Measurement of fragmentation cross sections of 12C ions on a thin gold target with the FIRST apparatus

PHYSICAL REVIEW C 93, 064601 (2016) Measurement of fragmentation cross sections of 12Cions on a thin gold target with the FIRST apparatus M. Toppi,1Z. Abou-Haidar,2C. Agodi,3M. A. G. Alvarez,2T. Aumann,4F. Balestra,5,6G. Battistoni,7A. Bocci,2 T. T. B ¨ ohlen,8A. Boudard,9A. Brunetti,10,11 M. Carpinelli,10,11 R. Cirio,5,12 G. A. P. Cirrone,3M. A. Cortes-Giraldo,13 G. Cuttone,3M. De Napoli,14 M. Durante,4J. P. Fern´ andez-Garc´ ıa,13 Ch. Finck,15 B. Golosio,10,11 E. Iarocci,1,16 F. Iazzi,5,6 G. Ickert,4R. Introzzi,5,6D. Juliani,15 J. Krimmer,17 A. H. Kummali,5,12 N. Kurz,4M. Labalme,18 Y. Leifels,4A. Le F` evre,4 S. Leray,9F. Marchetto,5V. Monaco,5,12 M. C. Morone,19,20 D. Nicolosi,21,3P. Oliva,10,11 A. Paoloni,1L. Piersanti,22,16 R. Pleskac,4N. Randazzo,14 R. Rescigno,15 F. Romano,3,23 D. Rossi,4V. Rosso,24,25 M. Rousseau,15 R. Sacchi,5,26 P. Sala,7 S. Salvador,18 A. Sarti,1,16,23,*C. Scheidenberger,4C. Schuy,4A. Sciubba,22,16,23 C. Sfienti,3,27 H. Simon,4V. Sipala,10,11 E. Spiriti,1,28 S. Tropea,3M. Vanstalle,15 H. Younis,29 and V. Patera22,16,23 (The FIRST Collaboration) 1Istituto Nazionale di Fisica Nucleare-Laboratori Nazionali di Frascati, Frascati, Italy 2Centro Nacional de Aceleradores (CNA), Universidad de Sevilla, Junta de Andaluc´ ıa-CSIC 41092 Sevilla, Spain 3Istituto Nazionale di Fisica Nucleare-Laboratori Nazionali del Sud, Catania, Italy 4GSI Helmholtzzentrum fur Schwerionenforschung, Darmstadt, Germany 5Istituto Nazionale di Fisica Nucleare-Sezione di Torino, Torino, Italy 6Dipartimento di Fisica, Politecnico di Torino, Torino, Italy 7Istituto Nazionale di Fisica Nucleare-Sezione di Milano, Milano, Italy 8EBG MedAustron GmbH, Marie Curie-Straße 5, A-2700 Wiener Neustadt, Austria 9CEA-Saclay, IRFU/SPhN, Gif sur Yvette Cedex, France 10Istituto Nazionale di Fisica Nucleare-Sezione di Cagliari, Cagliari, Italy 11Universit` a di Sassari, Sassari, Italy 12Dipartimento di Fisica, Universit` a di Torino, Torino, Italy 13Departamento de F´ ısica At´ omica, Molecular y Nuclear, University of Sevilla, 41080 Sevilla, Spain 14Istituto Nazionale di Fisica Nucleare-Sezione di Catania, Catania, Italy 15IPHC, Universit´ e de Strasbourg, CNRS, UMR7178, 67037 Strasbourg, France 16Dipartimento di Scienze di Base e Applicate per l’Ingegneria, “La Sapienza” Universit` a di Roma, Roma, Italy 17IPN-Lyon, Universite de Lyon, Universite Lyon 1, CNRS/IN2P3, Villeurbanne, France 18LPC-Caen, ENSICAEN, Universit´ e de Caen, CNRS/IN2P3, Caen, France 19Istituto Nazionale di Fisica Nucleare-Sezione di Roma Tor Vergata, Roma, Italy 20Dipartimento di Biomedicina e Prevenzione, Universit` a di Roma Tor Vergata, Roma, Italy 21Dipartimento di Fisica, Universit´ a di Catania, Catania, Italy 22Istituto Nazionale di Fisica Nucleare-Sezione di Roma 1, Roma, Italy 23Centro Studi e Ricerche e Museo Storico della Fisica “Enrico Fermi,” Roma, Italy 24Dipartimento di Fisica, Universit´ a di Pisa, Pisa, Italy 25Istituto Nazionale di Fisica Nucleare-Sezione di Pisa, Pisa, Italy 26Dipartimento di Fisica, Universit´ a di Torino, Torino, Italy 27Medical Radiation Physics, Karolinska Institutet and Stockholm University, Stockholm, Sweden 28Istituto Nazionale di Fisica Nucleare-Sezione di Roma 3, Roma, Italy 29Department of Physics, COMSATS Institute of Information Technology, Islamabad, Pakistan (Received 18 November 2015; published 1 June 2016) A detailed knowledge of the light ions interaction processes with matter is of great interest in basic and applied physics. As an example, particle therapy and space radioprotection require highly accurate fragmentation cross-section measurements to develop shielding materials and estimate acute and late health risks for manned missions in space and for treatment planning in particle therapy. The Fragmentation of Ions Relevant for Space and Therapy experiment at the Helmholtz Center for Heavy Ion research (GSI) was designed and built by an international collaboration from France, Germany, Italy, and Spain for studying the collisions of a 12Cion beam with thin targets. The collaboration’s main purpose is to provide the double-differential cross-section measurement of carbon-ion fragmentation at energies that are relevant for both tumor therapy and space radiation protection applications. Fragmentation cross sections of light ions impinging on a wide range of thin targets are also essential to validate the nuclear models implemented in MC simulations that, in such an energy range, fail to reproduce the data with the required accuracy. This paper presents the single differential carbon-ion fragmentation cross sections on a thin gold target, measured as a function of the fragment angle and kinetic energy in the forward *Corresponding author: [email protected] 2469-9985/2016/93(6)/064601(21) 064601-1 ©2016 American Physical Society M. TOPPI et al. PHYSICAL REVIEW C 93, 064601 (2016) angular region (θ6◦), aiming to provide useful data for the benchmarking of the simulation softwares used in light ions fragmentation applications. The 12C ions used in the measurement were accelerated at the energy of 400 MeV/nucleon by the SIS (heavy ion synchrotron) GSI facility. DOI: 10.1103/PhysRevC.93.064601 I. INTRODUCTION Interest in the study of the mechanisms underlying the ion fragmentation in collisions at energies in the 10–1000 MeV/nucleon range has been constantly rising in the recent past, being driven by the possible use in space [1,2] and particle-therapy applications [3–5],whereanimproved description of the light-ion interactions with matter is eagerly needed. Accurate measurements of fragmentation cross sections of light ions interacting with thin targets are also needed to benchmark and improve the nuclear interaction models implemented in Monte Carlo (MC) simulation algorithms. Nowadays, the disagreement between MC predictions and experimental data could be mainly ascribed to the lack of available data and their limited precision [5]. To provide an improved experimental to tune the MC simulations, a small set of measurements can be used: The interpolation of cross sections for different energies and target materials composition makes it possible, starting from a selected number of target-energy combinations, to build a model covering all the application needs. In particular, for the cited applications, one of the most interesting ion-type–energy-range combinations to be explored is 12C in the 200–1000 MeV/nucleon kinetic-energy range. As recently pointed out by NASA [6], cross-section measurements in this region using “a range of targets across the periodic table” are needed to provide the missing information in the nuclear fragmentation databases. The ion fragmentation process has already been the object of several experimental campaigns in the past, aiming at either thin- or thick-target, single- or double-differential crosssection (DDCS) measurements [7–12]. Such measurements have been performed under different experimental conditions, covering in some cases only the very forward fragment emission region and in other cases a few other fixed-angle configurations. Recently a double-differential cross-section measurement in thin targets was performed using 12C ions of 95 MeV/nucleon kinetic energy as projectiles, with an experimental setup able to cover a large angular range: 0◦ [13] and 4◦–45◦[14]. The principal aim of the Fragmentation of Ions Relevant for Space and Therapy (FIRST) Collaboration is to perform DDCS measurements using fully stripped 12C ions as projectiles on thin targets in the energy range not yet covered by other