Secondary radiation measurements for particle therapy applications: nuclear fragmentation produced by 4 He ion beams in a PMMA target
M. Marafini, R. Paramatti, D. Pinci, G. Battistoni, F. Collamati, E. De Lucia, R. Faccini, P. M. Frallicciardi, C. Mancini-Terracciano, I. Mattei, S. Muraro, L. Piersanti, M. Rovituso, A. Rucinski, A. Russomando, A. Sarti, A. Sciubba, E. Solfaroli Camillocci, M. Toppi, G. Traini, C. Voena, V. Patera
SSecondary radiation measurements for particletherapy applications: nuclear fragmentationproduced by He ion beams in a PMMA target
M. Marafini a,b , R. Paramatti a,c , D. Pinci a , G. Battistoni d ,F. Collamati e , E. De Lucia e , R. Faccini a,c , P. M. Frallicciardi f ,C. Mancini-Terracciano a,c , I. Mattei d , S. Muraro d ,L. Piersanti a,g , M. Rovituso h , A. Rucinski a,g ,A. Russomando a,c,i , A. Sarti b,d,g , A. Sciubba a,b,g ,E. Solfaroli Camillocci a,c , M. Toppi e , G. Traini a,c , C. Voena a ,V. Patera a,b,g a INFN - Sezione di Roma, Italy b Museo Storico della Fisica e Centro Studi e Ricerche “E. Fermi”, Roma, Italy c Dipartimento di Fisica, Sapienza Universit`a di Roma, Italy d INFN - Sezione di Milano, Italy e Laboratori Nazionali di Frascati dell’INFN, Frascati, Italy f Istituto di ricerche cliniche Ecomedica, Empoli, Italy g Dipartimento di Scienze di Base e Applicate per Ingegneria, Sapienza Universit`a diRoma, Italy h GSI Helmholtzzentrum f¨ u r Schwerionenforschung, Darmstadt, Germany i Center for Life Nano Science@Sapienza, Istituto Italiano di Tecnologia, Roma, ItalyE-mail: (corresponding author) [email protected]
Abstract.
Nowadays there is a growing interest in Particle Therapy treatments exploitinglight ion beams against tumors due to their enhanced Relative Biological Effectivenessand high space selectivity. In particular promising results are obtained by the useof He projectiles. Unlike the treatments performed using protons, the beam ionscan undergo a fragmentation process when interacting with the atomic nuclei in thepatient body. In this paper the results of measurements performed at the HeidelbergIon-Beam Therapy center are reported. For the first time the absolute fluxes andthe energy spectra of the fragments - protons, deuterons, and tritons - produced by He ion beams of 102, 125 and 145 MeV /u energies on a poly-methyl methacrylatetarget were evaluated at different angles. The obtained results are particularly relevantin view of the necessary optimization and review of the Treatment Planning Softwarebeing developed for clinical use of He beams in clinical routine and the relative bench-marking of Monte Carlo algorithm predictions. a r X i v : . [ phy s i c s . m e d - ph ] A ug
1. Introduction
The efficacy of the treatment of radio-resistant tumors with Particle Therapy (PT)is nowadays well established, and the number of centers that can carry out a PTtreatment is steadily increasing. The advantage of using hadron beams with respectto the conventional radio therapy is related to the mechanism of energy loss in matter,characterized by a loss of a small fraction of energy in the first part of the hadron pathwithin the patient body with a following release of almost all the hadron energy inthe very small region where the energy loss per distance traveled reaches its maximum,called Bragg Peak (BP).In the interaction with the atomic nuclei of the patient body, the ions can fragmentin nuclei with lower atomic number Z which penetrate more in depth causing an energyloss tail beyond the BP region. A precise knowledge of the ion-target cross sectionfor different type of fragments is therefore fundamental to estimate the additional doseabsorbed by the healthy tissues and organs at risk surrounding the tumor. Detailedmeasurements were performed in the past on the fragmentation of heavy ion beams as,for example, on carbon (Haettner et al. 2013, Gunzert-Marx et al. 2008).In last years, there is a growing interest in the usage of beams of He ions fortheir high Linear Energy Transfer (LET) and Relative Biological Effectiveness (RBE)characteristics (Tommasino et al. 2015, Kr¨ a mer et al. 2016, Durante & Paganetti 2016).In this work we present detailed measurements of the production of protons( p ), deuterons ( d ) and tritons ( t ) by an He ion beam impinging on a Poly MethylMethacrylate (PMMA) target. Data were collected at the Heidelberg Ion-Beam Therapycenter (HIT), in Germany, with He beams of 102, 125 and 145 MeV /u kinetic energy.The absolute fluxes and the angular and energy spectra of secondary fragments werestudied as a function of the beam energy.A precise measurement of the projectile fragmentation process cross section isessential to correctly evaluate the corresponding dose released to the patient and takeit into account in the Treatment Planning Software (TPS) (Kr¨ a mer et al. 2000).A similar work (Rovituso et al. 2016) presents the loss of He beams on waterand PMMA at different depths and the double differential fragment yields with watertargets.In this paper the experimental setup is described in Section 2, the strategy ofthe measurement and the particle identification are discussed in details in Section 3.Section 4 summarizes the correction factor definition and computation, like geometricalacceptance and detector efficiency, to be applied to the fragment flux measurements.Finally the cross section results are reported in Section 5.
