight of the α-cluster studies is the Hoyle state (0 + 2 ) in 12 C at 7.65 MeV. This resonance state, above the 3α threshold, is the doorway for the abundance of 12 C in the universe through the nucleosynthesis process [1], which resulted with life on earth. In the 1960s, Ikeda et al. [2] predicted that α-cluster states should exist closely above the particle-emission thresholds in light nuclei. In finite nuclei, the αcluster state may exist in excited states with a dilute density composed of a weakly interacting gas of α particles [3,4], where the degrees of freedom of the individual nucleons are no longer crucial [5]. Cluster structures in nuclei have been discussed in a wide range of theoretical models, such as, resonating group methods (RGM) [6], generator coordinate methods (GCM) [7], self-consistent mean-field theory framework [8,9], ab-initio calculations [10], Tohsaki-Horiuchi-Schuck-Röpke wave function [11] etc. In a cluster state, the α-clusters condense into the lowest S-wave orbit [11] and thus, it is analogous to the Bose-Einstein condensed states of bosonic atoms. The condensation could occur in a low-density region. However, almost no exper-imental information on such states has been obtained except for light nuclei. It is now established that the lightest α-conjugate system 8 Be (it has been known for a long time that the ground state of this nucleus decays into two α particles) has a dumbbell configuration comprising two α particles [12] separated by a distance of 4.4 fm [13,14]. The search for the α-cluster state was then extended towards the α-conjugate nucleus 12 C [15] to enrich our understanding of the characteristics of the Hoyle-state [1,16,17,18,19,20]. In the case of 16 O, the α-cluster structure has been also studied [START_REF] Wakasa | RCNP annual report[END_REF][START_REF] Wakasa | [END_REF] to explore experimentally the state in 16 O equivalent to the Hoyle-state in 12 C, which renewed the interest in this field [23]. Recently, the α-cluster state in 40 Ca has been investigated [24]. More details about the theoretical and experimental efforts to search and understand the cluster structures in nuclei have been elaborated in Refs. [START_REF] Beck | Clusters in Nuclei[END_REF][START_REF] Beck | Clusters in Nuclei[END_REF][START_REF] Beck | Clusters in Nuclei[END_REF].

The search for cluster structures in unstable nuclei became relevant in the past few decades with the availability of the radioactive ion-beam facilities and the state-of-theart particle detectors. Inelastic α-particle scattering has been found suitable to search for the condensate state because it has a selectivity to excite the natural parity states with T = 0 in self-conjugate nuclei. Moreover, inelastic αparticle scattering is a surface reaction, and the angular distributions are characteristic of the transferred angular momentum ∆L. It has been successfully established in finding the condensate state in light nuclei [15,[START_REF] Wakasa | [END_REF]28,29]. The effort to study the α-cluster state in unstable nuclei with inelastic α-particle scattering has been reported in Refs. [30,31].

We present here the experimental results of inelastic α-particle scattering off 56 Ni, which suggest the signature of a possible α condensate in the unstable N = Z doublymagic 56 Ni nucleus, potentially composed of 14α clusters. A preliminary report has appeared in Ref. [31].

Experimental setup

We performed the experiment of inelastic α-particle scattering off 56 Ni (T 1/2 = 6.075 days [32]) in inverse kinematics at GANIL. The 56 Ni beam at 50 A.MeV incident energy was obtained via the process of nuclear fragmentation of a 75 A.MeV 58 Ni beam bombarding a 526 µm thick Be target. The 56 Ni beam was selected and purified using the "Ligne d'Ions Super Epluchés" LISE spectrometer which consists of two dipole magnets with a 500 µm thick achromatic degrader (made of beryllium) [33]. The secondary 56 Ni beam intensity was 2 × 10 4 pps on average with a purity of 94.7%. The dominant contaminants were 55 Co (purity 5.0%) and 53 Fe (purity 0.3%). They were identified along with the ion of interest using the energy loss (∆E) and the time-of-flight information for lowintensity beam. The ∆E signal was derived from a Si detector placed before the MAYA active target, whereas the time-of-flight information was obtained using the trigger signals from the cyclotron radio frequency and a plastic scintillator placed before the MAYA setup. The Si detector, before the MAYA setup, was retracted from the beam For readability, the mask below the beam path is not drawn here.

Frisch grids

line during the data-taking time with the high-intensity beam. In the offline analysis, the 56 Ni beam was selected by putting a proper selection window in the time-of-flight spectrum; for details, see Ref. [34].

Since the measurement was performed in inverse kinematics, an active target, MAYA [35], was employed. MAYA, developed at GANIL, is a time-charge projection chamber with an active volume of 28(l) × 25(w) × 20(h) cm 3 filled with helium gas (acting as α-particle target) at 500 mbar pressure (with 5% of CF 4 as a quenching gas). The pressure was adjusted to cover as much as possible all the ranges of the recoiling particles necessary for the study of inelastic α scattering in the excitation-energy range of 0 to 35 MeV, i.e. including the regions of the isoscalar giant monopole, quadrupole and octupole resonances at angles from 3 • up to 8 • in the center-of-mass (c.m.) frame.

As shown in Fig. 1, both the incoming 56 Ni beam and the scattered α particle ionize the gas along their trajectories inside MAYA. The cathode plate at the top of MAYA was set to -3 kV, whereas the Frisch grid was maintained at ground potential. Due to the applied electric field between the Frisch grid and the cathode plate, electrons, generated in the ionization process, drift towards the Frisch grid. Furthermore, a high voltage of +1.3 kV was applied to 32 amplification wires that were below the Frisch grid and were parallel to the beam direction. The avalanches on the wires induced signals on a matrix of 32 × 32 hexagonal pads of 5 mm side length, which were individually recorded [35]. Thus, a two-dimensional picture of the reaction was reconstructed on the pad plane. The drift velocity of electrons was 1.7 cm/µs. The drift time of electrons to each wire was recorded in order to determine the reaction plane in the three-dimensional space.