experiments [15]. This paper presents the fragmentation cross section of 400 MeV/nucleon 12C ions impinging on a thin gold target: a valuable input for the benchmarking of the nuclear models used for the description of the high-Ztargets fragmentation. The data taking took place in the GSI laboratory (Darmstadt) in summer 2011 and about 5 ×106events of collisions between a12C ion beam with a thin (500 μm thickness) gold target were recorded. The experimental setup, which included a trigger counter, a beam monitor, a vertex pixel detector, a large-angle plastic scintillator compact detector, and a time-of-flight wall (TW) made of plastic scintillators, is fully described in Sec. II, together with the experiment data acquisition (DAQ) system. The performances obtained by the various subdetectors are outlined together with their calibration strategies and results. Details on the data sample and on the Monte Carlo (MC) simulation are given in Sec. III, the description of the global reconstruction algorithms used to fully reconstruct all the fragments and particles traversing the detector in each event can be found in Sec. IV, while the results are presented in Sec. V. The studies performed to assess the systematic uncertainties are documented in Sec. VI, while the conclusions are presented in Sec. VII. II. EXPERIMENTAL SETUP Fragmentation cross sections are measured in FIRST using an experimental setup, already described in Ref. [15], that has been designed and optimized using a dedicated MC simulation. The schematic view of the FIRST experimental setup is shown in Fig. 1, together with the axis orientation of the reference frame. The detection of the incoming 12C ions has been accomplished by means of a start counter (SC), described in detail in Sec. II A, made of a thin layer of plastic scintillator whose geometry and readout were optimized to maximize the counting efficiency while keeping the pretarget fragmentation as low as possible. The SC was used to trigger the data acquisition using a minimum bias strategy: Whenever a 12C ion was detected inside the SC the event was acquired. In addition, the SC provides the reference timing for time-of- flight measurements. A pixel silicon detector (VTX), described in detail in Sec. II C, was placed just behind the target, allowing a precise reconstruction of the fragment tracks produced in the target and their angle with respect to the incoming beam direction, as well as their production vertex. The technology adopted for the vertex detector [16,17] made it possible to have the required efficiency with thin detection layers that minimized the out-of-target fragmentation of an elastically scattered 12C ion or other fragments coming out from the target. The long readout time (115 μs) of the pixel detector, with an incoming beam rate in the 1–10-kHz range, required the development of a dedicated fast beam monitor (BM) detector capable of resolving the event pileup (PU) ambiguity in the VTX by providing the position of the impinging 12C ion in the target. The technology chosen and the performances of this detector are presented in Sec. II B. A plastic scintillator compact detector (kinetic energy and time resolution optimized on scintillator, KENTROS) has been designed to detect fragments, mainly hydrogen and helium 064601-2 MEASUREMENT OF FRAGMENTATION CROSS SECTIONS . . . PHYSICAL REVIEW C 93, 064601 (2016) FIG. 1. (Left) Perspective view of the FIRST detector interaction region before the ALADIN magnet. The beam pipe after the last collimator and the beam exit window are shown with a black arrow superimposed, marking the beam direction (zaxis). The SC surrounding the BM and KENTROS detector can be seen on top of the supporting table. (Right) Top view (x,z plane) of the FIRST experiment. From left to right: the table supporting the SC, the BM, and the VTX detectors, enclosing the target holder; the KENTROS detector, just before the magnet entrance window; the ALADIN magnet region; the TW detector at the rightmost position. ions, emitted at large angles. This detector surrounds the target and vertex detector region covering the polar angle (defined as the angle between the incoming 12C ion and the fragment direction) region between 6◦and 90◦. The results obtained in that region are not presented here and will be the subject of a dedicated paper in the future, where a fully detailed description of the detector technology will be published. The charged fragment momentum is determined by measuring the bending of the trajectory in the z-xplane produced by the magnetic field provided by the large acceptance dipole magnet (ALADIN) magnet, whose description is reported in Sec. II D. The fragment identification is performed using scintillating detectors placed 6 m away from the target region, arranged in a wall (TW), described in Sec. II E. Together with the time- of-flight (TOF) measurement, the TW provides the fragment coordinates and a measurement of the energy released inside the plastic scintillators: This information allows a clean separation of fragments with different charge. An additional detector, a large-volume time projection chamber (TP-MUSIC IV [18]), was placed after the ALADIN magnet and before the TW, but could not be operated during the data taking: The full MC simulation of the experiment takes this detector into account to properly evaluate the material traversed by each fragment before reaching the TW and to account for possible secondary fragmentation. A. Start counter detector The SC detector, shown in Fig. 2,isusedinFIRSTto provide the measurement of the total number of 12C ions used for the cross-section evaluation and the trigger signal for the data acquisition system. The SC also provides the reference time for all the other detectors, allowing the measurement of the drift time inside the BM and of the fragment TOF using the TW information. The detector consists of a 250-μm-thick plastic scintillator disk and the light is collected by 160 plastic optical fibers grouped into four bundles, each connected to a photomultiplier. The layout optimization, described in detail in Ref. [19], was hence performed carefully balancing the detector time resolution and the thickness minimization to have a pretarget particle interaction probability that is less than 1% with respect to the on-target one. The efficiency [19] showed an excellent stability during the whole data taking, with a measured mean value of (99.7± FIG. 2. Schematic view of the mechanical installation of the SC and BM detectors. The picture shows the BM, with six wire planes on both xz and yz views, encapsulated by the SC mechanical structure. The four arms of the SC, holding the fibers and the photomultiplier tubes used for the readout, can be clearly seen. The beam axis (z) is also shown, crossing the SC and the BM in the middle of their entrance windows. On the right, the aluminum box that encapsulates the target holder and the vertex detector is shown. 