2. Experimental setup
Beams of He ions of different energies relevant for PT have been used to irradiatea PMMA target in order to study the projectile fragmentation at different angles.Such measurements were part of a complex experiment, exploited with a multi-purposedetector setup, aiming for the characterization of the interactions of different ion speciesof several energies with the purpose of studying the secondary particle emission troughthe measurement of prompt photons, charged and β + -emitter fragments. More detailscan be found in (Mattei et al. 2016, Rucinski et al. 2016, Toppi et al. 2016).A simplified view of the HIT experimental set-up is sketched in Fig. 1 showing onlythe detector and geometrical configuration that is relevant for the forward fragmentationstudies. The origin of the reference frame was placed in the Bragg Peak position,evaluated for each beam energy by means of a dedicated Monte Carlo software, shortlybefore the PMMA exit face. The beam, running from left to right in the figure, cameout from the vacuum pipe about 50 cm upstream the PMMA target. It had a FullWidth at Half Maximum size dependent on the energy and ranging from 6.9 mm to 9.3mm in the transverse plane. To detect the incoming primary particles, a 2 mm thickplastic scintillator (EJ200), readout by two Hamamatsu H6524 photo-multiplier tubes(PMTs) and referred as Start Counter (SC) in the following, was placed at about 37 cmupstream from the PMMA. The time resolution of the SC tubes was measured to beabout 250 ps.In order to keep the BP position close to the end of PMMA, its thickness (t PMMA )was adjusted accordingly to the specific range of each beam, computed with a FLUKAMC simulation (Ferrari et al. 2005, Battistoni et al. 2007, Battistoni et al. 2015). Thebeam energies and the corresponding values for the BP depth and t
PMMA are reportedin Table 1. The PMMA face dimensions were 5 . × . . Table 1.
Bragg Peak depth (with respect to the ion entrance point) and thickness ofthe PMMA target for data taking at different beam energies. E beam BP Depth t PMMA (MeV /u ) (cm) (cm)102.34 6.68 7.65124.78 9.68 10.00144.63 12.63 12.65Three identical arms ( a, b and c in Fig. 1) were assembled and placed downstreamfrom the PMMA. Each arm was instrumented with: • two thin scintillators, STS (4 . × . × . ) and STS (4 . × . × . ), readby a H10580 PMT, placed 175 cm apart from each other, to measure the fragmentTime of Flight (ToF); • a matrix of 2 × Ge O (BGO) crystals readout by an EMI-9814B PMT to Figure 1.