In order to measure both the recoil particle and the beam efficiently, an electrostatic mask [36] was placed 1 cm below the beam axis in MAYA (not shown in Fig. 1) to reduce the number of electrons produced through the high ionization by the 56 Ni beam and thereby reduce spacecharge effects. The mask was extended through the central region of the cathode pad plane along the beam direction and did not interfere with the electric field where the recoil α particles were detected. It consisted of 9 wires of 50 µm diameter with a 1 mm pitch. The three central wires were biased at -900 V, the next two wires on each side were biased at -1000 V, and the outermost wires were biased at -1100 V (See Fig. 3.13 of Ref. [34]) to capture electrons originating from the beam ionization. The outer-most wires were kept at the same potential as that generated by the applied drift electric field at the height of the wire mask. Therefore, the amount of charge collected on the central wire due to the ionization by the beam is greatly reduced and the detection of charge produced by the less ionizing recoil α particles becomes more sensitive. As shown schematically in Fig. 1, 20 ∆E-E telescopes, each consisting of one 700 µm thick Si detector having dimensions of 5 × 5 cm 2 (∆E) followed by four 2-cm thick CsI scintillators (E) with surface area of 2.5 × 2.5 cm 2 (resulting in 80 separate ∆E-E segments), were placed 5 cm downstream of the active region. The 20 ∆E-E telescopes were arranged in a 5 (horizontal) × 4 (vertical) matrix, and allowed the identification of all light charged particles with kinetic energies high enough to pass through the Si layer. The pre-amplifiers of the Si detectors were connected to CAEN N568B spectroscopy amplifiers with dual outputs comprising a normal signal and a signal amplified by a factor of ten, which allowed us to achieve a better resolution at low energy (typically for p, d, and t identification). Because we had only one Si detector followed by four CsI detectors, we deduced the corresponding ∆E energy loss in the Si detector by dividing the measured total energy with the number of CsI-detector hits at the back. This approach was validated with simulations. Energy calibration for the Si detectors was performed up to 7.7 MeV using a 226 Ra 4α-line source. The responses of the CsI detectors were calibrated from the extrapolation of the energy deposited in the Si detectors. The light-output correction for the CsI detectors was performed following the procedure described in Ref. [37]. The resulting twodimensional scatter plot of deposited E versus ∆E energies is presented in Fig. 2. The total energy deposited by an α particle is then obtained as the sum of the ∆E and E signals.

One must note that the aim of this experiment was originally to search for the compression modes in 56 Ni using inelastic α-particle scattering in inverse kinematics [34,38]. The detailed discussions about the setup, the calibration and analysis procedures are given in Refs. [34,39].

Analysis

Due to the limitation of the phase-space covered by the experimental setup, excitation energies of 56 Ni only up to ∼ 35 MeV could be reconstructed using the missing-mass method. Hence, the extraction of the resonance energy of a possible α-condensate state in 56 Ni, which is well above 35 MeV excitation energy, is not feasible experimentally in the present setup. The analysis of the particle-emission data was performed here with the wall of solid-state detectors as shown in Fig. 1. In this analysis, we found that many particles are emitted at forward angles with high multiplicities. In Fig. 3, the distributions of the observed multiplicities (n) of α particle, proton, deuteron, and 3 He are shown. The pile-up events due to multiple particles hitting the same CsI crystal were simply discarded. Note that experimentally the number of pile-up events was negligible because of the limited intensity of the incoming 56 Ni beam. This can also be deduced from Fig. 2, which shows no evidence of events between the loci of the different ejectile nuclei and thus confirming the absence of pile-up events in case of the present analysis. As can be seen in Fig. 3, the maximum multiplicity observed for α particles is seven. This means that in the limited phasespace acceptance of the present experiment, half of the mass of 56 Ni is observed to be carried away by means of emitted α particles. The multiplicity distributions are well reproduced by an exponential function exp (-λn), where n is the measured multiplicity. The multiplicity slope λ is determined to be 2.17 ± 0.07 for α particles.

The λ value for α-particle emission is the smallest compared to the multiplicity slopes for proton, deuteron, and 3 He, which are 2.37 ± 0.11, 2.88 ± 0.21, and 3.98 ± 0.32, respectively. The parameter λ reflects the dependence of the measured α multiplicity, n, on the cross section for a total decay of mα particles in the 56 Ni(α, α mα) reaction and on the experimental acceptance. This experimental result is surprising, because it is natural to expect that the charged-particle decay from states at high excitation energies is suppressed by the Coulomb barrier relative to neutron decay. Furthermore, one would expect α emission to be more suppressed than proton and deuteron emission. In fact, the maximum multiplicities of protons and deuterons are smaller than that of α particles. The observation of multiple α-particle decay in the present experiment would be a signature of a possible existence of an α-condensed state in 56 Ni at high excitation energy.

Statistical-decay model

In order to examine the possibility of statistical decay from compound states, which may have a small overlap with an α-cluster state, we performed statistical-decay model calculations based on the Hauser-Feshbach formalism using the code CASCADE [40], which was modified to take spin, isospin and parity exactly into account in the calculations [41]. In that respect, global level-density parameters were used to describe the unknown levels at high excitation energies in daughter nuclei applying proper spin, isospin, and parity quantum numbers to these input parameters. Furthermore, individual level parameters for the low-excitation-energy region were taken from the experimental data. All the decay channels, i.e. γ, neutron, proton, and α decays, are taken into account applying the proper spin and isospin Clebsch-Gordan coefficients coupling decaying states to final states. The spin, parity and isospin for the initial decaying states in 56 Ni that have been excited by inelastic α scattering were set to be J π = 0 + and T = 0, assuming that a monopole resonance is strongly excited at high excitation energies around 100 MeV (see the next section for detailed explanation). However, it should be noted that the performed statisticalmodel calculations show that results do not change significantly if we assume a low-spin initial state instead of a monopole state. The maximum angular momentum for decay products was set to be 40h. Figure 4(a) shows the average multiplicities of protons, neutrons, and α particles estimated in the statistical-decay model using the CASCADE code. Even for an excitation energy, E x , of about 150 MeV, the estimated average multiplicity for decay α particles is found to be significantly less than five. In the statistical-model calculations, competition between different decay channels is automatically taken into account. We have performed statistical-model calculations for decay of 56 Ni excited to 110 MeV (Fig. 4(b)) using CASCADE taking spin, isospin and parity properly into the calculations. These calculations have been used to estimate the number of α particles emitted by statistical decay from the excited state of 56 Ni. The CASCADE code is not a Monte-Carlo statistical code, and therefore the decay chains cannot be followed separately. We have deduced the α multiplicity from the population of 52 Fe, 48 Cr, 44 Ti, 40 Ca, 36 Ar, 32 S, and 28 Si. In the statistical-model calculations with the CASCADE code, one cannot distinguish between an α emission or 2p-2n emission through which a nucleus is populated, although the energetics are quite different, since 2p-2n corresponds to full breakup of an α particle requiring 28.3 MeV extra energy. Due to these processes, the statistical model calculation overestimates the α multiplicities. This implies even a larger discrepancy with the experimental data.