064601-3 M. TOPPI et al. PHYSICAL REVIEW C 93, 064601 (2016) 0.15)%. A good performance was also observed for the time resolution (σt), with a measured average value of σt=(150 ± 2) ps, where marginal fluctuations (maximum ≈5 ps) were observed. B. Beam monitor detector The BM, described in detail in Ref. [19] and shown in Fig. 2, is a drift chamber designed for the reconstruction of the charged-particle trajectory. This detector is used to measure the ion impinging point on the target, crucial information needed to resolve the PU ambiguity in the VTX detector (see Sec. II C 2). The detector is made of 12 alternated horizontal (along the xaxis) and vertical (along the yaxis) wire planes. Each plane is composed of three rectangular cells centered around the sense wires, with dimensions x(y)×z=16 mm (16 mm) × 10 mm, for a total of 36 cells/sense wires. The geometrical layout has been optimized to minimize the ion interactions with the wires while still maintaining the required cell resolution. The 12 planes (6 on each “view”) provide tracking redundancy and ensure a high tracking efficiency and an excellent spatial resolution. The BM was operated at 1.8 kV with an Ar/CO2 (80%/20%) gas mixture at atmospheric pressure. The detector tracking calibration has been performed using the tracks reconstructed in the VTX detector in a dedicated run in which the target was removed, thus allowing the detector alignment and the track intercalibration. Details of the tracking algorithms have been presented elsewhere [19]. The chamber hit detection efficiency was measured to be ∼97% and was stable during the data taking, as shown in Fig. 3 (black triangles): The largest run-by-run variations are within ±3%. The mean track spatial resolution at the chamber center was measured to be σx≈140 μm, with the dependence on the distance from the cell center described in Ref. [19]. Run number 200 250 300 350 400 450 500 Efficiency 0.75 0.8 0.85 0.9 0.95 1 1.05 FIG. 3. BM tracking efficiency as a function of the run number. The small fluctuations (⩽3%) that can be observed against the mean value of 96.8% are attributable to the changes in the beam position, as well as to changes in the temperature and pressure of the gas mixture. C. Vertex detector The main purpose of the vertex detector (VTX) is the trajectory and fragmentation vertex reconstruction, with the largest possible angular coverage, of the fragments produced in the target. The whole detector thickness should not exceed a few percent of the target thickness to keep the probability of fragmentation inside the sensors at a few percent level. A dynamic range from about two minimum ionizing particles (MIPs), for the proton signal to the two-orders-of-magnitude- larger signal from low-kinetic-energy 12C ions has also to be considered. To satisfy those requirements, the MIMOSA26 (M26) pixel sensor has been chosen to equip the vertex detector with four sensor layers, corresponding to the best compromise between the need for having redundancy in the reconstruction and for minimizing the sensor total thickness. M26 is a sensor chip developed by the Strasbourg group [16,17] for high-energyphysics experiments. A sensitive area of 10.6×21.2 mm is covered by 576 rows and 1152 columns of pixels with 18.4-μm pitch. All the pixels are read out per column with a row readout time of 200 ns for a total readout time of 115.2 μs per frame. At the end of each column a discriminator is used to produce the input to the following zero suppression logic, which removes the empty pixel information and stores the data in two buffer memories. The data is sent off chip with two 80-MHz serial differential outputs. Only four discriminator thresholds, each common to 288 discriminators, are provided. To fit the experimental conditions, a custom housing board has been designed with two M26 sensors glued on both sides of a square hole to obtain a sensitive area of ∼2×2cm 2 including a small superposition region essential to align all the VTX sensors. The use of a 1-mm-thick printed circuit board (PCB) and low-profile components, allowing a distance of two consecutive boards of 2 mm, produces an overall thickness of the four vertex stations of 12 mm, as shown in Fig. 4. Under these conditions the angular coverage is ±40◦. Finally, the overall thickness of about 50 μm per sensor makes it possible to minimize the lateral straggling of the impinging particles. FIG. 4. Sketch of the VTX detector arrangement. The beam is impinging on the 500-μm-thick gold target. Each of the four following PCB planes is housing two sensors, one on each side, placed over a square hole (2 cm side length) in the PCB itself. 064601-4 MEASUREMENT OF FRAGMENTATION CROSS SECTIONS . . . PHYSICAL REVIEW C 93, 064601 (2016) 1. Performances The VTX detector data processing starts from the raw data file reading, from which a list of fired pixels is extracted, and proceeds through the cluster reconstruction, centroid evaluation, and combination into a list of tracks and vertices. A clustering algorithm is used for each sensor to reconstruct the crossing point of the ionizing particles through the M26 sensor. The algorithm is based on a recursive method looking for the next neighboring fired pixel and is able to reconstruct correctly the clusters with an efficiency higher than 99.9% [20]. The tracking reconstruction is based on standard algorithms tuned for the specific applications of CMOS sensors aiming for the reconstruction of a track going from a given plane to the next. Starting from the last plane and proceeding backwards with respect to the beam direction, a path to the position given by the intersection of the BM track with the target is defined. Then all the available clusters on each plane within this path are identified and selected. The tracking reconstruction efficiency, evaluated on Monte Carlo simulation events (see Sec. III), is 98.7±0.1%, with a measured proportion of fake tracks of 1.99 ±0.01% [20]. Two other different tracking approaches have been implemented and tested to assign a systematic uncertainty on the VTX tracking: One is based on the Hough transformation, while the other implements a different iterative procedure to scan the VTX planes to assign fired pixels to a given track in which consecutive planes are used. In the following, the first algorithm is used for track reconstruction because it is faster and exhibits a lower proportion of fake tracks. The fragmentation vertex reconstruction is performed using an algorithm based on a probability distribution approach. Using the MC simulation a vertex reconstruction efficiency of 98.6±0.2%,witha2.30 ±0.01% proportion of fake vertices, has been estimated. The resolution of the vertex reconstruction, evaluated using Monte Carlo events, is better than 10 μmin the xand ydirections and ∼50 μminthezdirection [20]. More than one 12C ion can impinge on the VTX detector during the M26 sensor integration time (PU effect). Using a Poisson distribution for PU events, with a λ parameter determined by data collected with the SC detector, it was found that only in (2.4±0.1)% of the events the vertex reconstruction algorithm could not disentangle the different vertices. From the data we obtain λ=0.63 ±0.12, where the uncertainty comes from the distribution of the λvalues for different data samples. More details about the performance of the VTX detector can be found in Ref. [20]. The VTX alignment procedure is based on the minimization of the distance between the reconstructed cluster centroid and the intersection of the reconstructed tracks on the sensor plane. The free parameters to be minimized are the displacement in the orthogonal plane with respect to the beam (x-yplane) and the rotation around the beam axis (zaxis) for each sensor. Other rotations are neglected because the tracking procedure is less sensitive to them. The minimization is stopped once the variation of the displacement and angle is lower than agivenvalue(x,y < 5μm and angle <0.1◦). Figure 5 shows the residuals obtained using straight tracks of 12C ions at 400 MeV/nucleon for the xand ycoordinates after the m]μx residual [ 40−20−0 20406080100 Counts 0 2 4 6 8 10 12 3 10× (a) = σ mμ 0.02 ±5.49 Tail = 0.1 %±12.3 m]μy residual [ 40−20−0 20406080100 Counts 0 2 4 6 8 10 12 14 3 10× (b) = σ mμ 0.01 ±4.37 Tail = 0.1 %±11.5 FIG. 5. The residuals obtained for the reconstructed tracks are shown in the xand ydirections in the (a) and (b) images, respectively. In both plots the data distribution is shown in blue, while the result of a Gaussian fit to the histogram is superimposed as a black dashed line. alignment procedure. The residuals are defined as the distance between the cluster positions and the fitted track line: Their distribution was used to evaluate the resolution of the tracking device given by the σof a Gaussian fit. The resolution in x and ydirections is better than σ=6μm and the fraction of tails outside a 4σwindow is smaller than 13%. 