Top view of the experimental setup. The beam runs form the leftand crosses the Start Counter (SC) before impinging on the PMMA target. Onthe right three measurement arms: two Time of Flight detectors (STS) and acrystal calorimeter (BGO) per arm. measure the energy deposited by the fragments. Each crystal has a trunk pyramidshape with a front face of 2 . × . , a rear face of 3 . × . and a lengthof 20 cm. The matrices were placed straight after the STS at a distance of about2 m from the origin of the reference frame (see Fig. 1)Analog and discriminated signals were acquired by a VME system instrumentedby a 19-bit multi-hit TDC (CAEN V1190B) with a time resolution of 100 ps, a 12-bitQDC (CAEN V792N) with a charge resolution of 0.1 pC and a 32-bit scaler (CAENV560N) able to operate up to a maximum input rate of 100 MHz. The effective dynamicrange of the QCD was increased by splitting in three the response of the BGO-PMTand sending it, via different attenuators, to three channels of the QDC. The time gatechosen for the BGO signal acquisition was 1 µ s.The performance of all these detectors were studied and optimized in laboratoryby means of cosmic rays and radioactive sources:- the time resolution of the STS was measured to be 250 ps;- given their larger thickness, the STS have a slightly better time resolution of about200 ps and are able to measure an energy release with a precision of about 10%;- the energy resolution of a single BGO crystal was found to have a stochasticcontribution of about 20%/ (cid:112) E [MeV] with an effective constant term always below1 MeV. However, since the crystal responses were not equalized among themand the lateral containment was not perfect, the effective energy resolution of thematrices was about ten times larger. The time resolution of the BGO was measuredto be about 700 ps.By placing these arms at different positions, it was possible to investigate thefragment fluxes in five angular configurations: 0 ◦ and 5 ◦ (arm a ), 10 ◦ and 15 ◦ (arm b ) and 30 ◦ (arm c ). The measurement at 30 ◦ has been performed twice to test thereproducibility of the results. The trigger signal was provided by the coincidence, within a 80 ns time window, of thelogical OR of the two SC photo-multipliers (SCOR) and at least one of the BGO matrixdiscriminated signals.The threshold used to discriminate the BGO signal was equivalent to an energyrelease in the crystal matrix of about 20 MeV. The output rate of the discriminatorfor the BGO in arm a was down-scaled to not saturate the DAQ capabilities and notsuppress the event rate at the other angles.At each event, the trigger signal was vetoed during data conversion giving rise to adead time ( DAQ dead time or δ DT in the following) of the order to few hundreds of µ s.The beam rate ranged from about 300 kHz up to 3 MHz, while the trigger and DAQrates ranged from about 300 Hz to 2 kHz (being the DAQ rate limited to a maximumof 6 kHz). The fraction of acquired events triggered by the BGO was about the 85% ofthe total. In order to estimate the effect of δ DT on the total efficiency, the vetoed andthe un-vetoed trigger rates were acquired by the scaler. The value of δ DT is thereforedefined as the number of vetoed triggers over the number of un-vetoed triggers and itdepends on the beam rate.The total number of primary ions N He has been computed using the informationprovided by the SC. Since the beam rate was well below the maximum operatingfrequency of the scaler, N He had to be corrected only for the effect of the dead timeintroduced by the width of the SC discriminated signal (100 ns). This correction C He has been evaluated by means of a dedicated toy Monte Carlo that reproduces thetemporal beam structure of each data taking. The value of C He ranges from 1 . .
6, depending on the beam rate. A detailed description of how the correction factorsand their statistical and systematic uncertainties have been computed can be foundin (Mattei et al. 2016).
3. Measurements strategy
The study of the interactions of the He ions with a PMMA target and of thefragmentation that can occur resulting in the production of protons, deuteronsand tritons, proceeds through the correct fragment identification and kinetic energymeasurements. The adopted strategies and the related performances are outlined below.
In order to separate the different populations of projectile fragments, several observableswere measured event by event by each arm:- E : the deposited energy in the BGO matrix.- ∆ E : the energy released in the STS in front of the BGO.- T oF : the Time of Flight between the two scintillators STS and STS .- ∆ t BGO − SC : the time interval between the passage of the beam ion in the StartCounter and the signal detected in the BGO matrix.The correlations between the above variables are shown in Fig. 2 for the He125 dataat 10 ◦ . In all the different combinations it is possible to clearly identify three differentevent populations, related to the protons, deuterons and tritons. The most effectiveseparation method is achieved when using E , the deposited energy in BGO, and T oF as shown in Fig. 2, Bottom Right plot. The red lines show the cuts used to separatethe kinetic regions associated to the three different fragments.
The energy calibration of BGO detectors hasbeen performed by means of a dedicated data acquisition using proton and helium beamsof different energies. The light yield has been found to be proportional to the energyof the incoming particles in the kinetic energy ranges [48 ÷
209 MeV] for protons and[50 ÷
180 MeV /u ] for He ions. The observed linearity, in the kinetic energy range ofinterest for the measurements presented in this paper, proved to be of great importancein order to obtain a good particle identification. However, since the fragment kineticenergy measurement derived from the
T oF is more accurate (see Sect. 3.1.2), the BGOcalibrated energy was only used for particle ID purposes.