The lightest nuclei produced by the decay were found to be 32 S, 31 S and 31 P. Lighter nuclei than these are produced with a probability of less than 0.1×10 -7 , which is the minimum of the calculation accuracy of CASCADE. The probability of emitting six α particles sequentially was estimated to be 0.7×10 -6 . In Fig. 4(b), the total number of counts in the statistical model is normalized to the experimental observation at multiplicity 1. Therefore, with the above-mentioned probability in the statistical model, the total number of counts for multiplicity six is estimated to be around 0.7. On the other hand, the experimentally observed number of counts for multiplicity six is around 20, which is about a factor 30 higher than the statisticalmodel prediction. The difference is even higher in the case of multiplicity seven. In Fig. 4(b), there is a sharp kink in the statistical-model curve showing the total number of counts is decreasing rapidly to zero for multiplicities larger than five. Hence, the absolute discrepancy between the statistical model and the experimental observation is large as is also evident from the average multiplicity in Fig 4(a). Furthermore, in the sequential decay chain of α particles, a proton or a neutron can be emitted preceding or following one of the α emissions. The probability of emitting six α particles and one proton is estimated to be 0.4×10 -6 , and the probability of emitting six α particles and one neutron is estimated to be less than 0.1×10 -7 . In fact, these background processes add up to the pure sequential α decay and make the probability of six-α emission a bit larger in the statistical model. This, together with the overestimation of the α multiplicities due to the 2p-2n emission discussed above, implies that the α multiplicities calculated in the statistical model with CASCADE should be (much) lower than shown in Fig. 4(b) and therefore highly underestimate the observed α multiplicities.

The decay constant of the probability of emitting n α particles via the statistical decay processes were estimated to be 2.49. Therefore the statistical decay model cannot explain the value 2.17 ± 0.07 obtained in the experiment. Moreover, the statistical-model calculations are not able to explain the highest observed α multiplicities.

Ideal-gas model

One of the possibilities to explain the observation of such a high multiplicity of α particles is to introduce the concept that many-α-particle emission may come from an exotic high-lying state such as a dilute α-gas state. In order to understand qualitatively whether this hypothesis is correct, we performed a simulation based on the simple statistical model. In this model, we have assumed that the excited state in 56 Ni consists of fourteen independent α clusters, and that the distribution of the kinetic energy for each α particle follows the Boltzmann distribution for the classical ideal gas at a relatively low temperature T . The highly excited 56 Ni nuclei are assumed to move along the z direction with a kinetic energy of 50 A.MeV and emit fourteen α particles. The kinetic energy and the direction in the c.m. system of the produced 56 Ni nuclei were randomly given by assuming the Boltzmann distribution. We have used the Boltzmann distribution to describe the decay of the excited α condensate. In principle, the Bose-Einstein distribution should have been used. However, this is beyond the scope of this article for two reasons. The experimental reason has to do with our experimental detection system, which does not have the necessary granularity for high spatial resolution needed for forward-boosted α particles due to the high velocity of the c.m. system. This makes differentiation between models difficult. The second Multiplicity (n) reason for adopting the classical ideal gas model is that classical statistics have only one free parameter (kT ). Using the Bose-Einstein distribution instead requires fitting more parameters, which is not justified by the quality of our experimental data. This is an experimental task for the future.

In the simulation, the detection probability was estimated event by event for emitted α particles. We reconstructed the deposited energy in the Si+CsI array by taking into account its segmentation. We also simulated the thickness of the 4 He gas target (28 cm in length) by randomly choosing the vertex point of the reaction. The polar and azimuthal angles of the recoil α particles are then reconstructed accordingly.

Figure 5 shows the results of the simulation for the detection efficiency of α particles from 56 Ni at kT = 0.4, 1.5, and 4.0 MeV, where k is the Boltzmann constant. The variable n is defined as the number of α particles detected within the limited phase-space acceptance of the present experimental setup. In the simulation, pile-up events were discarded as has been done in the experiment. When the simulation is carried out with the temperature of kT = 0.4 MeV, the corresponding parameter λ = 1.99 ± 0.8 is in close agreement with the experimentally determined value for α particle emission within the errors. The temperature of 0.4 MeV corresponds for m = 14 to an excitation energy of 3 2 mkT = 8.4 MeV above the fourteen-α separation threshold energy in 56 Ni. Since the 14α separation threshold energy is E 14 th = 87.9 MeV, this means that the condensate is close to it at a corresponding excitation energy of E x ≈ 96 MeV.

In Fig. 5, we see that the efficiency for detecting α particles becomes lower with the increasing number of detected α particles. Furthermore, the efficiency is especially low at lower temperatures, because at the lower temperatures the α particles move with small kinetic energies in the c.m. system of the highly excited 56 Ni nucleus, and are therefore boosted to very small angles in the laboratory system. Since no particle detectors were placed on the incident-beam axis, it was impossible for us to measure α particles scattered in the very forward direction close to the beam axis. Also, when more than one α particle (pileup event) enter the same detector telescope, it is excluded from the number of α particles detected in the simulation since it cannot be identified.

Since the spread of the α particles in the x -y direction in the laboratory system becomes small when the temperature is low (kT < 1 MeV), the detection efficiency sharply decreases with increasing the number of detected α particles as shown in Fig. 5. At kT = 0.4 MeV, the detection efficiency for an event with seven α particles detected out of fourteen in total is < 10 -4 %. Taking this into account, the cross section for excitation of the αcondensate state via inelastic α scattering is estimated to be unexpectedly large for kT = 0.4 MeV, although the experimental multiplicity slope λ is well reproduced.

At kT = 1.5 and 4 MeV, the detection efficiency for an event with seven α particles detected out of fourteen in total are 0.06% and 0.8%, respectively. At high kT , the detection efficiency cannot be reproduced by a simple exponential function and the probability of detecting α particles of 4 or less does not depend strongly on the number of detected α particles. This is because the angles in the laboratory system of the emitted α particles become on the average larger for lower multiplicities, so that more α particles are detected in the counter telescopes.

