Modular Apparatus for Nuclear Reactions Spectroscopy (MARS): Characterization and First Application to Determine 12C(6Li,4He)14Ng.s Nuclear Reaction Cross Sections

Eur. Phys. J. Plus (2025) 140:367 https://doi.org/10.1140/epjp/s13360-025-06305-0 Regular Article Modular apparatus for nuclear reactions spectroscopy (MARS): characterization and first application to determine 12C(6Li,4He)14Ng.snuclear reaction cross sections L. Garrido-Gómez1,a, A. Vegas-Díaz1,2,M.A.G.Alvarez 1,J.P.Fernández-García 1, B. Fernández1,2, F. J. Ferrer1,2, D. Lopez-Aires3 1Departamento FAMN, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain 2Centro Nacional de Aceleradores, Universidad de Sevilla, Junta de Andalucía-CSIC, 41092 Sevilla, Spain 3Institute for Transuranium Elements ITU, European Commission - Joint Research Centre, Box 2340, 76125 Karlsruhe, Germany Received: 23 February 2025 / Accepted: 6 April 2025 © The Author(s) 2025 Abstract This work presents MARS (Modular apparatus for nuclear reactions spectroscopy) and its characterization prior to its first application to measure 6Li+12C nuclear reactions. Measurements were performed at the 3 MV tandem accelerator of the CNA (National Accelerator Center), in Seville, Spain. The 6Li projectiles were accelerated at energies around the 6Li+12C Coulomb barrier (Vcm B∼3.0 MeV - center of mass and Vlab B∼4.5 MeV - laboratory frame). Using a 6Li2+ beam, we measured at 13 laboratory energies from 4.00 to 7.75 MeV. Thus, we present the excitation function of 12C(6Li,4He)14Ng.s.reaction, at 2 backward angles (110.0◦and 140.0◦). The projectile dissociation, leading to this reaction, increases with the bombarding energies around the Coulomb barrier. This dissociation is favored at an optimum energy Eop b≥VB+|Qbu|,whereVBis the Coulomb barrier of the system, and |Qbu|is the module of Q-value for the 6Li dissociation into 4He+2H. This result corroborates a systematic analysis of weakly bound projectiles reacting on several targets [1]. 1 Introduction First nuclei, isotopes of hydrogen (H) and helium (He), originated during primordial nucleosynthesis as a result of the big bang, with very low yield rates of exotic 7Be and weakly bound stable 7Li nuclei [2]. Heavier nuclei originated much later, during stellar nucleosynthesis, by nuclear reactions of lighter elements, from isotopes of hydrogen H (Z 1) and helium He (Z 2),inthestars’ birth, life, and death. The latter with the consequent nucleosynthesis of heavier nuclei in supernovae events [3]. Thus, all matter known in the Universe originates from nuclear reactions. Measurements and analysis of nuclear reactions are key to understanding the yield rate and abundance of elements in the cosmos, the dynamics of stellar bodies, and the different Astrophysics scenarios [2–9]. Regarding the abundance of light elements in the cosmos, there is a gap between He and C, where the abundances of Li, Be and B elements are very low and the nuclei with masses A 5andA8 are not stable. The truth about such abundances must be related to the nuclei structure and reaction dynamics and their probability of being formed or dissociated in nuclear reactions. Different works reported on Li nuclear reactions. For example, Pfeiffer and collaborators [10] reported on the cross section of the emerging 4He (alpha particles), derived from 6Li dissociation into 4He and 2H, peak at the grazing angle. Mayer and Schneider [11] established an energy threshold above which the Rutherford decrease is accompanied by a strong increase in the reaction cross section of 6Li on 12C, at bombarding energies below 5.50 MeV, analyzing the scattering angle at 165.0◦. Capurro et al. reported the 6Li breakup excitation function, at 170.0◦,forthe6Li+144Sm system [12]. Luong and collaborators [13] reported the predominance of transfer reactions, at sub-barrier energies, in triggering the breakup of 6, 7Li reacting on 144Sm and 207,208,209Pb targets. Pandit et al. [14] determined the nuclear reaction tcapture as dominant (∼70%) for the 7Li+93Nb. The systematic capture of tand the inclusive production of α(cross section) for reactions involving 7Li, over a wide mass range, was also reported. The elastic scattering angular distributions of 6, 7, 9, 11Li impinging on 64Zn, 120Sn and 208Pb