2. Matching with the BM Because the tracks reconstructed by the VTX are the seed for the global track reconstruction algorithm (see Sec. IV), it is crucial to preselect the tracks that belong to each event, getting rid of the PU tracks that may have been reconstructed. The ambiguities on which tracks belong to the current event can be resolved by using the information from the BM track extrapolated to the target, because the BM readout time is fast enough to ensure that tracks belonging to different events cannot be mixed. The track reconstructed in the BM is used to predict the impact point in the center of the target. The vertex positions reconstructed by the VTX for each event are compared with the carbon ion-target intersection point which is reconstructed by extrapolating the BM track. The closest vertex to the BM extrapolation is selected as a matched vertex. The impact of this selection on the final result and the relative systematic uncertainty on the cross section measurement is discussed in Sec. VI. The BM and VTX detectors were software aligned using calibration events taken without any target, with tracks traversing both detectors without any fragmentation or scattering. The alignment constants were tuned by minimizing the distance between the two predicted track intersections with a virtual plane in the target position (VTX-BM residual distribution) and the difference between the track parameters (like the angle with respect to the beam axis θ). The alignment result is shown in Fig. 6, where a bias in the VTX-BM residual distribution smaller than 200 μm and a resolution of the order of 300 μm for the xcoordinate are shown, with similar results for the y 064601-5 M. TOPPI et al. PHYSICAL REVIEW C 93, 064601 (2016) Run number 200 250 300 350 400 450 500 m)μ VTX-BM x residual ( 1000− 800− 600− 400− 200− 0 200 400 600 800 1000 FIG. 6. Mean values of the residuals obtained for the xcoordinate of 12C ion tracks at the target position, as measured using the BM and VTX detectors. The error bars show the σobtained from a fit done with a Gaussian probability density function (PDF) to the residual distribution and are consequently representing the detector matching resolution. coordinate. Such results are compatible with the performances of the BM detector, reported in Ref. [19]. The 12C ion beam has been monitored using both the VTX and BM detectors: A Gaussian-shaped beam spot has been observed during the data taking with a stable resolution (∼1.3 mm) along both the xand the yaxes. D. ALADIN magnet The p/Z ratio of charged fragments is reconstructed using the horizontal deflection (x-zplane) in the ALADIN. The magnetic field acts on the particles traveling in the magnet gap, operated in vacuum, that has an approximate volume of 155(H)×50(V)×230(L)cm 3. The magnet angular acceptance is limited to 5.7◦by a circular collimator of 15 cm diameter positioned 75 cm from the target. The value of the magnet current has been chosen so that a noninteracting beam particle crosses the central region of the TW, and it has been kept constant during the data taking within ±0.5%. The corresponding deflection for a 400 MeV/nucleon 12Cionis5.3◦. The values of the magnetic field used in the reconstruction and simulation comes from the interpolation of maps measured at GSI along the three coordinate axes on about 104grid points for different current values. The actual current value used for the data analysis (∼680 A, corresponding to a magnetic field of ∼0.55 T) is determined with the MC by requiring that a beam particle crosses the TW in the same positions as measured in special runs with and without the magnetic field. The uncertainty on the magnet current and field scale is limited by the TW position resolution and estimated to be 2.5%. The uncertainty on the field scale and on the position of the magnet with respect to the rest of the apparatus is taken into account in the evaluation of the cross-section measurement systematic errors. E. TOF-wall detector The TW detector has the aim of measuring the arrival time, the released energy, and the impinging positions of ions FIG. 7. Sketch of the TW scintillator modules and of the readout electronics with splitters, constant fraction discriminators (CFDs), digital delays, and TDC and ADC boards. or fragments produced within the angular acceptance of the ALADIN entrance collimator. Moreover, exploiting the information of energy release and arrival time, the TW allows the identification of the charge of each detected particle, from either the primary 12C beam or the fragments. The detector, described in detail in Ref. [15], consists of two walls of BC-408 plastic scintillator slats (110 cm long, 1 cm thick, 2.5 cm wide) divided into 12 modules of eight slats each. The detector is placed at a distance d≃600 cm from the target, along the trajectory of the 12C beam. The two walls are 8 cm from each other. At the top and bottom ends of each slat, the signal of the crossing particle is read by two photomultiplier tubes. The output signals are split into two branches, as shown in Fig. 7. The first branch is read out by FASTBUS analog-to-digital converters (ADCs) for charge measurements. The second branch is processed by constant fraction discriminators (CFDs) and passes digital delay modules before entering time to digital converters (TDCs) that provide the time information. 1. TW calibration As mentioned before, the TW detector is fundamental in the experiment layout because it measures the horizontal and vertical coordinates (x,y) of the impact point, the arrival time (TOF) and the energy released in the slats (Eloss) of each detected particle. In particular, the coordinate in the horizontal plane is related to the slat number, which gives information on the xposition of the particle and also on the fired wall (i.e., zcoordinate). The sum of the top and bottom TDC readings, which is independent of the hit position in the slat, is used to derive the particles’ TOF. The ADC channel measurements, providing information on the collected charge, make it possible to calculate the energy (Eloss) lost by the particle in the slat. Eloss is determined as the geometric mean of the upper and lower ADC values and it is independent of the fragment impact 064601-6 MEASUREMENT OF FRAGMENTATION CROSS SECTIONS . . . PHYSICAL REVIEW C 93, 064601 (2016) position under the assumption of an exponential attenuation of the light in the scintillator. The calibration of the quantities of interest have been performed exploiting particular data sets, called “sweep-runs,” collected without a target, in which the beam conditions were known. In these runs the 12C ion beam (at 400 MeV/nucleon) has been deflected on the horizontal plane over all the slats by varying the magnetic field. 