Distributed mα-decay ensemble model

In the de-excitation process of the α-cluster state in 56 Ni, it is natural to assume that there is a process for decay not only by emitting 14α particles but also by emitting multiple (< 14)α particles decaying to residual nuclei. We investigated whether the process of decaying into a number of α particles can be understood by using a model that considers such a decay process, i.e. a decay process in which mα particles are emitted from an excited state in 56 Ni leading to a residual nucleus with a mass number A = 4(14 -m). Therefore, according to this scenario, we assume that the multiplicity distribution of α particles observed in the experiment is due to an ensemble of various mα decay processes. The excitation energy of 56 Ni was obtained from the theoretical value calculated by Yamada and Schuck [3] based on the dilute mα-condensate model. They estimated the excitation energy of the mαcluster state up to m = 12. The excitation energy of the α-cluster state for m = 14 system is simply estimated extrapolating their result to be E 14 T = 25 MeV above the 14α separation threshold energy of E 14 th = 87.9 MeV. In the following discussion, the excitation energy E x is fixed to be E x = E 14 th + E 14 T = 113 MeV and it is assumed that mα-particles share the energy E m T = E x -E m th according to the Boltzmann distribution. Here, E m T is the temperature of mα particles and E m th is the threshold energy for separation of (m)α particles resulting in a nucleus with mass number A = 4(14-m) as residue. The recoil energy in the c.m. system was not taken into account. This is a reasonable simplification at low multiplicities for which the recoil energy is small and will have little effect on the emitted α particles since the α particles are boosted with high energies in the forward direction. At high multiplici-ties, the α-particle emission has no preferred direction and therefore the recoil energy of the residue is on the average small. When the number of emitted α particles is one or two, the decay process is not necessarily that of a state having an α-cluster structure, but also includes the case of a statistical decay process. We did not take into account αparticle emission processes for estimation of the α-cluster structure. We define here n as the number of α particles detected within the limited phase-space acceptance of the present experimental setup and m as the number of α particles emitted from the excited states of 56 Ni. Figure 6(a) shows the results of simulations of detection efficiencies for m = 14, 11, 9, 7, 5, 3 α-particle decay events. Using these results, we determined the branching ratio for decay of mα particles using the formula,

Y n = 14 m=3 X m m (kT, n), (1)
to fit the experimental data. Here, X m is the estimated number of source events for mα-particle decay, m (kT, n) is the detection efficiency for nα particles out of mα particles at temperature T in mα-particle decay, and Y n is the yield of α particles for observed multiplicity n. The multiplicity distributions of α particles are well described with the sum of decay branches (see Fig. 6(b)).

Figure 7 shows the X m plot. Since events up to n = 7 were measured in the experiment, the branching ratios up to m = 7 are well determined for the given E th . Furthermore, since no events with n > 7 were detected, the estimated number of source events for mα-particle decay is not well determined. Although the simulation of the detection efficiency of multi-α particles varies depending on E x as described above, the experimental data are well fitted even when the excitation energy E x is varied between 8 and 40 MeV. Therefore, an uncertainty remains in determining the excitation energy in this experiment in the range of E 14 T = 8 to 40 MeV. Since the extrapolation gives E 14 T to be 25 MeV, the associated errors can be assigned to the excitation energy, that is 113 +15 -17 MeV. We performed additional simulations in order to confirm the validity of the present approach. Figures 8(a) and (b) show the two-dimensional scatter plots of the momentum distributions of α particles obtained by simulations at E T = 25 MeV. Figure 8(a) shows the superposition of all the events with a multiplicity ≥ 6. Figure 8(b) shows an example of the momentum distributions for a single event with multiplicity six. Figures 8(c momentum distributions obtained from the experiment rather well.

Summary and conclusion

We performed the α( 56 Ni, α ) inelastic scattering experiment in inverse kinematics at an incident energy of 50 A.MeV. Multi α-decay events were observed with a maximum multiplicity of seven particles within the limited phase-space acceptance of the present experimental setup. This result cannot be described by performing a simple calculation in the framework of the statistical-decay model and suggest a signature of the possible existence of an αcluster state at high excitation energies in 56 Ni. We used the ideal α-gas model and the distributed mα-decay ensembles to interpret the experimental findings. The results from both methods, albeit with large error bars, are compatible and can well reproduce the experimental data. The first method places the excitation energy of the α condensate around 96 MeV, whereas the second method yields an excitation energy of 113 +15 -17 MeV. As suggested by the results of this experiment, the α-cluster resonance state occurs at high-excitation energy in nuclei. Efforts should be made in the future to understand precisely the nature of the condensate state in α-conjugate nuclei at high-excitation energies [13].

Fig. 1 .

 1 Fig. 1. (Color online) Schematic view of the experimental setup with the MAYA detector. A 56 Ni beam (red) enters the active volume of MAYA and interacts with the helium gas resulting in the excitation of 56 Ni and a recoil (scattered) α particle (blue). The α particles from the decay of 56 Ni (dashed green) are forward focused and stop in the Si-CsI telescope.For readability, the mask below the beam path is not drawn here.

Fig. 2 .

 2 Fig. 2. (Color online) Two-dimensional scatter plot of energies deposited by charged particles in the CsI detectors versus energies deposited in the Si detectors after CsI light-output correction. The experimental loci are compared with theoretical calculations for light particles.

Fig. 3 .

 3 Fig. 3. (Color online) Multiplicity distributions of α particle (a), proton (b), deuteron (c) and 3 He (d). The histograms and solid lines correspond to the experimental data and the results of fitting, respectively.

Fig. 4 .

 4 Fig. 4. (Color online) (a) Excitation-energy dependence of average multiplicities estimated using the CASCADE code for the emission of α particles (solid line), protons (dashed line), and neutrons (dotted line). (b) Multiplicity distribution of α particles at Ex = 110 MeV: (solid line) estimated using the CASCADE code, (histogram) experimental data and (dashed line) result of fitting experimental data with an exponential function.

Fig. 5 .

 5 Fig. 5. (Color online) Estimated detection efficiency for a fourteen-α event at kT = 0.4 MeV (dotted histogram ), 1.5 MeV (solid histogram), and 4.0 MeV (dashed histogram). The solid lines are the results of fitting with an exponential function exp (-λn).

Fig. 6 .Fig. 7 .

 67 Fig. 6. (a) Detection efficiencies for m = 14 (solid), 11 (dashed), 9 (dotted), 7 (dot-dashed), 5 (dot-long-dashed), and 3 (dot-dot-dot-dashed) α particles are shown. See text for definition. (b) Experimentally observed multiplicities for α particles are shown in black filled squares. Fit to the experimental data with efficiencies for m = 14 to 3 α particles is shown with the thick solid line. Decomposition of partial contributions of m = 14 (solid), 11 (dashed), 9 (dotted), 7 (dot-dashed), 5 (dotlong-dashed), and 3 (dot-dot-dot-dashed) α particles is shown. For comparison, exponential fitting (e -λn ) with λ = 2.17±0.07 to the data is also shown (thick dashed).

Fig. 8 .

 8 Fig. 8. (Color online) Two-dimensional scatter plots of the momentum distributions of α particles. Results of simulations based on the classical ideal-gas model from events with multiplicity ≥ 6 (a), and from a single event with multiplicity six (b). Experimental momentum distributions of α particles from events with multiplicity ≥ 6 (c), and from a single event with multiplicity six (d).