heavy targets, at bombarding energies around the respective Coulomb barriers, have been previously analyzed [1,15–17]. The systematic optical model (OM) analysis and the respective optical potentials (OP) were shown to strongly correlate with the projectile nuclear structure and its breakup probability. At an optimum bombarding energy, dependent on the Q-value of the projectile breakup and the Coulomb barrier of the system, the projectile tends to dissociate (through breakup and/or transfer reactions). This fact requires adapting the OM to the projectile structure. Stable tightly bound nuclei reactions require short-range Coulomb and nuclear potentials; weakly bound nuclei reactions require accounting for very strong short-range nuclear absorptive processes; and exotic nuclei reactions require shortand long-range Coulomb and nuclear ae-mail: [email protected] (corresponding author) 0123456789().: V,-vol 123 367 Page 2 of 12 Eur. Phys. J. Plus (2025) 140:367 Fig. 1 MARS electronic system based on CAEN SpA desktop and VME modules potentials, to account for extreme absorption processes, which extend to longer distances, far away from the nuclear short-range interaction [15–17]. In this context, we propose to investigate further the 6Li nuclear reactions. We concentrate on the production of 4He, derived from the dissociation of 6Li into 4He and 2H, through breakup or transfer of 2H (capture - incomplete fusion) to the 12C, lighter target, that forms 14N, in the ground and excited states. This investigation is proposed as a function of the bombarding energy and the detection angle. It completes and improves previous data [11,18]. The MARS spectrometer benefits from the state-of-the-art in radiation detection, digital signal processing, and data acquisition. Today, this state-of-the-art links two main features: (i) the increasing use of digital techniques in processing pulses from detectors and (ii) the increasing trend of digitizing pulses closer to radiation detectors [19,20]. Among the 3 major data acquisition standards used in nuclear and particle Physics, VME (VERSA module eurocard) [19] bus modules communicate through digital signals bussed over the backplane, and data transfer occurs by direct memory access. Within VME, the parameters are set through the software, allowing for automated control. The GUI (Graphical user interface) is located on an embedded computer within a VME bus module. Overcoming the limits of traditional analog acquisition chains, new waveform digitizers have been developed [21–25]. They consist of models that differ in sampling frequency, resolution, number of channels, form factor, and memory size. Further developments include DPP (Digital pulse processing) algorithms [26–29], installed in an FPGA (Field programmable gate array), allowing online analysis and new acquisition methods that go beyond the simple waveform record. Thus, a DPP-equipped digitizer provides a fully digital replacement for most traditional modules. Digitizers are available in VME and desktop form factors and represent the latest in pulse processing and data acquisition systems. MARS integrates detection, electronic, and data acquisition in a very compact system. The electronic sub-system combines desktop (preamplifiers) and VME (digitizer, among other modules) form factors. MARS consists of 16 channels spectrometer for studying charged particles outgoing nuclear reactions. In Sect. 2, we present MARS as a spectrometer. In Sect. 3, we present MARS characterization: (i) on a laboratory bench with emulated electronic pulses; (ii) coupled to a reaction chamber and a silicon detector irradiated by a radioactive triple alpha source; and (iii) coupled to a reaction chamber, placed in one of the experimental beam lines at the CNA [30], to measure 6Li+12C nuclear reactions. In Sect. 4, we present the first results of the application of MARS to the 6Li+12C measurements. Finally, in Sect. 5,we draw our main conclusions. 