Experimental spectra analysis in THM with the help of simulation based on Geant4 framework
Chengbo Li, Qungang Wen, Shuhua Zhou, Yuanyong Fu, Jing Zhou, Qiuying Meng, Zongjun Jiang, Xiaolian Wang
aa r X i v : . [ nu c l - e x ] A ug Experimental spectra analysis in THM with the help of simulation based on Geant4framework
Chengbo Li ∗ Beijing Radiation Center, Beijing 100875, China andKey Laboratory of Beam Technology and Material Modification of Ministry of Education,College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China
Qungang Wen † Anhui University, Hefei 230601, China
Shuhua Zhou, Yuanyong Fu, Jing Zhou, and Qiuying Meng
China Institute of Atomic Energy, Beijing 102413, China
Zongjun Jiang and Xiaolian Wang
State Key Laboratory of Particle Detection and Electronics, USTC, Hefei 230026, China (Dated: September 11, 2018)The Coulomb barrier and electron screening cause difficulties in directly measuring nuclear reac-tion cross sections of charged particles in astrophysical energies. The Trojan-horse method has beenintroduced to solve the difficulties as a powerful indirect tool. In order to understand experimentalspectra better, Geant4 is employed to simulate the method for the first time. Validity and reliabilityof the simulation are examined by comparing the experimental data with simulated results. TheGeant4 simulation can give useful information to understand the experimental spectra better indata analysis and is beneficial to the design for future related experiments.
PACS numbers: 26.90.+n,29.85.Fj
I. INTRODUCTION
Understanding energy production and nucleosynthesisin stars requires increasingly precise knowledge of the nu-clear reaction rates at the energies of interest [1]. How-ever, at astrophysical temperature, nucleus react at verylow energies much lower than the Coulomb barrier forcharged particles. The reaction cross sections are verysmall due to the Coulomb barrier, so that the direct mea-surement is almost imposable. To overcome the experi-mental difficulties arising from the small cross sectionsand the electron screening, the Trojan-horse method(THM) [2–10] has been introduced.THM provides a valid alternative approach to measureunscreened low-energy cross sections of reactions betweencharged particles. In the method, suitable three body re-actions are measured under the quasi-free kinematic con-ditions with beam energies above their Coulomb barrier.The method can also be used to retrieve information onthe electron screening potential when ultra-low energydirect measurements are available.Geant4 [11, 12] is a toolkit for the simulation of thepassage of particles through matter. Its application areasinclude high energy, nuclear and accelerator physics, as ∗ Supported by National Natural Science Foundation of China(11075218, 10575132) and Beijing Natural Science Foundation(1122017); Electronic address: [email protected] † Electronic address: [email protected] a bxA Cc(B) quasi-freebreakupvirtual 2-body reaction
FIG. 1: Diagram of Trojan-horse method well as studies in medical and space science.In this paper, for the first time, we develop a simula-tion program based on the Geant4 framework for THMresearch in order to understand the experimental spectrabetter.
II. TROJAN HORSE METHOD
The Trojan-horse method belongs to an indirect mea-surement method in experimental nuclear astrophysics.The basic assumptions of the THM have been discussedextensively elsewhere [1–4, 6] and detailed theoreticalderivation of the formalism employed can be found in[3] .The diagram of THM is shown in Figure 1. Themethod is based on quasi-free (QF) reaction mechanism,which allows us to derive indirectly the cross section of atwo-body reaction A + x → C + c (1)from measurement of a suitable three-body process A + a → C + c + b (2)The nucleus a is considered to be dominantly composedof clusters x and b ( a = x ⊕ b ).After the breakup of nucleus a due to the interactionwith nucleus A , the two-body reaction occurs betweenthe transferred particle x and nucleus A whereas nucleus b does not participate and acts as a spectator. The energyin the entrance channel E Aa is chosen above the height ofthe Coulomb barrier, so as to avoid a reduction in crosssection.At the same time, the effective energy of the reactionbetween A and x can be relatively small, mainly becausethe energy E Aa is partially used to overcome the bindingenergy ε a of x inside a (Eq.(3)), and the Fermi motionof x inside a compensates at least partially for the A + a relative motion (Eq.(4)) . E qfAx = E Aa (cid:18) − µ Aa µ Bb µ bx m x (cid:19) − ε a (3) E Ax = E qfAx ± E xb (4)Since the transferred particle x is hidden inside thenucleus a (so called Trojan-horse nucleus) and the col-lision of A with x takes place in the nuclear interactionregion, the two-body reaction is free of Coulomb sup-pression and, at the same time, not affected by electronscreening effects.Thus the interesting two-body reaction cross sectioncan be extracted from the measured three-body reactionusing the relation formulation Eq.