Acknowledgements

This work was supported by the European Commission within the Seventh Framework Program through IA EN-SAR (Contract no. RII3-CT-2010-262010), GSI, Darmstadt, Germany, the United States National Science Foundation (Grants No. PHY-1068192 and PHY-1713857), the Hungarian NKFI Foundation (No. K124810), and the Hirao Taro Foundation of the Konan University Association for Academic Research.


J R B Oliveira

M Moralles

D Flechas

D Carbone

M Cavallaro

D Torresi

L Acosta

C Agodi

P Amador-Valenzuela

D Bonanno

T Borello-Lewin

G A Brischetto

S Calabrese

D Calvo

V Capirossi

F Cappuzzello

E R Chavez-Lomelí

I Ciraldo

F Delaunay

H Djapo

C Eke

P Finocchiaro

S Firat

M Fisichella

A Foti

G Gallo

M A Guazzelli

A Hacisalihoglu

F Iazzi

R Linares

D Lo Presti

J Ma

N H Medina

A Pakou

L Pandola

H Petrascu

F Pinna

S Reito

P Ries

G Russo

O Sgouros

S O Solakci

V Soukeras

G Souliotis

A Spatafora

S Tudisco

J S Wang

Y Y Yang

A Yildirim

V A B Zagatto

First comparison of GEANT4 hadrontherapy

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The NUMEN project [1] is an international collaboration involving more than 30 institutions led by the Istituto Nazionale di Fisica Nucleare -Laboratori Nazionali del Sud (INFN-LNS), Catania, Italy. In this project, double charge exchange (DCE) reaction cross sections of interest to neutrino physics, particularly neutrino-less double-beta decay [2], are to be experimentally evaluated. Many heavy-ion systems have been explored in the initial phases of the NUMEN scientific program, including the system of the present study. In the advanced phase of NUMEN, very large intensity beams from the CS superconducting cyclotron accelerator (LNS) will be available for experiments [3], reaching the order of 10 12 beam particles/s or more, and requiring modifications of the experimental apparatus [4][5][6][7][8][9][10]. Reliable estimates of the radiation field expected during such experiments are important for evaluation of the performance and possible radiation damage of detectors, electronics and other equipment. In association with the MAGNEX spectrometer [11], which will identify the species of the DCE projectile-like fragment (PLF), a gamma-array spectrometer [10] will assist the identification of the specific nuclear state which has been populated, by coincidence/anti-coincidence with the gamma transitions of the PLF and/or the target-like fragment (TLF), in the cases which MAGNEX energy resolution is insufficient for this task. With the high beam intensity, a large random coincidence rate is expected which could contaminate the DCE data. This contamination would come from uncorrelated nuclear reactions of all types of exit channels which can originate from the same beam/target combination of the entrance channel. Extensive Monte-Carlo simulations were performed for various reactions of interest to NUMEN in an attempt to provide a set of expected scenarios in which the detection system and accessories will operate, helping to choose the best design of the project. In the present work, one of these reactions ( 18 O + 76 Se at 275 MeV) was experimentally investigated in a first evaluation of the performance of those simulations in the project context. The EDEN array of liquid scintillators [12][13][14] was used for the detection of neutrons and gamma rays. The data were taken during the period of a present phase DCE measurement (November/December 2018).

Section 2 presents the description of the experimental setup and calibration procedures, Sect. 3 the simulations, Sect. 4 the results and discussion, while conclusions and perspectives are presented in Sect. 5.

The experimental setup and calibrations

The beam, 18 O at 275 MeV, was provided by the CS superconducting cyclotron of the LNS, pulsed at a 20 MHz fre-quency. About 1.5 nA (electric) of 8 + state beam ions impinged on the target, which consisted of enriched 76 Se (274 µg/cm 2 thickness) on a natural C backing (78 µg/cm 2 thickness). The target was placed at the center of the MAG-NEX scattering chamber, towards which the EDEN array of detectors are oriented. The EDEN array [12][13][14] consists of 36 NE-213 liquid scintillator detectors capable of n/γ discrimination. However, in the experiment only 21 detectors, those which presented the best performance in terms of energy and time resolution, noise, etc., were used in the analysis. Fast and Slow components of the pulse were separately digitized as described in [13]. The master gate for data acquisition was provided by a logical "or" of the time pulses of all detectors. The master gate in logical "and" with the RF pulse of the CS served as the common start of the time-todigital converter (TDC) with individual delayed stop signals from each detector. A data acquisition live time of 25.4% was determined for this measurement. During the experiment, the MAGNEX spectrometer was on and tuned to select the DCE PLF ( 18 Ne), since a standard NUMEN project measurement was under way. The 18 O beam was transported and stopped in a Faraday cup (FC) at the MAGNEX focal plane [15]. The EDEN data reported in the present work, however, were taken totally independently of the MAGNEX focal plane detector data.

The gamma-ray energy calibration of each EDEN detector was obtained in separate measurements of a 22 Na calibration source placed in front of each detector. In order to adjust the parameters of a linear calibration function, the spectra were compared to a GEANT4 simulation of the corresponding experimental conditions (see Sect. 3 for details). The simulation was smeared by convolution with a energy dependent width (according to Ref. [16]) Gaussian function in order to reproduce the experimental energy resolution, and normalized to show the same number of counts as the measured data between a selected threshold (around 0.25 MeV) and 1.5 MeV. This calibration procedure is necessary because of the low probability of photoelectric effect within the scintillator volume. Only the structure around the Compton edges of the 511 keV and 1275 keV gamma rays can be identified in the spectra. Figure 1a, b present typical samples of the simulation results in comparison to experimental data after calibration and subtraction of the ambient background (BG) spectra. The BG spectra were measured in a separate run with no gamma source. The correspondence is quite good except in the energy region below 0.3 MeV, where the experimental data show a relative enhancement of the number of counts probably due to the limited detail in the material surrounding the scintillator considered in the simulation. The concrete ceiling of the experimental hall, for example, which could back-scatter gamma rays towards the detectors, was not included in this simulation.