12C ions flew at known energy— and thus at known velocity—along paths which could be reconstructed by geometrical calculations. The hit coordinates (x,y,z), TOF, and Eloss are known, on average, for sweep-run hits: Delays, constant factors and gains can thus be calibrated comparing the measured quantities with the known values. An additional data sample has been collected with dedicated runs to take into account the time dependence on the energy released by the fragments in each slat. A scan of the TW with the beam hitting an aluminum bar placed immediately before the scintillator front plane was performed. The time dependence on the released energy (time-walk effect) has been found to be <0.5 ns and thus it has been neglected in the TW hit reconstruction. In calibration data samples, obtained scanning the TW with the primary C ions, the TOF is determined by the known energy (i.e., velocity) and the path length to the individual slats. The fragment impact vertical position (y) can be obtained by using the ADC or TDC information, respectively. The first possibility is to calculate ythrough the ADCs (yADC), assuming that an exponential attenuation is responsible for the signal decrease as a function of the length traversed along each slat and that the two photomultipliers can have different light gains. The calibration parameters have been measured by using the positions (ycoordinates) of the intercept between the VTX track extrapolation and the TW planes as a reference. The second possibility is, instead, to use the TDC readings and the light speed in the scintillator (vsl, slat dependent) to compute the ycoordinate (yTDC). However, this latter method suffers from a bigger uncertainty in the position and is only used for slats in which only one ADC was working. After the pedestal subtraction, the ADC readings can be related to the scintillation light released by the particle by knowing the attenuation and the gain of the photomultipliers for each slat. In sweep runs the 12C ion energy is known and the average energy loss can be evaluated according to the Bethe-Bloch formula. The computed Eloss is hence used to calibrate the TW detector parameters, taking also into account the nonlinear response of plastic scintillators to the ionization density by applying the semiempirical Birks’ formula [21], with parameters that are determined from the data. 2. TW efficiency The efficiency of the TW for hydrogen detection is limited by the minimum signal needed to trigger the CFDs and to digitize the time information in the TDCs. To simulate accurately this effect, for each TW channel the fraction of events with a detected TDC hit is studied as a function of the ADC counts after pedestal subtraction. The minimum released energy needed to trigger the TDC in each channel is estimated using the calibration parameters and Birks’ factors, and is used in the Monte Carlo simulation to discard hits with an energy below threshold. The minimum TW energy that can be detected in at least one of the two TDCs depends on the threshold values and on the yposition along the TW, owing to the light attenuation along the slats. The energy threshold is generally below the energy released by a minimum ionizing particle, with a few exceptions. These include specifically the region close to the impact point of the carbon beam, where higher thresholds are set and an efficiency loss for hydrogen ions of high kinetic energies is observed (a detailed discussion of the reconstruction efficiency can be found in Sec. IV C 3). 3. TW resolution The resolutions in the TW reconstructed quantities (Eloss, y, TOF) are estimated by comparing the values measured for hits in the two planes compatible with the same particle. The selection of the hits in different planes, optimized using the full Monte Carlo simulation, is based on the geometrical topology of the event and uses as input information the hit slat and y positions. The resolutions are used for the tuning of the Monte Carlo signal processing. The yADC coordinate resolution was also evaluated using uncertainty propagation, obtaining similar results. The measured resolution, averaged on the whole detector for different slats and ypositions, is shown in Fig. 8(top left) as a function of the energy released in the scintillator by the fragment. [MeV] loss E 0 20 40 60 80 100120 140 ) [cm] ADC (yσ 0 2 4 6 8 10 12 DATA MC (a) [MeV] loss E 0 20 40 60 80 100120140 loss ) / E loss (Eσ 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 DATA MC (b) [MeV] loss E 0 20 40 60 80 100 120 140 (ToF) [ns]σ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 DATA MC (c) [MeV] loss E 0 20 40 60 80 100120140 ) [cm] TDC (yσ 0 2 4 6 8 10 12 DATA MC (d) FIG. 8. The yADC resolution is shown in (a). The energy resolution is shown in (b). The TOF resolution is shown in (c). The yTDC resolution is shown in (d). All the distributions are shown for data (red squares) and MC (blue circles) event samples as a function of the released energy. A red line, showing a ∝1/√Eloss distribution is superimposed to the energy resolution distribution. 064601-7 M. TOPPI et al. PHYSICAL REVIEW C 93, 064601 (2016) The energy resolution is shown in Fig. 8(top right) for data and Monte Carlo as a function of the released energy. The TOF resolution, shown in Fig. 8(bottom left), is about 800 ps, while the yTDC resolution (bottom right) is 8 cm and is nearly independent of the energy. F. Trigger and DAQ The readout of the detector electronics is performed on an event-by-event basis using the multibranch system (MBS) [22], a general DAQ framework developed at GSI. For each trigger, the MBS system handles the readout of the bus controllers hosted in different crates and takes care of the trigger synchronization through signals distributed on a common trigger bus. The event fragments collected from all the individual controllers are transmitted during the beam interspill period to a host PC, where the data merging and saving is performed. The signals from single detectors are locally processed with NIM electronics to generate trigger primitives. The final trigger logic is implemented in a FPGA programmable VME module (VULOM4 [23]), where the local trigger primitives are combined in logic matrices. The accepted triggers for different logical conditions are propagated to the readout electronics via the trigger bus. Different trigger outputs are generated with downscale factors or at random times for calibration purposes, while the main physical trigger is based only on the signal from the SC detector, thus providing an unbiased selection of primary beam particles for the data analysis. The typical beam rate during the data taking was around 1 kHz, with instantaneous fluctuations related to the spill structures provided by the SIS. The mean acquisition rate was 150 Hz owing to the dead times of the single readout nodes. III. DATA SAMPLE AND MC SIMULATION The collected data sample of 400 MeV/nucleon 12C ions collisions on a thin (500 μm thickness) gold target corresponds to 4.5×106unbiased triggers. The simulation of the experiment is based on the generalpurpose Monte Carlo (MC) code FLUKA [24–26]. FLUKA includes sophisticated state-of-the-art models for nonelastic hadronic interactions and the successive deexcitation and radioactive decay of produced fragments. Two different MC samples have been produced using the FLUKA code. The first one was obtained simulating the interactions of 400 MeV/nucleon 12C ions with a thin gold target and consists of 250 ×106events. In the following we refer to this sample as the full unbiased sample. A second sample was produced to compute the kinetic-energy unfolding matrices and the tracking reconstruction efficiencies: In this sample the different fragments were generated with a flat energy and angular spectrum, originating from the target center. Ten million events of this kind were generated for each