2 MARS description MARS (Modular apparatus for nuclear reactions spectroscopy) is a compact and portable spectrometer that can measure the angular and energy distributions of charged particles emerging from nuclear reactions. Its design allows different types of digitizer, firmware, and then acquisition systems to be applied. In particular, the different firmware allows for different pulse analysis techniques. MARS detection system is composed of 16 totally depleted silicon (Si) SBD (surface barrier detectors) from ORTEC with active areas of 50 mm2. Eight of them have 15 µm thickness (model ED-35-050-15) (commercial value), which are named by their serial number (899–906). The other eight have 500 µm thickness (Model TB-15-050-500) and are also named according to their serial 123 Eur. Phys. J. Plus (2025) 140:367 Page 3 of 12 367 Fig. 2 SetupusedforMARS characterization using the DT4800 emulator number (52–59). Thus, MARS allows one to coupling 8 Si telescopes. These detectors, in single or telescope configurations, are suitable for charged-particle identification and their respective high-resolution spectroscopy. The manufacturer specifies resolutions, respectively, of 35 keV (15 µm) and 15 keV (500 µm), for 241Am alphas (5.486 MeV (85% of intensity)) [31,32]. The efficiency of Si SBD detectors, for mediumto high-energy particles, is commonly assumed to be at unity ([33] and references therein). A simple Monte Carlo simulation performed with SRIM [34], considering the 241Am alpha particles, with 5.486 MeV, at incident angle of 0◦, shows that less than 0.01% are backscattered. Figure 1shows MARS electronic system. It combines desktop and VME modules from the CAEN SpA company. It consists of two charge sensitive A1422 preamplifiers [35], one DT5423 power distributor [36], three V6519P HV power supply modules [37], one V1725S digitizer [38] and one V1718 bridge [39]. The V6519P, V1725S and V1718 modules are connected in an 8 slot VME crate VME8008B [40]. The V1725S digitizer runs the DPP - PSD (Pulse shape discrimination) or DPP - PHA (Pulse height analysis), firmware. Event selection can be performed using a LED (leading edge discriminator) or a CFD (constant fraction discriminator). The PHA firmware allows the digitizer to obtain an energy spectrum by applying a trapezoidal filter to the input pulse and is suitable for processing pulses with long decay times, such as those produced by alphas and heavy ions in semiconductor detectors [41]. The 16 channels V1725S digitizer is ideal for working with 16 silicon detectors. In particular, their association allows for coupling 8 telescopes, the respective coincidence measurements and data acquisition. Finally, a PC handles the data acquisition from the V1725S digitizer by means of CoMPASS (CAEN Multi-PArameter Spectroscopy Software) [41]. 3 MARS characterization As a proof-of-concept, prior to its first application, MARS has been tested in a laboratory environment. Figure 2schematizes the first setup used to characterize the MARS electronic system. The test pulses were generated by the 419 ORTEC precision pulse generator [42] or the digital detector emulator DT4800 [43]. The DT4800 (Fig. 2) can generate random pulses that emulate radiation sources (for example, a triple alpha source) and detector signals, with the respective energy and time distributions. According to Fig. 2, MARS system is divided into 8 individual electronic chains (1–8) related to each 8 channels A1422 (13323 and 13324) preamplifier and 16 data acquisition (DAQ) chains (0–15) related to the V1725S digitizer. The pulse height and time response of the two preamplifiers have been characterized using the pulse generator. For a precise calibration proposal, individual amplification factors (F) have been determined for each A1422 channel. For comparison, the mean values of F1.075 (34) and 1.084 (39) were obtained, respectively, for the modules A1422-13323 and 13324. For both A1422 modules, the rise time is tout r≈13 ns (for input pulses with fast rise times tin r<15 ns), which is in agreement with the data sheet value (tout r<25 ns). For long input pulses (tin d>1.5 ms), the output decay time remains constant at tout d≈46 µs, which can be compared to the data sheet value (tout d50 µs). The maximum pulse height digitized by MARS is 1.7(1) V. The uncertainty takes into account differences related, for example, to the A1422 amplification factors (F). These voltage values correspond to energies of 19(1) MeV, according to the sensitivity of 90 mV/MeV of A1422, given by the data sheet [35]. Using DT4800 (Fig. 2), we determined the relation between the input pulse height and the spectrum channel. With emulated spectra, processed by each of 16 electronic / acquisition chains, we were able to guarantee the MARS linearity. It was further verified with a triple alpha radioactive source (Sect. 3.1) and during the nuclear reaction experiment (chapter 4). We estimated the dead time of the system by transmitting constant pulses at different frequencies. CoMPASS calculates the dead time percentage using equation (1): 1−O+U+S I(1) where Ois the number of output events, Uis the number of user-discarded events, Sis the number of saturation events, and Iis the number of input events. We observed that increasing the input frequency from 102to 103Hz increases the dead time from 0.2% 123 367 Page 4 of 12 Eur. Phys. J. Plus (2025) 140:367 Fig. 3 MARS (left) coupled to a vacuum chamber (in the middle) with a triple alpha source, in front of a Si detector (right), to study the spectral response of the system Table 1 The energies and intensities of the main radioactive triple alpha source emissions Isotope Energy (MeV) Intensity (%) 233U 4.729 1.6 4.783 13.2 4.824 84.3 239Pu 5.106 11.9 5.144 17.1 5.157 70.8 241Am 5.388 1.7 5.442 13.1 5.486 84.8 The most instense emissions are identified in bold to 1.1%, and increasing the frequency from 103to 104Hz increases the dead time from 1.2% to 11.6%. Thus, for nuclear reaction measurements, this property must be under control for optimizing the counting rate. The DT4800 (in Fig. 2) has also been applied to verify the resolution for different emulated pulse heights. With the DT4800, we emulated a spectrum of a triple alpha source composed of 239Pu (5.15 MeV), 241Am (5.48 MeV) and 244Cm (5.80 MeV). The resolution values obtained vary from R0.12% to R0.14%. It allows for resolving typical triple alpha peaks, between 4 and 6 MeV, of which the main peaks are separated by ∼300 keV. This characterization process was carried out considering the maximum number of V1725S digitizer acquisition channels (214 16384 channels). It should be mentioned that most of the values presented here go beyond data sheets, being crucial for a precise calibration, counting rate optimization and/or particle identification proposals. 3.1 Triple alpha source measurements 3.1.1 Laboratory equipment and setup To validate MARS in a relevant controlled environment, we used the vacuum chamber located in the Applied Laboratory On Heavy-ions Analysis (ALOHA), at the Department of Atomic, Molecular and Nuclear Physics of the University of Seville (Fig. 3). 3.1.2 Resolution of 500 µmSiSBD Next tests aim to determine the resolution of the thicker (500 µm) detectors. For this, we used a real triple alpha source composed of 233U, 239Pu, and 241Am. The energies and intensities of the main alpha emissions are presented in Table 1. Figure 4shows a typical triple alpha (233U, 239Pu, and 241Am) spectrum. With spectra obtained for all individual detectors, we verified the linearity of MARS and studied the detector resolution. As expected, the main (triple) alpha peaks, between 4 and 6 MeV, 123 Eur. Phys. J. Plus (2025) 140:367 Page 5 of 12 367 Fig. 4 Typical triple alpha source spectrum, related to Table 1, measured with MARS separated by ∼300 keV, are very well resolved. In Fig. 4, the peaks are slightly asymmetric (to the left) due to other decay modes (see Table 1) with lower yields and lower energies (from 10 to 100 keV), with respect to the main peaks. In Fig. 4, the full width at half maximum (FWHM) of the three main peaks are, respectively, 32, 39 and 36 keV and the resolutions R(%) are 0.67%, 0.74% and 0.60%. For the sake of comparison, the PHA parameters were kept constant for all chains. Thus, we achieved resolutions ranging from 0.7% to 2.2%. By individually fine-tuning the PHA parameters, we were able to improve the resolutions below 2.0%, getting, on average, much closer to 1.0%. It is the case of the triple alpha source results presented above and illustrated by Fig. 4.These adjustments tend to decrease fluctuations between detectors and the different electronic/acquisition chains. The resolution pattern validates MARS for applications in nuclear reactions. 