Figure 2 shows the sum of the energy-calibrated Fast versus Slow component spectrum of all EDEN detectors obtained during the in-beam measurement. A clear separation can be observed between γ -related and neutron-related signals. Figure 3 shows the corresponding sum of the TDC timecalibrated spectra of all 21 EDEN detectors (corresponding to the dead-time corrected number of 52.5×10 10 beam particles hitting the target). The time range is limited within the 50 ns interval between beam pulses from the cyclotron. This time interval is too short for appropriate neutron time-of-flight (TOF) measurements, which were therefore not attempted. The edges of the limits are not sharp due to small variations in cable length and CFD threshold among the different detectors. The gamma-gated individual spectra of each detector present a first peak which was shifted in the time calibration to the origin of the axis (t = 0 ns) for simplicity. This peak is associated with the prompt gamma rays emitted from nuclear reactions with the target. A secondary peak, located at t ≈ 25 ns is associated with gamma transitions generated at the FC (nearly 6 m downstream). The intensity of this peak varies considerably among the detectors due to different amount of material shielding the radiation between the FC and the specific detector, being negligible in some of them (see Fig. 4). The structure beyond 32 ns is due, mostly, to instrumental effects related to the partial overlap of the logic time pulses of the detectors and the CS RF pulse in the coincidence module, and should be disregarded. The neutron gated spectra (e.g. red dotted line in Fig. 3) present a very flat distribution.

Details of the simulations

The experiment was simulated using two programs based on the GEANT4 Monte Carlo toolkit [17][18][19] version 10.04.

The first program has as input the beam parameters (ion and energy) and the target characteristics (materials and thicknesses). The environment is vacuum and the target is positioned in the center of a virtual sphere defined as a detector. Information on all reaction products that cross the surface of this sphere as well as those remaining on the target is recorded in an N-tuple object in a ROOT [20] file. The information consists of the particle identification through the PDG code [21], volume (sphere or target), energy, momentum vector and time. This program is used to simulate reactions that occur on the target as well as on the FC. The data saved in the files permit also the calculation of target and FC activation.

The second program simulates the transport of all emerging particles from the target and from the FC through the MAGNEX experimental hall and their eventual interaction with the EDEN detectors. The modeling of the experimental hall was based on a floor plan of the facility. For simplicity, besides the floor, the walls and the ceiling, only the volumes are valid for the energy deposited by γ -rays by primary interaction with electrons. For neutrons, they correspond to electron-equivalent (ee) values, which are less than the actual energy deposited by the interactions (mainly with protons) in the detector with major contributions to scattering and absorption of particles were included in the simulation. These volumes are simplified versions of the EDEN detectors, the scattering chamber, the magnetic quadrupole and dipole of the MAGNEX, the focal plane detector and the FC. Each EDEN detector was simplified by one cylindrical volume (20 cm diameter by 5 cm length) with the scintillating material and a tube-shaped volume for its outer casing. Figure 5 shows a schematic of the GEANT4 modeled assembly. This program has as input the output file of the first program. It produces another file with N-tuples containing the PDG code, the time and the energy deposited in the scintillator for all particles that interact with the EDEN detectors.The recording and reading of the files was done using GEANT4's specific library to handle ROOT files. Note that in the case of the interaction with neutrons (mainly with protons) the energy deposited into the detector active volume is not converted to the detection pulse electric charge with the same proportionality constant as that of electrons (e.g. from gamma-ray interactions). No attempt to convert the deposited energy to the integrated pulse charge was attempted in the simulations. Therefore, care should be taken when comparing the electron-equivalent values, which are the ones experimentally obtained for neutrons, with the simulations.

The sensitive material of the EDEN detectors is the NE-213 liquid scintillator. The properties of this scintillator that allows gamma and neutron discrimination by pulse shape analysis have been well studied. GEANT4 has already been successfully used by Hartwig and Gumplinger [22] and by Scherzinger et al. [23] to simulate the NE-213 scintillators response to gammas and neutrons. As mentioned above, we have also successfully simulated the detector response to a 22 Na calibration source (Fig. 1).

The typical reactions explored in the NUMEN experiments employ beams of 18 O and 20 Ne with energies ranging from 15 to 60 MeV/u. The present measurement was incorporated into one of these experiments, which in the present phase are concentrated near 15 MeV/u. Among the options of physical models to simulate these reactions, we chose the set of processes used in the hadrontherapy example provided by the GEANT4 distribution, namely the physics list called "Hadrontherapy1". This option includes the well established processes for electromagnetic interactions that are responsible for the transport of photons and charged particles through the materials and the ParticleHP package which includes high-precision models for neutrons and light charged particles. It contains also the physical processes which describe the decay of excited nuclei and the transport and interactions of neutrons. The "G4BinaryLightIonReaction" physics model was used for the nucleus-nucleus collisions, which is an extension of the Binary Intranuclear Cascade model (BIC) for reactions with light ions [24]. Comparisons of this and other GEANT4 physics models (QMD-Quantum Molecular Dynamics, and INCL-Liège Intranuclear Cascade) with experimental results were reported for 12 C beam at 95 MeV/u on different targets [25], 55. 6 MeV/u on human tissues [26], 400 MeV/u on water [27], and 62 MeV/u on nat C [28]. None of these models appears to outperform the others in a general sense, while they were all tested in a higher energy range than in our case. We consider the BIC model suitable for our purpose of describing the background produced by reactions with cross sections that are several orders of magnitude larger than the DCE reactions.

Results and discussion

Gamma-ray spectra

Figure 6 shows the sum of the gamma cut energy spectra determined from the Slow pulse component (similar results were also obtained using the Fast component) of all detectors, gated in time around the prompt peak (-2.5 ns < t < 4.5 ns) and accidental-coincidence subtracted, in comparison to the corresponding simulation, following 14 × 10 10 primaries, normalized to the same number of projectiles of the experiment (N p = 45.0(14)×10 10 , determined from the integrated FC charge, dead-time corrected). The shape of the simulation spectrum fits well the experimental one above E > 0.25 MeV (i.e. above threshold of all detectors). The integral of the simulation spectrum in the interval between E = 0.25 and 2.5 MeV (within the active range of all detectors) corresponds to the experimental one if multiplied by a factor of 0.80. Although this indicates an overestimation of a factor of 1.26(4) by the simulation, the result is quite remarkable, considering the complexity and variety of nuclear reactions that can be involved in such a measurement.