fragment type (Znumber from one to five, most abundant isotopes). We refer to this sample in the following as to the flat biased sample. The detector geometry and materials are modeled in considerable detail to properly evaluate the interactions in all [MeV] loss E 0 102030405060708090 Entries / [1 MeV] 10 2 10 3 10 DATA MC (a) ToF [ns] 26 28 30 32 34 36 38 40 Entries / [0.2 ns] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 3 10× (b) DATA MC [cm] ADC y 50−40−30−20−10−0 1020304050 Entries / [1 cm] 0 0.2 0.4 0.6 0.8 1 3 10× (c) DATA MC FIG. 9. Comparison of data and Monte Carlo distributions for TW reconstructed variables in fragmentation events. The data and MC spectra have been normalized to have the same integral. The Eloss,TOF,andydistributions are shown, respectively, in panels (a), (b), and (c). the active detectors and the production of secondary particles in out-of-target fragmentation processes. The absolute positions of the detectors in the experimental area are fixed on the basis of the results of the optical survey measurement performed at the end of the data taking, complemented with alignment studies from the collected data. The comparison of Eloss, TOF, and ycoordinate measured from the TW detector for DATA and full unbiased MC events in which a fragmentation occurred are shown in Fig. 9, where the distributions have been normalized to have the same integral. The fragmentation events are defined as those in which at 064601-8 MEASUREMENT OF FRAGMENTATION CROSS SECTIONS . . . PHYSICAL REVIEW C 93, 064601 (2016) least one vertex has been reconstructed in the VTX detector and more than one track is associated with it. The energy-loss distribution for data is shown up to 100 MeV for fragments with Zranging from 1 to 5, because energy releases above 100 MeV are related to carbon ions. A detailed discussion on the charge identification of the fragments on the basis of energy loss and time of flight can be found in Sec. IV A. The PU of VTX tracks from different primary particles is simulated by adding additional tracks from events stored in a software FIFO, according to a Poissonian distribution determined from the full data sample. The detailed MC simulation of the geometry and of the detector response is needed to evaluate the acceptances and resolutions for the cross-section measurement. For this purpose each reconstructed track is associated with a MC- generated track and the reconstructed variables (kinetic energy, mass, charge, emission angle, momentum) are compared with the corresponding true value at generator level. The full unbiased MC sample has been used to evaluate the tracking resolutions and to tune the combinatorial and misidentification background components subtraction in the mass spectra analysis (see Sec. IV C). IV. GLOBAL RECONSTRUCTION The fragment reconstruction in FIRST proceeds along two possible strategies, in accordance with their production angle: For small-angle production (polar angle θless than ∼6◦) the fragment enters the ALADIN magnet region, where the momentum is determined measuring the bending in the x-zplane, and is then detected by the TW; for large-angle production (θlarger than ∼6◦), the fragment cannot enter the magnet region and hence are detected by the KENTROS detector. The data analysis presented here covers only the smallangle production region: Fragments are reconstructed, in this case, using an iterative procedure providing the value of pc/Z and the trajectory path for each combination of VTX tracks and TW hits detected in the event. The selection strategy and the algorithms used to identify the right pairing of VTX tracks and TW hits from all the possible combinations is presented in Sec. IV B. An example of a fully reconstructed fragmentation event, in which four fragments are produced at small angle, is shown in Fig. 10. The fired BM wires/cells are highlighted in blue in the grayish box in the bottom left corner of the picture. The KENTROS blue barrel and end-cap modules, surrounding the target-VTX region (not visible in this global view scale) are shown as well. The fragment tracks are represented as “dots” in space connecting the target origin position, and the relative four fragment tracks in the VTX, with the four pairs of red bands on the TW (two for each fragment as it traverses both the front and the rear wall) representing the TW slats that have been hit. The TW hits used to build the track are shown as tiny spots in green. The track bending happens in the gray box, representing the ALADIN magnet region: Before and after that region the magnetic-field intensity is negligible and the track trajectory is assumed to be a straight line. FIG. 10. Three-dimensional view of a fully reconstructed fragmentation event, with four fragments produced in the small-angle region. Fragment tracks are built by pairing tracks reconstructed in the VTX detector (not visible in this figure) with the hits detected by the TW (tiny green dots placed within the light pink lines, which identify the TW slats that have been hit in the top right light blue region representing the TW). The tracks are represented as dots connecting the target-VTX region with the green dots on the TW. The magnet region is represented as a gray box between the KENTROS detector and the TW. A. Fragment charge identification To compute the fragment momentum, the fragment charge (ZID) has to be measured. Two algorithms, based on the information from the TW and VTX detectors, have been developed. The TW ZID identification is performed using the Eloss and TOF measurements. The TW resolution allows the discrimination of six spots in the Eloss-TOF plane, related to different fragment charges as shown in Fig. 11. The Bethe- Bloch formula parameters, used to describe the measured Eloss vs TOF of the ions with different Z, were experimentally tuned by means of a fit to the Eloss vs TOF projection to achieve the best description of the data. Figure 11 shows the measured distributions for 12C ions on carbon target data, with fitted Bethe-Bloch curves superimposed in black. The TW ZID algorithm assigns to a given fragment the charge that minimizes its normalized distance, in the Eloss- TOF plane, with respect to the different Bethe-Bloch curves relative to the different Zhypothesis. The normalized distance [(dist −μdist)/σdist] is computed, for each Zhypothesis, using the mean (μdist) and the σ(σdist) evaluated from a Gaussian fit to the distance of each hit to each Bethe-Bloch curve, in the full data sample. The VTX detector identification algorithm exploits the correlation between the size of the hit clusters and the fragment charge, as outlined in Ref. [27]. 