3.1.3 Experimental thickness of 15 µmSiSBD The15µmthick(commercialvalue)ofSiSBDrepresentsthetechnologicallimitintermsof thickness. This limit implies accentuated thickness variations and therefore uncertainties that must be quantified. The detector thickness determination is mandatory to allow telescope (E+E) configuration, coincidence measurements, as well as the consequent spectroscopy and identification of charged particles. The linear stopping power Sfor charged particles in silicon is defined as the particle differential energy loss within Si divided by the differential path length: S−dE dx(2) The total energy deposited (E) at the path length can be expressed by: Et 0 dE dxdx(3) where trepresents the Si thickness. The Bethe formula classically describes the specific energy loss as a function of the fragment charge: −dE dx4πe4z2 m0v2NB (4) where BZln 2m0v2 I−ln1−v2 c2−v2 c2(5) being vthe velocity of the incoming particle, ze its charge, Nrepresents the number density, Zis the atomic number of Si (in this case), m0is the electron rest mass, eis the electronic charge, Iis the average excitation and ionization potential of the Si and cis the velocity of light in the vacuum. For non-relativistic (v<<c) charged particles, only the first term of B is significant [20]. According to the Bethe formula and the telescope configuration, different charged particles lose different amounts of energy passing through the forward thinner detector. A typical spectrum (Eversus Etotal, with Etotal=E+E) allows for charge separation and identification. In addition, the detector thickness will determine which particles stop in the first (forward) detector and which do not (passing through and leaving the remaining energy in the second (backward) detector). Thus, thickness determination is a key step in the characterization of the detection system. 123 367 Page 6 of 12 Eur. Phys. J. Plus (2025) 140:367 Fig. 5 Typical triple alpha spectra obtained with single and telescope configurations Table 2 Nominal (from detectors data sheet) and measured thicknesses of the thin 15 µm (commercial value) detectors Detector Nominal thickness (µm) Measured thickness (µm) 899 8.0 9.4(4) 900 8.0 11.5(1) 901 14.8 14.2(1) 902 14.6 14.4(3) 903 14.0 13.7(2) 904 14.7 14.5(3) 905 10.4 9.6(2) 906 10.4 10.0(1) Using the same radioactive triple alpha source (233U, 239Pu, and 241Am), we determined experimentally the thicknesses of the Si detectors by measuring the energy deposition (E) of the alpha particles in a telescope. The results are presented in Table 2and compared to the respective nominal thickness value obtained from each detector data sheet. As a procedure, we first acquired a spectrum using a single thick (500 µm) Si detector (see Fig. 5a on the right/red solid line). Then, we acquired coincidence (logic AND) spectra (Fig. 5a) on the left/dashed blue line and Fig. 5b) from a (E+E) telescope. For completeness and to demonstrate the capability of the system, Fig. 5b shows the 2D spectrum. Figure 5a shows how the alpha peaks are shifted to the left when placing the thin Si detector in front of the thick one. In this case, the shift (E) is, respectively, 1.88, 1.79, and 1.72 MeV. As expected, according to the Bethe formula, the lower the incident energy, the higher the energy loss. Measurements were performed with a collimator with 2 mm diameter placed between the source and the detector/telescope. The stopping power (S) for alpha particles, in silicon, was obtained from SRIM (Stopping and range of ions in matter) [34]. According to equation (3), to obtain the experimental thicknesses (t), the stopping power (S) is integrated in steps dx, until the measured Eis reached. The sum of the steps provides the final value of t. In Table 2, the nominal thickness (data sheet of each individual detector) ranges from 8.0 to 14.8 µm. According to the manufacturer, the sensitive depth (minimum) can vary from 7 to 15 µm. In Table 2, each nominal (absolute) thickness value can be compared with the experimental value (within its uncertainty). The mean nominal (absolute) value is t(11.9±3.0) µm, assuming the standard deviation (1σ). It implies a relative error of 25%. The measured thickness ranges from 9.4 to 14.5 µm. The respective mean value is t(12.2±2.3) µm, assuming the standard deviation (1σ). It implies a relative error of 19%. These nominal and measured mean thicknesses differ, respectively, 21% and 19% from the commercial value (15.0 µm). 