Gamma-ray fold distribution

Table 1 presents the experimental coincidence gamma-ray fold K (number of EDEN detectors fired within the -2.5 to 4.5 ns time gate) distribution in comparison to the simulated one. The simulation results were multiplied by the number of projectiles normalization factor (3.2) in order to correspond to the experimental value of N p = 45 × 10 10 . An accidental coincidence BG time gate was set in the range from -11.5 to -4.5 ns for the experimental data. The accidental BG was subtracted from the data assuming a flat uncorrelated time distribution from -11.5 to 4.5 ns (i.e. comprising the peak range) and a binomial combination of the two time gates, the fold K being defined when all K events occur within the time peak gate. The uncertainties presented in the table are from counting statistics origin only. An additional systematic error of about 4% can be estimated from the normalization factor and other origins like the choice of specific energy and time gate widths. For K = 2 the simulation underestimates the experimental rate by a factor of about 2, thus in opposite direction to the K = 1 trend. This means that the average gamma multiplicity of the nuclear reactions is larger than expected by the simulation, and/or the Compton scattering between detectors is more frequent in the experiment. This last hypothesis is less probable since the actual amount of structure material between detectors is about the same or somewhat larger than modelled for the simulation, which should lead to a small reduction of the Compton cross talk due to absorption. For K = 3 the experimental result is dominated by the random coincidence statistics (absent in the simulation) and only an upper limit could be evaluated. The value is apparently smaller than the simulation value but consistent with it within two error bars.

Gamma-ray angular distribution

Figure 7 presents the angular distribution of the ratio R S/E between the simulated and the experimental integrals for K = 1 (in the same energy interval: 0.25-1.5 MeV) of the prompt gamma spectrum of each detector as a function of its (a) polar angle (θ L AB ) and (b) azimuthal angle (φ L AB , with reference on the horizontal plane, pointing to the left, looking downstream). The values of the ratio lie between 1.0 and 1.5 (the dashed lines in Fig. 7), with exception of the two data points above 2.0 [in both (a) and (b) plots] of largest azimuthal angles, for which there may be larger absorption by interposed material between the target and the detectors in the experiment than considered in the simulation. Since the geometry of the equipment material in this region is rather complex, no attempt was made to improve the simulation. With exclusion of these two data points [in both (a) and (b)] one can say that there is a rather constant R S/E ratio as a function of either angle. The data points distribution then shows a mean value of 1.22 with a standard deviation of 0.15. The rather small variations might be due to imperfect modelling of the target chamber material geometry in the simulation. Figure 8 presents both the experimental and simulated gamma detection angular distributions. Again excluding the abnormal data points (in this plot, those below 1500 counts), it appears that there is no strong dependence of the count rate with polar angle.

Gamma-ray and neutron time spectra

As it is apparent in Fig. 3, a considerable amount of (flat) accidental coincidence BG is present in the experimental time spectrum. In order to obtain the corresponding simu-123 Table 1 Gamma-ray fold distribution data. Number of cases corresponding to N p = 45 × 10 10 (the FC integrated value, dead-time corrected) 18 O projectiles impinging on the target

K Experiment Simulation S/E ratio
T = (T 0 + t p ) mod T b -t r (1)
The parameters t p = 9 ns and t r = 15 ns were adjusted to reproduce the peak position and range of the experimental spectrum, respectively. However, the spectrum of Fig. 9 shows a very small accidental BG (for example, the region below T ≈ -4 ns). To the right of the prompt peak a broader structure of delayed events appears with a maximum around T = 9 ns, decaying back to the height of the accidental event rate towards the end of the time range at 35 ns. The presence of this structure is not clear in Fig. 3, possibly due to the larger background of the experimental data. The experimental gamma spectrum shows also the secondary time peak at around T = 25 ns produced by the interaction of the beam with the FC. This time value is consistent with the sum of the delay of the 18 O beam ions to reach the FC (about 111 ns along the 6 m ion optical trajectory distance), with the delay of the gamma rays form the FC back to the Eden detectors (around 20 ns), minus the delay of the gamma rays from the target to the Eden detectors (6 ns), minus 2 beam periods (100 ns). Separate simulations were then performed including the interaction of the beam with the FC (consisting of aluminium sufficiently thick to stop the beam). The simulations were performed with and without the material of the concrete walls (floor and ceiling) of the MAGNEX experimental hall. The results are presented in Fig. 10. In this case a value of t p = 19 ns was used in Eq. 1 in order to reproduce the location of the experimental peak, due to the different time reference of the simulations for the FC events (which do not include the beam time-of flight). It is clear from these results that the presence of the walls is paramount for the increase of the accidental BG proportion in the spectra. The gamma BG increases by a factor of 36, while neutron one increases by a factor of 6. This can be attributed mostly to scattering of neutrons and gamma-ray production by secondary neutron reactions from the walls. It is to be noted that the concrete walls were already Fig. 9 Simulated time spectra from target originated events. Green, shaded: gamma rays. Red: neutrons. The deposited energies were limited to the 0.25-2.5 MeVee range Fig. 10 Simulated time spectra from FC originated events. Green: gamma rays (peaking near 24 ns). Red: neutrons. The shaded spectra were obtained without the presence of the experimental hall walls. The deposited energies were limited to the 0.25-2.5 MeVee range included in the target simulation of Fig. 9, with a very small increase in the background. This means that the main source of neutrons which contribute to the accidental BG is, by far, the beam interactions with the FC.

Figure 11 presents the time sum spectra of the target and FC originated events of the simulation in comparison to the experimental results, for gammas and neutrons. The simulation has a good correspondence with the experiment for gamma rays. The target prompt and accidental BG levels are similar. The secondary FC prompt peak, however, is overestimated by the simulation. The magnitude of this peak is compatible with zero, within error bars, for both the simulation and the experiment for all detectors below φ L AB = 100 • . Above this value, corresponding to the detectors which are un-shielded or only partially shielded by the MAGNEX iron (the bottom seven EDEN detectors in Fig. 5), this peak is significant in both experiment and simulation, but the simulation overestimates the experiment by one order of magnitude or more, depending on the detector. This is, in part, due to discrepancy between the actual material interposed between the FC and some of the detectors of the EDEN array, but it is also possible that it comes from deviations of the actual production of gamma radiation in the FC with respect to the simulation. Indeed it is not expected that the reaction model would remain good down to very low beam energies. Further measurement are necessary for a reliable evaluation of this issue. The figure also indicates a larger rate of neutrons in the simulation in comparison to the experiment, but this can be an artifact in the simulation due to the different neutron deposited energy threshold of 1 MeV assumed to correspond to 0.25 MeVee electron-equivalent deposit from the neutron interaction with protons in the detector, and less importantly, the correspondence of 5 MeV to the upper level discrimination of 2.5 MeVee . These values are a rough estimate from [23] in which a Fast/Slow decomposition of the pulse was performed in similarity to our case. Unfortunately we do not have experimental values specifically for our case, since the 50 ns range was insufficient for neutron time of flight (TOF) measurements. Again more detailed experiments including TOF are in order for a deeper investigation.