(5) after selecting thequasi-free events: d σdE Cc d Ω Bb d Ω Cc = KF | W | P l dσ l d Ω ( Ax → Cc ) (5)where KF is the kinematical factor, W is the momentumdistribution of the spectator b inside the Trojan-horsenuclei a , and P l is the penetration functionIn our work, the THM have been used to study two im-portant astrophysical nuclear reactions related with Be abundance. H ( Be, α Li ) n = ⇒ Be ( p, α ) Li (6)and H ( Be, d Be ) n = ⇒ Be ( p, d ) Be (7)where deuteron is used as the Trojan horse nucleus, dueto its d = p ⊕ n structure [5] , the proton acts as aparticipant while the neutron is a spectator to the virtualtwo-body reaction. FIG. 2: Experiment setup of Trojan-horse method for thereaction Eq.(7)
III. EXPERIMENT SETUP
The measurements of the reactions Eq.(6) and Eq.(7)were both performed in Beijing National Tandem Accel-erator Laboratory at China Institute of Atomic Energy.The experimental setup for the reaction Eq.(7) was in-stalled in the nuclear reaction chamber at the R60 beamline terminal as shown in Figure 2. A Be beam at22.44 MeV provided by the HI-13 tandem accelerator wasused to bombard a deuterated polyethylene target CD placed vertically to the beam axis. The thickness of thetarget is about 160 µ g / cm . In order to reduce the angleuncertainty coming from the large beam spot, a lineartarget with 1 mm width was used.A position sensitive detector (PSD ) was placed at15 ◦ ± ◦ to the beam line direction and about 240 mmfrom the target to detect outgoing deuterons, and aDPSD (Dual Position Sensitive Detector, consisted ofPSD u in the upside and PSD d downside ) was used at8 . ◦ ± ◦ in the other side of the beam line and 250mm distance from the target to detect two alpha par-ticles decayed from the unstable outgoing particle Be.The arrangement of the experimental setup was modelledin Monte Carlo simulation in order to cover a region ofquasi-free angle pairs. The trigger for the event acqui-sition was given by coincidence of signals from the PSDand DPSD.The reactions Eq.(6) can also be measured with PSD detecting alpha and PSD u detecting Li particles in co-incidence.
IV. EXPERIMENTAL SPECTRA ANALYSISWITH THE HELP OF GEANT4 SIMULATION
The first step of the data analysis work is the energyand angle calibration of PSD and DPSD. After the cali-bration of the detectors, we have the energe and momen-tum of the particles detected by PSD , PSD u and PSD d .Then we reconstructed Be from (E u , E d , θ u , θ d ) on theassumption that the particles detected by DPSD are two α . The energy and momentum of the third particle n ofthe exit channel Be + d → Be + d + n are calculatedfrom (E , E , θ , θ ), where particle1 is d and particle2is Be.The most important thing to do before using THM toextract information of the 2-body reaction Be + p → Be+d from the 3-body reaction Be+d → Be+d+n is toselect the right events which satisfied with the three bodyreaction of quasi-free reaction mechanism apart from allthe other outgoing channels. There are many exit chan-nels from the same entrance channel of Be+d, for exam-ple, the Be + H → α + Li + n channel can be detectedas well. Other than the exit channels from Be + d, thereare more other outgoing channels from the reaction ofthe beam bombard to other elements in the target suchas C and H.Therefore, it is particularly important to understandthe experimental spectrum in the events selections. Inorder to understand the experimental spectrum better,Geant4 simulation is applied to the THM study in ourwork.Geant4 [11] [12] developed by CERN is a well estab-lished Monte Carlo framework for simulation of particlespassage through matter. Detector and target construc-tion parameters in Geant4 simulation program of THMwere defined according to the experiment setup. And thedefault FTFP BERT physics list was used in the pro-cess. An event generator code was written in C ++ tocreate momentum information of outgoing particles fromdifferent nuclear reactions.Some of the Geant4 simulation results will be shownbelow comparing with the experimental data. A. E − θ spectrum of 2-body reactions FIG. 3: Comparison of experimental spectrum E u − θ u (left) with simulated one (right) Figure 3 (left) shows the experimental spectrum ofE u − θ u detected by PSD u . The red points in Fig-ure 3 (right) shows Geant4 simulation of the reaction Be + H → Be + H. The E Be − θ Be curve looked likeparabola is easy to find in the experiment spectrum.There is also a small arc between E u (16MeV − Be + H → Be + H elastic scatteringprocess (the bule points in Figure 3 (right) ).This meansthat