064601-9 M. TOPPI et al. PHYSICAL REVIEW C 93, 064601 (2016) [deg]θ 024 ] -1 [b srΩ/dσd 2− 10 1− 10 1 10 2 10 3 10 H He Li Be B FIG. 22. SDCS of different charge (Z) fragment production, as a function of the fragment angle with respect to the ion incoming direction, measured using Eq. (2). The total uncertainty (stat. and syst. added in quadrature) is shown. no correction has been applied to the measured cross sections on the data sample. The measured SDCS as a function of θand Ekin are shown respectively in Figs. 22 and 23. The uncertainty shown in the plot is the total uncertainty and accounts also for the systematic contribution, evaluated as described in Sec. VI.TheEkin results are shown for fragments in the ALADIN acceptance (6◦). The histograms for each atomic number have been obtained by summing up all the non-negligible contributions from different isotopes that have the same ZID. A discussion of the [MeV/nucleon] kin E 0 200 400 600 800 ] -1 /dE [b (MeV/nucleon)σd 5− 10 4− 10 3− 10 2− 10 H He Li Be B FIG. 23. SDCS of different charge (Z) fragment production, as a function of the fragment normalized kinetic energy, measured using Eq. (3) for fragments within the ALADIN angular acceptance (6◦). The total uncertainty (stat. and syst. added in quadrature) is shown. [deg]θ 012345 ] -1 [b srΩ/dσd 1 10 2 10 default SCC Cls/Sco BM mat Eff Xfeed TW pos+ TW pos- Bkg model (a) [MeV/nucleon] kin E 0 100 200 300 400 500 600 700 800 ] -1 /dE [b (MeV/nucleon)σd 5− 10 4− 10 3− 10 2− 10 default SCC Cls/Sco BM mat Eff Xfeed TW pos+ TW pos- Bkg model (b) FIG. 24. Effect of systematic checks on the production cross sections of 2Hfragments. The angular (a) and kinetic-energy distributions (b) are shown. The production cross sections obtained changing the analysis strategy, algorithm, and cuts are shown. The details on the different spectra labels can be found in the text. systematic uncertainties affecting the results is presented in the following section and shown, for 2Hfragments, in Fig. 24. A full set of tables and plots for all the detected isotopes is provided in the Appendix: the cross sections are reported in detail in Tables I,II,III, and IV and shown in Figs. 25 and 26. VI. SYSTEMATIC CHECKS Several systematic checks have been performed to assess the impact of the detector resolution and discrepancies between data and MC on the SDCS measurements. The analysis has been repeated several times, changing the reconstruction algorithms, MC samples, and measurement strategies: Thesystematic uncertainty relative to each measurement has been assigned by assessing the spread of the results (semidispersion). 064601-16 MEASUREMENT OF FRAGMENTATION CROSS SECTIONS . . . PHYSICAL REVIEW C 93, 064601 (2016) TABLE I. Single differential cross sections (b sr−1) as a function of the polar angle θ. The halved bin size is shown in parentheses ( ) in the first column. The total uncertainty (stat. and syst. added in quadrature) is shown in parentheses ( ) beside the measured value. The shown values refer to the main isotopes of the hydrogen and helium fragment species. θ1H2H3H3He 4He (deg) dσ/d (b sr−1)dσ/d (b sr−1)dσ/d (b sr−1)dσ/d (b sr−1)dσ/d (b sr−1) 0.2(0.2) 41 (15) 2.510 2(1.310 2) 33 (11) 13 (15) 74 (30) 0.6(0.2) 12 (3.4) 49 (28) 18 (4.4) 12 (4.1) 78 (11) 1(0.2) 24 (2.9) 15 (6) 16 (3.5) 12 (3.2) 59 (7.5) 1.4(0.2) 20 (2.4) 12 (1.7) 12 (3.2) 12 (2) 65 (6.8) 1.8(0.2) 17 (1.8) 11 (2.4) 10 (2.1) 11 (1.7) 50 (4.8) 2.2(0.2) 15 (2.6) 9.9 (2.9) 7.2 (1.7) 7.9 (1.7) 42 (3.9) 2.6(0.2) 16 (2.3) 10 (1.7) 6.8 (0.89) 8.1 (0.94) 34 (2.6) 3(0.2) 14 (1.7) 9.6 (1.3) 4.5 (0.76) 8.1 (0.98) 25 (2.1) 3.4(0.2) 13 (2.6) 7.6 (1.6) 3.9 (0.65) 9.2 (1.3) 20 (1.7) 3.8(0.2) 10 (1.3) 7.7 (0.75) 3.8 (0.69) 7.5 (0.71) 15 (1.3) 4.2(0.2) 9.6 (1.3) 6.3 (0.63) 3.1 (0.58) 4.7 (0.79) 11 (0.99) 4.6(0.2) 10 (1.7) 6.2 (0.7) 2.9 (0.7) 4.2 (1.7) 13 (1.5) 5(0.2) 9.3 (2.3) 5.2 (1.2) 3.2 (0.77) 6 (1.8) 7.8 (2.2) In the following we refer to the result obtained by following the prescriptions and strategies outlined in the previous sections as the default result. An important contribution to the systematic uncertainty quoted for the production cross section of H fragments comes from the modeling of the TW hit detection efficiencies. In the TW detector, designed to have a wide dynamic range to detect heavy Zfragments, the H fragment signals are close to the minimum threshold needed to have a signal in the CFDs. For this reason, the events in which only one TDC gives a signal when a slat is hit are used to improve the efficiency for low-charge fragments. To evaluate the impact of the threshold modeling in our MC simulation, the analysis has been repeated, rejecting the events in which only one TDC per slat gave a signal: The change with respect to the default is a measurement of the goodness of the MC simulation of our thresholds and the relative hit reconstruction efficiency. The difference observed is, as expected, significant only for Hfragments and is shown, in red full topside-down triangles in Fig. 24 (SCC spectrum). The analysis has also been redone by changing both the scoring function, using different weights, and disabling the TW hits clustering algorithm. The weights used for the systematic checks were alternatively the set WChg =8, yW=0(cm −1), the set WChg =0 and yW=1(cm −1), and the set WChg =6 and yW=1(cm −1) to test the impact of a charge-based and ymatching-only strategy and the impact of the choice of the best weight pair. The results for 2Hfragments, taking the largest observed difference, are shown in Fig. 24 (Cls/Sco spectra). The VTX tracking robustness and the matching of BM and VTX information has been checked by changing the reconstruction algorithms relaxing the requirement of having TABLE II. Single differential cross sections (b sr−1) as a function of the polar angle θ. The halved bin size is shown in parentheses ( ) in the first column. The total uncertainty (stat. and syst. added in quadrature) is shown in parentheses ( ) beside the measured value. The shown values refer to the main isotopes of the lithium, beryllium, and boron fragment species. 9Be and 10Be are shown together as measured by the mass fit and explained in Sec. V. θ6Li 7Li 7Be 9,10Be 10B11B (deg) dσ/d (b sr−1)dσ/d (b sr−1)dσ/d (b sr−1)dσ/d (b sr−1)dσ/d (b sr−1)dσ/d (b sr−1) 0.2(0.2) 5.5 (7.8) 6 (4.7) 5 (6.1) 12 (8.5) 79 (27) 14 (24) 0.6(0.2) 11 (2.7) 5.8 (1.6) 3.8 (2.7) 6.1 (2.9) 24 (3.4) 15 (5.5) 1(0.2) 3.4 (1.4) 8.5 (2.3) 4.5 (2) 3.9 (1.3) 6.2 (2.8) 12 (4.6) 1.4(0.2) 3.2 (1.1) 6.1 (1.1) 3.4 (1.5) 1.9 (0.76) 2.5 (1.6) 1.7 (2.2) 1.8(0.2) 4.8 (1.7) 4.1 (0.69) 1.9 (0.77) 1.4 (0.59) 2 (1.3) 0.51 (0.67) 2.2(0.2) 2.4 (0.6) 2.9 (0.7) 1.6 (0.54) 0.65 (0.28) 0.63 (0.97) 0.81 (0.75) 2.6(0.2) 0.91 (0.4) 1.7 (0.44) 1.9 (0.56) 0.69 (0.31) 1.1 (0.42) 0.67 (0.32) 3(0.2) 1.7 (0.73) 1.2 (0.32) 1.1 (0.28) 0.16 (0.21) 0.41 (0.18) 0.22 (0.19) 3.4(0.2) 1.1 (0.37) 0.74 (0.26) 0.89 (0.28) 0.26 (0.16) 0.098 (0.071) 0.26 (0.11) 3.8(0.2) 1.4 (0.45) 0.19 (0.35) 0.72 (0.21) 0.19 (0.1) 4.2(0.2) 0.3 (0.18) 0.1 (0.23) 0.23 (0.11) 0.0076 (0.038) 4.6(0.2) 0.41 (0.18) 0.13 (0.16) 5(0.2) 0.34 (0.16) 0.046 (0.099) 064601-17 M. TOPPI et al. PHYSICAL REVIEW C 93, 064601 (2016) TABLE III. Single differential cross sections (b nucleon/MeV) as a function of the normalized kinetic energy for fragments within the ALADIN angular acceptance (6◦). The halved bin size is shown in parentheses ( ) in the first column. The total uncertainty (stat. and syst. added in quadrature) is shown in parentheses ( ) beside the measured value. The shown values refer to the main isotopes of the hydrogen and helium fragment species. Energy 1H2H3H3He 4He (MeV/nucl.) dσ/dE (b nucl./MeV) dσ/dE (b nucl./MeV) dσ/dE (b nucl./MeV) dσ/dE (b nucl./MeV) dσ/dE (b nucl./MeV) 100(100) 1.58×10−4(6.35×10−5)1.42×10−4(1.36×10−5)4.45×10−5(1.02×10−5)2.47×10−5(6.60×10−6)1.09×10−5(4.79×10−6) 215(15) 2.12×10−4(7.64×10−5)9.60×10−5(3.86×10−5)6.69×10−5(2.77×10−5)2.01×10−5(1.84×10−5)1.65×10−5(1.36×10−5) 245(15) 3.12×10−4(1.32×10−4)1.84×10−4(6.50×10−5)3.18×10−5(4.55×10−5)2.22×10−5(1.90×10−5)1.37×10−5(1.21×10−5) 275(15) 3.30×10−4(9.42×10−5)2.55×10−4(9.00×10−5)2.89×10−4(5.72×10−5)1.13×10−4(4.81×10−5)5.21×10−5(2.28×10−5) 305(15) 5.91×10−4(1.26×10−4)5.89×10−4(1.72×10−4)3.07×10−4(7.49×10−5)2.11×10−4(5.57×10−5)2.79×10−4(6.13×10−5) 335(15) 8.68×10−4(1.32×10−4)1.24×10−3(2.79×10−4)6.30×10−4(1.57×10−4)3.84×10−4(1.02×10−4)1.25×10−3(2.50×10−4) 365(15) 1.39×10−3(1.32×10−4)1.28×10−3(2.99×10−4)8.09×10−4(1.52×10−4)8.84×10−4(2.54×10−4)3.94×10−3(4.76×10−4) 400(20) 1.60×10−3(1.46×10−4)1.44×10−3(1.91×10−4)1.18×10−3(1.39×10−4)1.04×10−3(5.44×10−4)5.65×10−3(8.09×10−4) 440(20) 