Figure 12 presents the (FC origin) accidental BG simulation (normalized by the number of beam particles) in comparison to the experimental results for gamma rays, as a function of the azimuthal angle (φ L AB ) of each EDEN detector. It can be seen that a slowly rising distribution is observed, in mutual compatibility. The rise of the simulation points above 110 • might be due to the smaller than real absorption of the FC related events in the simulation for this angular region as already pointed out. The diffuseness of the origin of this secondary radiation should explain the relatively small variation with angle, in contrast to the secondary time peak, which is detected directly from the FC.

Conclusions and perspectives

The prompt gamma spectrum of the 18 reproduced by GEANT4 simulations with the "Hadronther-apy1" physics list. The integral of the spectrum in the 0.25-2.5 MeV was reasonably well reproduced, although overestimated by 26(4)%, which can be considered a quite good result in face of the complexity of the task. A similar result, obtained in a different context (proton therapy monitoring, with protons at somewhat higher energy per nucleon) was reported in Ref. [29].

The angular distribution of the gamma rays was also well described in the θ = 92 • -128 • angular range of the detector array. Two-fold (K = 2) gamma coincidences (gamma signals within the 7 ns width gate around the prompt peak) were observed with about 4% of the intensity of the K = 1 rate, in the same energy range, and were underestimated by the simulation, indicating a possible underestimation of the average multiplicity of gamma rays produced by the nuclear reactions, and/or, less likely, an underestimation of the Compton cross talk between detectors.

The order of magnitude of accidental gamma BG (the flat portion of the time spectrum) was also well reproduced by the simulation after the inclusion of the events originated by the reactions of the beam with the Faraday cup a few meters away downstream from the target, at the MAGNEX focal plane, and the secondary scattering and nuclear reactions of the FC generated neutrons (mainly) with the MAGNEX dipole and quadrupole iron cores and the concrete walls of the experimental hall.

The neutron spectra were also measured with the EDEN detectors, and, differently from the gamma rays, presented a very flat distribution in the 50 ns range between cyclotron accelerator beam pulses. This flat distribution was appropriately described by the simulations after restraining the neutron event deposited energies to the 1-5 MeV range, which was roughly estimated to correspond to the 0.25-2.5 MeVee accepted range of the detector array electronics. The order of magnitude of the count rate appears to be well reproduced, but this result is uncertain due to the lack of a precise knowledge of the neutron detection energy calibration of the system used.

The results obtained in the present work are important for the NUMEN project, and encourage the use of the GEANT4 hadrontherapy model for the production of reliable predictions supporting the design of the future detection system. Care should be taken, however, to not overstate and generalize the good results of this specific case to all reactions and energies to be used in the NUMEN project. Additional measurements of other reactions and energies should be performed for a more comprehensive validation of the simulations, including neutron time-of-flight measurements, if possible. The importance of the inclusion of the material of the experimental hall and heavy equipment has also been evidenced by the present results. The accidental coincidence BG is a very relevant issue particularly for the design and performance prediction of the future gamma calorimeter array of the NUMEN project. It has become apparent that the bunker shielding of the beam dump which will have to be designed has to be very effective in reducing the radiation emanating from it and bringing the secondary reactions with the material of the experimental hall to an acceptable level.

The validation of nuclear reaction models in Monte-Carlo simulations is also important for medical physics (e.g. hadrontherapy) [25][26][27]29,30] and other applications such as high intensity beam accelerators for secondary radioactive beam production, and accelerator driven reactors. Experimental data for this purpose is still rather scarce in the literature.

Fig. 1 Fig. 2

 12 Fig. 1 Typical samples of the energy calibrated spectra in comparison with the corresponding simulation for a 22 Na source placed close to the face of each detector. The error bars (standard deviation) are smaller than the symbols. Hatched, in red: Experimental spectra for 2 different detectors, (a, b), after energy calibration. Blue square data points: simulation

Fig. 3 Fig. 4

 34 Fig.3Sum of all calibrated γ -selected (solid green line) and nselected (dashed red line) time spectra. A requirement of one and only one detector hit with the detector deposited energy range corresponding to 0.25 < E < 2.5 MeVee (electron equivalent) was imposed

Fig. 5

 5 Fig. 5 The MAGNEX and EDEN setup modeled in GEANT4. The location of detectors number 6 (θ = 105 • , φ = 126 • ) and number 29 (θ = 122 • , φ = 60 • ) mentioned in the caption of Fig. 4 are indicated

Fig. 6

 6 Fig. 6 Sum of the gamma spectra of all detectors, gated on the (target associated) time peak and K = 1, accidental BG subtracted (red, shaded). The corresponding simulation is shown with blue data points. The same simulation spectrum multiplied by a factor of 0.80 is shown in green. The error bar in this and in all other figures represent 1 statistical standard deviation

5 Fig. 7 Fig. 8

 578 Fig. 7The ratio R S/E between the simulated and the experimental integrals of the prompt gamma spectrum of each EDEN detector as a function of its laboratory frame a polar angle (θ L AB ) and b azimuthal angle (φ L AB )

Fig. 11

 11 Fig. 11 Simulated time sum spectra from target and FC originated events in comparison to the experimental ones. Experimental results: Green solid line for gamma rays and red dashed line for neutrons. Green and red data points with error bars are the simulations for gammas and neutrons, respectively. The deposited energies were limited to the 0.25-2.5 MeVee range

Fig. 12

 12 Fig. 12 Number of gamma-ray accidental BG events (corresponding to 45 × 10 10 beam particles) in the -11.5 to -4.5 ns time range as a function of the azimuthal angle (laboratory frame). Simulation (FC origin only): Blue closed circles with error bars. Experiment: Green solid squares (error bars smaller than symbols). The deposited energies were limited to the 0.25-2.5 MeV range

  O + 76 Se reaction at 275 MeV was measured with the NE-213 scintillators of the EDEN array. The shape of the energy spectrum was well

Acknowledgements

We acknowledge support from Fundação de Amparo à pesquisa no Estado de São Paulo, (FAPESP grants proc. 2016/04612-9 and 2017/50160-5), Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq and from Instituto Nacional de Ciência e Tecnologia-Física Nuclear e Aplicações (INCT-FNA, research project 464898/2014-5), Brazil.

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors' comment: Data can be made available uppon request, together with explanations of their acquisition conditions.]".


Asmae El Maangar

Ange Maurice

Varun Rai

Johannes Theisen

Christophe Penisson

Fabien Olivier

Jean Duhamet

Thomas Zemb

Jean-Christophe Gabriel
email: jean-christophe.gabriel@cea.fr

Christophe Penissonfabien Olivier

Jean- Christophe P Gabriel
email: jgabriel@ntu.edu.sg

The free energy of transfer in metal-extracting water-poor microemulsions as the crucial molecular driving force