there are also some H in the CD target.The simulation result of the Be + C → Be + Celastic scattering process is also shown in Figure 3 (right, the green points), which meets the curve of E u ∼ − θ curve of outgoing particles from two bodyreactions can give a validity test to the detector calibra-tion. It can also give information of elements in target. B. E − E u spectrum: kinematic focus / MeV E0 2 4 6 8 10 12 14 16 18 20 22 / M e V u E FIG. 4: Comparison of experimental spectrum E − E u (left) with simulated one (right) Figure 4 (left) is the two-dimensional energy spectrumE − E u of experimental data. Simulation results of dif-ferent reaction channels are shown in Figure 4 (right).The red points are the simulation of Be + H → α + Li + n reaction from quasi free process, which areinteresting for THM reaction Eq.(6).The bule points are the simulation of Be + H → α + Li reaction caused by the beam bombarding to H in thetarget.The green points are the simulation of Be + H → H + He + He reaction channel, which are not easy tofind out.All these points can be found in the experiment spec-trum.The black points, which puzzled us for a long time,are the simulation result of Be + H → Be + H elasticscattering results. Normally, the spots of the elastic scat-tering in the two-dimensional energy spectrum should bein the line of E + E u = 22 . µ m).It can be seen that the simulation program can give usgreat help to get a better understanding to the experi-ment spectrum. C. E u − E d spectrum: reconstruction of Be The important step in data analysis is the reconstruc-tion of Be particle from two α particles detected byDPSD. Figure 5 (left) is the experimental spectrum ofE u − E d . /MeV u E0 2 4 6 8 10 12 14 16 18 20 22 / M e V d E FIG. 5: Comparison of experimental spectrum of recon-struction for Be (left) with simulated one (right)
The simulation result of α particles decayed from Beof Be + H → Be + H + n reaction is shown in Figure5 (right, the red points). You can see the agreementbetween the simulated data and the low energy range ofthe experimental data (E u ∈ (5MeV − Be + H → Be + H + n reaction channelwhich is interested for us.A simulation of α particles decayed from Be of Be+ H → Be+ H reaction channel is given in Figure 5 (right,the green points). It is in good agreement with the ex-perimental data points located on the high energy area(E u ∈ (12MeV − α particles decayed from Beground state of Be + d → Be ∗ + H → Be + H + γ reaction channel after the Be ∗ transfered from the firstexcited state to the ground state by emitting a gammaray is shown in Figure 5 (right, the blue points), whichcan show good agreement with the middle energy range(E u ∈ (10MeV − D. Future applications
The simulation code is also very useful in the researchwork such as the energy loss and angle dispersion of theparticles passing through a ∆E detector or the dead layerof detectors. The simulation results can help us in thedesign of the THM experiment, as well as the particleidentification and error analysis in data analysis.
V. SUMMARY
A simulation system based on the Geant4 frameworkwas established and applied to the Trojan horse methodexperimental study for the first time. The validity andreliability of the simulation system are examined by com-paring the experimental data with the simulated resultsin our work. The simulation system can provide usefulinformation to understand the experimental spectra bet-ter in data analysis, an it is beneficial to the design forfuture related experiments.
Acknowledgments
We thank Dr. Chengjian Lin and Dr. Xia Li fromCIAE for their kind help during the experiment measure-ment. We also thank Prof. C. Spitaleri and his researchgroup from INFN-LNS laboratory of Italy for the pre-cious collaboration in the THM study. In addtion, wethank Dr. Zhiyi Liu for his kind discussion in the paperwritting. [1] E. G. Adelberger, A. Garcia, R. G. Hamish Robertson,et al., Rev. Mod. Phys. (2011) 195.[2] G. Baur, Phys. Lett. B (1986) 135.[3] S.Typel, G.Baur. Annals Phys, (2003) 228.[4] C. Spitaleri, S. Cherubini, et al., Nucl.Phys. A, (2003) 99c.[5] R. G. Pizzone, C. Spitaleri, A. M. Mukhamedzhanov, etal., Phys. Rev. C, (2009) 025807[6] A. Tumino, C. Spitaleri, S. Cherubini, et al., Few-BodySyst, (2013) 745.[7] Li Chengbo, R.G. Pizzone, C. Spitaleri, et al., NuclearPhysics Review, (2005) 248. [8] S. Romano, L. Lamia, C. Spitaleri, et al., Eur. Phys. J.A, (2006) 221.[9] Qun-Gang Wen, Cheng-Bo Li, Shu-Hua Zhou, et al.,Phys. Rev. C, (2008) 035805.[10] Qun-Gang Wen, Cheng-Bo Li, Shu-Hua Zhou, et al., J.Phys. G: Nucl. Part. Phys, (2011) 085103.[11] S. Agostinelli, J. Allison, K. Amako, et al., NuclearInstruments and Methods in Physics Research A, (2003) 250.[12] J. Allison, K. Amako, J. Apostolakis, et al., IEEETRANSACTIONS ON NUCLEAR SCIENCE,53