The time needed by a fragment to travel the distance L fromSTS to STS (175 cm) is related to its kinetic energy E kin and its mass m by thekinematic relation: E kin = mc (cid:32) (cid:112) − ( L/c · T oF ) − (cid:33) (1)Once the particle is identified and its mass is fixed, E kin can be evaluated fromeq. (1). Figure 2.
The correlations measured among the fragment discriminatingvariables are shown for He125 data at 10 ◦ . Top Left: the ∆ E as a function ofthe E . Top Right: E as a function of ∆ t BGO − SC . Bottom Left: ratio between∆ E and E as a function of the T oF . Bottom Right: E as a function of the T oF .
4. Monte Carlo Simulation
A fully detailed Monte Carlo (MC) simulation of the experimental setup has beenperformed by means of the FLUKA software (release 2011.2). The MC sample washence used to evaluate the geometric and detection efficiency of the STS (sec. 4.1)and the BGO (sec. 4.2) for the three different fragment populations and to tune theparticle identification algorithms (sec. 4.3). The obtained results are fully independentof the nuclear models implemented within the FLUKA software as they rely only onthe description of the interaction of the produced fragments with the PMMA andexperimental setup matter. No assumption on the production spectra of the fragmentswas used to compute the efficiency. The only relevant physical processes were thefragment interactions with matter that are very well reproduced by the FLUKA software.
The
T oF measurement requires a signal in both the STS detectors. Therefore themeasured fragment yields has to be corrected to take into account the STS geometricaland detection efficiencies (the acceptance of the experimental setup will be discussed inthe next section). The efficiency of each STS is derived as the ratio of the number ofcoincidences of the two STS and the number of events with a signal in the other STS intriggered events. The two scintillators are almost full efficient for charged particles but,given the its shape, in a sizable fraction of events a fragment hits laterally the BGOmatrix without crossing the STS . From simple geometrical calculations this effect hasbeen evaluated to give an inefficiency of about 20%. This value has been then checkedwith a dedicated simulation. The disagreement between data and simulation is taken assystematic uncertainty. The measured product of STS and STS efficiencies (includingthe geometrical contribution) is ε =76 ±
7% for arm a and ε =73 ±
7% for arms b and c . The BGO full detector efficiency, defined as the convolution of the geometricalacceptance of the experimental setup (related to the solid angle of the BGO matrix) andof the BGO detection efficiency, has been computed using a dedicated MC simulation.In order to take into account the production of the fragments than can occur along thebeam path, protons, deuterons, and tritons with a simulated kinetic energy in the rangeof [50-250]
M eV /u , are isotropically produced in a 12 .
65 cm length empty cylindricalvolume, aligned with the beam direction, with the radius corresponding to the beamsize and ideally positioned within the PMMA.The product of the BGO acceptance and efficiency ( ε BGO in the following) iscomputed as the fraction of p , d , and t reaching the BGO matrix and releasing a signalabove the trigger threshold. The statistical uncertainty on ε BGO is negligible.The systematic uncertainty is evaluated looking at the different fragment kineticenergies. The other geometry configurations (10 cm and 7 .
65 cm target) can beobtained by imposing that the projectiles are emitted in the correct volume, howeverthis different contribution ends up to a negligible effect. The ε BGO dependence, mainlyfrom geometrical acceptance, is on the angle of detection: (4 . ± . − at 0 ◦ up to(5 . ± . − at 30 ◦ . The MC simulation has also been used to evaluate the efficiency of the particleidentification algorithms used in the events selection (see Section 3.1) and thecontribution for possible cross feed of the different populations. As an example, Fig. 3shows the behavior of E as a function of the T oF for MC events in the 0 ◦ arm generatedfrom the fragmentation of a 125 MeV /u He beam. The p , d , and t components areshown with different colors: in red protons, in green deuterons and in blue tritons. Threeseparate bands are clearly distinguishable.The neutral component is not shown, being negligible. Indeed the ToF is computedusing the STS and the probability of having photons or neutrons releasing hits inboth the STS is very low; the MC predicts less than 1 (cid:104) background contamination.Therefore, the number of protons, deuterons, and tritons in data are hence obtainedcounting the number of particles in the regions defined as in Fig. 2 (Bottom Right). ToF (ns)
10 15 20 25 30 E ( M e V ) Figure 3.