1.13×10−3(9.93×10−5)1.06×10−3(1.66×10−4)6.41×10−4(1.11×10−4)7.76×10−4(1.43×10−4)3.32×10−3(3.27×10−4) 480(20) 8.59×10−4(9.48×10−5)5.30×10−4(1.34×10−4)2.83×10−4(7.02×10−5)4.15×10−4(1.38×10−4)1.33×10−3(2.46×10−4) 525(25) 6.14×10−4(1.22×10−4)2.75×10−4(8.90×10−5)1.89×10−4(4.92×10−5)1.74×10−4(3.20×10−5)4.49×10−4(1.37×10−4) 575(25) 3.75×10−4(8.74×10−5)1.95×10−4(7.73×10−5)1.35×10−4(5.69×10−5)7.11×10−5(6.00×10−5)8.40×10−5(5.21×10−5) 650(50) 8.73×10−5(3.81×10−5)9.86×10−5(5.95×10−5)4.29×10−5(3.75×10−5)7.00×10−5(4.80×10−5)8.45×10−7(1.09×10−6) 750(50) 2.64×10−4(7.46×10−5)1.28×10−4(6.89×10−5)4.00×10−5(2.36×10−5)1.37×10−5(1.36×10−5)1.02×10−7(4.83×10−7) a BM matched track: The results are shown in Fig. 24 as BM mat values. The observed variations, in most bins, are within the statistical uncertainty. To evaluate the impact on the limited precision of the TW position with respect to the general FIRST reference frame, the TW position in the reconstruction algorithm was changed by ±1 cm, corresponding to the resolution of the survey performed after the data taking. The result is shown in Fig. 24, labeled as TW pos+(−). The differences in the mass spectra between data and MC have to be taken into account in the Yraw imeasurement, to avoid any bias in the fit result. The mass fit study has been repeated after changing the ROOKEYSPDFsmoothing parameter (ρ) to test different descriptions of the peaking components in the observed mass distributions. The obtained result is, for most bins, well within the statistical uncertainty, as shown in Fig. 24 (spectrum labeled Bkg model). It has also to be noted that the different analyses strategies used for the evaluation of the systematic uncertainty explored several combinatorial background conditions (modified shapes and different background contamination): The final systematic uncertainty therefore covers also the background contamination subtraction under different background conditions. The systematic checks include the evaluation of the MC simulation impact on the estimate of the cross feed correction that is used to correct the Yraw iyields described in Sec. IV E. The data/MC difference rescaling used for the evaluation of the correction factors has been switched off to evaluate the maximum impact of this rescaling (spectrum labeled Xfeed in Fig. 24). Finally, the differences in the tracking reconstruction efficiency computed as described in Sec. IV C 3 with the full unbiased MC sample have been taken into account when producing the spectrum labeled Eff in Fig. 24. TABLE IV. Single differential cross sections (b nucleon/MeV) as a function of the normalized kinetic energy for fragments within the ALADIN angular acceptance (6◦). The halved bin size is shown in parentheses ( ) in the first column. The total uncertainty (stat. and syst. added in quadrature) is shown in parentheses ( ) beside the measured value. The shown values refer to the main isotopes of the lithium, beryllium, and boron fragment species. 9Be and 10Be are shown together as measured by the mass fit and explained in Sec. V. Energy 6Li 7Li 7Be 9,10Be 10B11B (MeV/nu.) dσ/dE (b nu./MeV) dσ/dE (b nu./MeV) dσ/dE (b nu./MeV) dσ/dE (b nu./MeV) dσ/dE (b nu./MeV) dσ/dE (b nu./MeV) 305(15) 3.79×10−7(3.59×10−6)4.30×10−6(5.47×10−6) 335(15) 6.88×10−6(9.20×10−6)3.45×10−5(1.05×10−4)9.89×10−6(6.82×10−6)2.73×10−8(1.64×10−7)7.59×10−8(1.97×10−7) 365(15) 1.68×10−4(8.64×10−5)1.28×10−4(2.00×10−4)1.49×10−4(4.40×10−5)8.01×10−5(5.04×10−5)1.99×10−4(7.98×10−5)6.12×10−5(8.40×10−5) 400(20) 6.33×10−4(1.43×10−4)4.57×10−4(8.42×10−5)3.29×10−4(1.47×10−4)3.01×10−4(8.15×10−5)7.20×10−4(2.79×10−4)7.58×10−4(2.62×10−4) 440(20) 1.43×10−4(6.59×10−5)2.48×10−4(2.16×10−4)2.52×10−4(1.95×10−4)1.30×10−4(4.40×10−5)2.37×10−5(2.72×10−5)6.34×10−5(2.03×10−4) 480(20) 5.82×10−5(3.33×10−5)4.76×10−5(2.61×10−5)8.10×10−5(3.01×10−5)1.42×10−5(3.45×10−5)1.19×10−5(4.70×10−5)6.07×10−5(4.78×10−5) 525(25) 6.25×10−5(3.59×10−5)1.04×10−6(2.33×10−6)1.81×10−5(1.27×10−5)1.09×10−5(8.97×10−6)7.77×10−6(2.63×10−5)2.07×10−5(1.42×10−5) 575(25) 3.89×10−6(1.06×10−5)1.96×10−8(1.05×10−7)3.20×10−8(3.61×10−8)8.30×10−8(9.08×10−8)1.30×10−8(5.72×10−7)1.69×10−8(2.37×10−8) 064601-18 MEASUREMENT OF FRAGMENTATION CROSS SECTIONS . . . PHYSICAL REVIEW C 93, 064601 (2016) [deg]θ 024 ] -1 [b srΩ/dσd 1 10 2 10 3 10 Z = 1 H 1 H 2 H 3 (a) [deg]θ 024 ] -1 [b srΩ/dσd 1− 10 1 10 2 10 3 10 Z = 2 He 3 He 4 (b) [deg]θ 024 ] -1 [b srΩ/dσd 1− 10 1 10 Z = 3 Li 6 Li 7 (c) [deg]θ 024 ] -1 [b srΩ/dσd 1− 10 1 10 Z = 4 Be 7 Be 9,10 (d) [deg]θ 024 ] -1 [b srΩ/dσd 1− 10 1 10 2 10 Z = 5 B 10 B 11 (e) FIG. 25. SDCS of different charge (Z) fragment production as a function of the fragment angle with respect to the beam axis, computed using Eq. (2). The results for each isotope are shown separately, together with their sum (in black squares). 9Be and 10Be are shown together as measured by the mass fit and explained in Sec. V. The total uncertainty (stat. and syst. added in quadrature) is shown. VII. CONCLUSIONS The FIRST experiment performed a measurement of fragment production SDCS as a function of production angles and kinetic energies, studying a data sample of 4.5×106 collisions of 12C ions impinging on a thin (0.5 mm) gold target. The measurement experimental configuration, as well as the 12C ion energy of 400 MeV/nucleon, made it possible to provide results that are particularly interesting for space applications. The results presented here achieve an unprecedented precision on the single differential cross sections of carbon ions on a thin gold target. This experimental input is highly valuable as it sets a reference point that will help the benchmarking of MC simulation 064601-19 M. TOPPI et al. PHYSICAL REVIEW C 93, 064601 (2016) [MeV/nucleon] kin E 0 200 400 600 800 ] -1 /dE [ b (MeV/nucleon)σd 5− 10 4− 10 3− 10 2− 10 Z = 1 H 1 H 2 H 3 (a) [MeV/nucleon] kin E 0 200 400 600 800 ] -1 /dE [ b (MeV/nucleon)σd 5− 10 4− 10 3− 10 2− 10 Z = 2 He 3 He 4 (b) [MeV/nucleon] kin E 0 200 400 600 800 ] -1 /dE [ b (MeV/nucleon)σd 6− 10 5− 10 4− 10 3− 10 2− 10 Z = 3 Li 6 Li 7 (c) [MeV/nucleon] kin E 0 200 400 600 800 ] -1 /dE [ b (MeV/nucleon)σd 6− 10 5− 10 4− 10 3− 10 Z = 4 Be 7 Be 9,10 (d) [MeV/nucleon] kin E 0 200 400 600 800 ] -1 /dE [ b (MeV/nucleon)σd 6− 10 5− 10 4− 10 3− 10 Z = 5 B 10 B 11 (e) FIG. 26. SDCS of different charge (Z) fragment production, as a function of the fragment normalized kinetic energy, computed using Eq. (3) for fragments within the ALADIN angular acceptance (6◦). The results for each isotope are shown separately, together with their sum (in black squares). 9Be and 10Be are shown together as measured by the mass fit and explained in Sec. V. The total uncertainty (stat. and syst. added in quadrature) is shown. software currently used for nuclear fragmentation studies for which a high precision is required and whose implications range from the space radiation to charged-particle-therapy applications. ACKNOWLEDGMENTS We would like to acknowledge M. Arba, L. La Delfa and M. Tuveri (INFN Sez. Cagliari), M. Anelli, S. Cerioni, G. Corradi, A. Mengucci, D. Riondino and R. Rosellini 064601-20 MEASUREMENT OF FRAGMENTATION CROSS SECTIONS . . . PHYSICAL REVIEW C 93, 064601 (2016) (INFN, LNF), M. Capponi and A. Iaciofano (INFN, Sez. Roma3) for the technical design and mechanical work on the Interaction Region and Filippo Bosi (INFN Sez. Pisa) for his help and suggestions. We also acknowledge Dr. H˚ akan T. Johansson for the invaluable help in setting up the trigger. This work has been supported by the European Community FP7 - Capacities, contract ENSAR no262010, and by FP7 - People, Contract No. PITNGA-2008-215840-PARTNER. 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