Example at 0 ◦ of the behavior of E of a function of T oF in MCevents. The simulation is referred to the 125 MeV /u He beam. The red, greenand blue colors correspond respectively to protons, deuterons and tritons. TheBGO energy cut at 20 MeV, to mimic the hardware threshold present in BGOread-out, is clearly visible.
In order to account for the mixing contribution, mainly due to particles the not fullycontained in the BGO that release only part of their energy inside the BGO matrix, theprobability for a fragment of type i to be measured in the region j of the ( E − T oF ) plane(with i, j = p, d, t ) was estimated as: ε ijmix = N ij /N i that is the number of generatedfragments of type i measured in the region j ( N ij ) normalized to the total number ofgenerated fragments i in the ( E − T oF ) plane ( N i ). The values obtained for the mixingmatrix ( ε mix ) have been obtained using the MC simulation and are reported below: ε mix = ε pp ε pd ε pt ε dp ε dd ε dt ε tp ε td ε tt = . ± .
02% 0 . ± . − − − . ± .
77% 98 . ± .
79% 0 . ± . . ± .
59% 1 . ± .
34% 97 . ± . The uncertainties are representing the spread of the matrix elements estimated fromthe simulation at different beam energies and different angles. As expected the largestcontributions are coming from the misidentification of tritons in protons and deuteronsor deuterons in protons that are related to the partial containment of the fragment inside0the BGO detector, while the matrix elements above the diagonal (in which a protons ismistaken as a deuteron or a deuteron as a triton) are almost consistent with zero.
5. Experimental Results
The total fragment yield produced by the He beam on the PMMA target is given bythe following formula:1 N He · dN frag d Ω ( sr − ) = 14 π · N frag N He · c DS · (1 − δ DT ) · ε ST S · ε BGO (2)where: • N frag is the total number of detected fragments. • N He is the number of beam particles impinging on the PMMA target corrected bythe C He factor described at the end of Section 2.1. • c DS is the correction due to the trigger downscale at 0 ◦ and 5 ◦ mentioned inSection 2.1, which is in the range [0.18-0.29]. • δ DT is the inefficiency introduced by the DAQ dead time also described in Section 2.1and evaluated comparing the VME scaler with the trigger rate acquired by the DAQsystem. It ranges from from 20% to 35% depending on the beam rate. • ε ST S is the STS efficiency, including the geometrical inefficiency of STS describedin Section 4.1. • ε BGO is the product of the BGO detection efficiency (including acceptance) asdescribed in Section 4.2.Aim of this paper is the measurement of the flux of fragments escaping the PMMA:no matter correction is computed to take into account the low energy fragments absorbedin the PMMA. The total fragment yield as a function of the detector angle is shownin Fig. 4 and reported in Table 2. The uncertainty associated to the measured yieldincludes both the statistical and systematic contributions. Being the former well below1% it resulted to be negligible with respect to the latter. The main contribution to thesystematic uncertainty comes from the STS efficiency (Section 4.1): the correspondinguncertainty on the fragment yield is about 10%. Other sources contributing to thesystematic error are the uncertainty on the number of He beam primaries N He impinging on the PMMA target (4%-6% for the different beam configurations) andthe error on ε BGO ( ∼ N frag due to the BGO selection cut threshold, and proven to betotally negligible with respect to the main contributions described above.For 0 ◦ , 10 ◦ and 30 ◦ configurations the absolute yields are not shown for 102 MeV /u energy data taking. This is due to the impossibility of normalizing the fragment yield:the number of incoming primary ions was not reliable in this data set, due to an hardwarefault that affected the VME scaler counting. However this issue does not affect therelative yields, reported in section 5.1.1 Figure 4.
Total fragment yield ( p + d + t ), as a function of the detection anglefor different beam energies. The 102 MeV /u is not available for 0 ◦ , 10 ◦ and30 ◦ configurations (see text for details). Table 2.
Total fragment yield ( p + d + t ), measured by the STS and BGO detectors,for different beam energies at different angles. The uncertainties include both thestatistical and the systematic contributions. beam energy 0 ◦ ◦ ◦ ◦ ◦ ◦ bis (MeV /u ) (sr − ) (10 − sr − ) (10 − sr − )102 - 1 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . The relative composition of protons, deuterons and tritons in the total fragment yield ismeasured by using the number of events counted separately in the three regions of the E − T oF plane (defined as shown in Fig. 2, Bottom Right), and normalized to the totalnumber of fragments. The fraction of fragments shows a strong angular dependence,being the proton more abundant than deuterons, and tritons at large angle while thetriton component is dominating at 0 ◦ . Conversely the dependence of the relative yieldsone the beam energy is quite small. A mixing correction is applied to take into accountthe small fraction of events placed in the wrong kinematic region due to a poor energymeasurement in the BGO, as explained in Section 4.3. The relative p , d , and t yieldsare reported in Table 3 and shown in Fig. 5 as a function of the angle and for differentbeam energies.Some systematic contributions to the measurement of the total yield, as the2 Table 3.
Relative proton, deuteron and triton composition in the total yield (in %),measured for different beam energies at different angles.
102 MeV /u ◦ (%) 5 ◦ (%) 10 ◦ (%) 15 ◦ (%) 30 ◦ (%) 30 ◦ bis (%)proton 20.4 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± /u ◦ (%) 5 ◦ (%) 10 ◦ (%) 15 ◦ (%) 30 ◦ (%) 30 ◦ bis (%)proton 22.3 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± /u ◦ (%) 5 ◦ (%) 10 ◦ (%) 15 ◦ (%) 30 ◦ (%) 30 ◦ bis (%)proton 23.8 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± • the uncertainty due to the partly arbitrary definition of the kinematic regions inthe BGO-TOF plane (Fig. 2, Bottom Right) is estimated, by moving the regionborders among the proton/deuteron and deuteron/triton populations, to be in therange 3%-6% for all the He beam runs; • the error related to the uncertainty on the mixing matrix ( ε mix ), obtained comparingin simulation samples the mixing size at different beam energies and angles, is lessthan 1%.The good agreement of the two results at 30 ◦ (experimental configurations 30 ◦ and30 ◦ bis ) in Tables 2 and 3 expresses the reproducibility on the whole process ofmeasurement. The kinetic energy of the fragment was derived from the
T oF (eq. 1) being this methodmuch more accurate than the measurement of the deposited energy in the BGO. Therelative yields of the fragments as a function of kinetic energy per nucleon for differentangles and beam energies are shown in Fig. 6 and reported in the Tables A1-A5 in thefollowing Appendix. The uncertainties on the kinetic energy per nucleon are obtainedpropagating a 0.5 ns ToF uncertainty through the eq. (1).The differential fragment yield expressed in (MeV · sr) − is given by:1 N He · d N p/d/t dEd Ω = (cid:18) N He · dN frag d Ω (cid:19) · (cid:18) N p/d/t N frag (cid:19) · (cid:18) N p/d/t · ∆ N p/d/t ( E )∆ E (cid:19) (3)3 Figure 5.
Fraction of protons, deuterons, and tritons normalized to the totalnumber of H fragments collected as a function of the detector angle for datacollected using 102 MeV/u (top), 125 MeV/u (center) and 145 MeV/u (bottom) He beams. /N He · dN frag /d Ω is the total yield given in Table 2, N p/d/t /N frag is the p/d/tfraction given in Table 3, and 1 /N p/d/t · ∆ N p/d/t ( E ) / ∆ E is the relative yield as a functionof the nucleon kinetic energy listed in Tables A1-A5 and normalized to the energy binsize ∆ E which is twice the uncertainty reported in the first column of the same tables. Figure 6.
Relative yield of protons (top plots), deuterons (center), and tritons(bottom) as a function of nucleon kinetic energy for different angles with 102MeV/u (left plots), 125 MeV/u (center) and 145 MeV/u (right) He beams.
6. Conclusions
This paper describes the results obtained with an experiment performed at theHeidelberg Ion-beam Therapy (HIT) center in Germany aiming at studying thefragmentation process of He interacting with a beam stopping PMMA target.By means of a suitable set-up, the identity, the kinetic energy and the absolute flux offragments produced in the interaction with the target were measured at five differentangles: 0 ◦ , 5 ◦ , 10 ◦ , 15 ◦ , and 30 ◦ with respect to the beam direction. A dedicated MonteCarlo simulation was developed to evaluate in detail the detector efficiencies and theireffect on the particle identification. Once calculated, these effects were used to correctthe experimental results.The detected fragments were, as expected, protons, deuterons and tritons. Threedifferent beam energies were studied: 102 MeV /u , 125 MeV /u and 145 MeV /u . Forall energies the total fragment flux was found to rapidly decrease with the angle (anorder of magnitude each 15 ◦ ). The relative yield of the different fragments shows twoevident behaviors: • the lighter the fragment, the higher is its relative abundance at large angles; tritonsare twice more abundant than protons at 0 ◦ while protons are about a factor 10more abundant than tritons at 30 ◦ . At 10 ◦ the yields of p , d and t contribute equallyto the total flux. • the heavy fragment component slightly decreases with the beam energy (e.g. at 10 ◦ triton component is 37.0% at 102 MeV /u and 30.6% at 145 MeV /u ).The energy spectra of fragments were also studied. For all species an evidentdependence of the spectrum maximum on the beam energy was found. For protons,spectra are quite large showing a tail above twice the beam energy with a smalldependence on the angle. For deuterons and even more for tritons, spectra decreaserapidly for energies larger than the beam nominal one. This behavior is moreaccentuated at large angles. Acknowledgments
Authors would like to sincerely thank Marco Magi (Dipartimento di Scienze di Base eApplicate per l’Ingegneria, Sapienza Universit`a di Roma) for his valuable effort in theconstruction of the several mechanical supports. This work has been partly supported bythe Museo storico della Fisica e Centro di studi e ricerche Enrico Fermi. The access to thetest beam at the Heidelberg Ion-beam Therapy center has been granted by the ULICEEuropean program. We are indebted to Prof. Dr. Thomas Haberer and Dr. StephanBrons for having encouraged this measurement, made possible thanks to their supportand to the help of the whole HIT staff.6
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Appendix A.
The relative yield of protons, deuterons, and tritons as a function of nucleon kineticenergy is reported for the different angles (Tables A1-A5).7
Table A1.
Relative p , d , and t yields as a function of nucleon kinetic energy at 0 ◦ nu c l e o n H e b e a m - ◦ H e b e a m - ◦ H e b e a m - ◦ e n e r g y ( M e V ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) . ± . ————————— . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . . ± . . ± . —— . ± . —— . ± . . ± . — . ± . ——— . ± . —— . ± . —— Table A2.
Relative p , d , and t yields as a function of nucleon kinetic energy at 5 ◦ nu c l e o n H e b e a m - ◦ H e b e a m - ◦ H e b e a m - ◦ e n e r g y ( M e V ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . —— . ± . . ± . — . ± . . ± . . ± . . ± . . ± . —— . ± . —— . ± . . ± . — . ± . . ± . —— . ± . —— . ± . —— Table A3.
Relative p , d , and t yields as a function of nucleon kinetic energy at 10 ◦ nu c l e o n H e b e a m - ◦ H e b e a m - ◦ H e b e a m - ◦ e n e r g y ( M e V ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . —— . ± . . ± . — . ± . . ± . . ± . Table A4.
Relative p , d , and t yields as a function of nucleon kinetic energy at 15 ◦ nu c l e o n H e b e a m - ◦ H e b e a m - ◦ H e b e a m - ◦ e n e r g y ( M e V ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . —— . ± . . ± . — . ± . . ± . — Table A5.
Relative p , d , and t yields as a function of nucleon kinetic energy at 30 ◦ nu c l e o n H e b e a m - ◦ H e b e a m - ◦ H e b e a m - ◦ e n e r g y ( M e V ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . —— . ± . . ± . — . ± . . ± . — . ± . . ± . —— . ± . —— . ± . . ± . — . ± . . ± . —— . ± . —— .0
Relative p , d , and t yields as a function of nucleon kinetic energy at 30 ◦ nu c l e o n H e b e a m - ◦ H e b e a m - ◦ H e b e a m - ◦ e n e r g y ( M e V ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . —— . ± . . ± . — . ± . . ± . — . ± . . ± . —— . ± . —— . ± . . ± . — . ± . . ± . —— . ± . —— .0 ±0
Relative p , d , and t yields as a function of nucleon kinetic energy at 30 ◦ nu c l e o n H e b e a m - ◦ H e b e a m - ◦ H e b e a m - ◦ e n e r g y ( M e V ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) p ( % ) d ( % )t( % ) . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . —— . ± . —— . ± . —— . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . — . ± . . ± . — . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . — . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . —— . ± . . ± . — . ± . . ± . — . ± . . ± . —— . ± . —— . ± . . ± . — . ± . . ± . —— . ± . —— .0 ±0 .0