123 Eur. Phys. J. Plus (2025) 140:367 Page 7 of 12 367 Fig. 6 MARS coupled to the 3 MV tandem accelerator, at the CNA, in Seville (Spain) Fig. 7 p-EBS spectrum of protons beam on C target, at 2.50 MeV and 165.0◦ 3.2 Beam test: nuclear reaction setup In order to validate MARS in an operational environment, a nuclear reaction experiment was proposed. The main goal was to measure the 6Li+12C collision at the 3 MV tandem accelerator of the CNA (National Accelerators Center), in Seville, Spain (Fig. 6). For the current study, we are most interested in the reactions that lead to the dissociation of 6Li into its cluster components, 4He+2H. For instance, the pure breakup of 6Li resulting on 12C+4He+2H with a Qvalue −1473.7 keV; deuteron transfer (capture) resulting on 14N+4He, with a Qvalue 8798.58 keV, and the 4He transfer (capture) resulting on 16O+2H, with a Qvalue 5688.18 keV, as a competitive reaction channel. The experiment was carried out in the reaction chamber of the BNP (Basic Nuclear Physics) line, located at the end of the +30◦ exit of the accelerator. The carbon (C) target was characterized in the same facility by p-EBS (proton Elastic Backscattering Spectroscopy), using a 2.5 MeV proton beam and a PIPS (Passivated Implanted Planar Silicon) detector set at 165.0◦. Figure 7shows the spectrum due to 3 different target components: C (12C, 13C) and O (16O). This spectrum, simulated by SIMNRA [44] (using the natural isotopic abundance), results in the mass density of each isotope: 115(2) µg/cm2for carbon (C) and 1.5(1) µg/cm2for oxygen (O). Finally, for normalization purposes, a thin layer (∼14 µg/cm2)of197Au was evaporated on the target. Figure 8shows the experimental setup inside the reaction chamber. A double-collimator system is installed in the entrance of the reaction chamber, on the same detectors base, just in front of the target. Thus, the beam is aligned and collimated, which guarantees the impact of the beam on the center of the target. Before colliding the 6Li beam with the 12C target, it was previously projected on a scintillator material (see Fig. 8, on the left). Thus, the beam was centered on the target and its current was optimized. Figure 8(in the middle) shows the target holder with the above-mentioned scintillator and the 12C target. The target is surrounded by Si detectors (Fig. 8, on the right). A similar double-collimator system is installed in front of each silicon detector/telescope. To normalize the response of the detection system, elastic scattering of the 6Li on the 197Au (evaporated on the 12C target) was measured. In the 123 367 Page 8 of 12 Eur. Phys. J. Plus (2025) 140:367 Fig. 8 Target holder and detection system placed into the vacuum reaction chamber energy range, Rutherford behavior, 1/sin4(θc.m./2), is expected for the entire angular range. Thus, the geometry of the setup can be fully checked, and the solid angles are calculated for each detector based on their distances to the target and laboratory angles. 4Resultson6Li+12C nuclear reactions The first measurement was carried out with an incident beam energy of Elab 6.00 MeV, which is above the Coulomb barrier (Vlab B∼4.5 MeV), for 6Li+12C system. For this, we used 6Li2+ beam accelerated by a terminal voltage of VT2.0 MV. The detectors were mounted in single and telescope configurations. Following dead time constraints, the intensity (current) of the incoming beam was around 20 nA, with a maximum counting rate of the order of 1 kHz in the detectors, which implies in ∼1.5% dead time. Figure 9shows 6Li+12C nuclear reaction spectra, measured at 6.00 MeV and 35.0◦. This angle was chosen for statistical reasons. Figure 9a shows a one-dimensional (1D) spectrum of the 6Li+12C reaction. Here, several nuclear reaction peaks can be identified. Most of the identified peaks are related to the 12C(6Li,4He)14N∗reaction, from which alpha particles (4He) are detected and completely stopped by the single thicker Si detectors. One of the peaks identified in the 1D spectrum is produced by the elastic scattering of 6Li on 16O (a target contaminant, determined by p-EBS analysis). Another wide peak, centered at ≈3.1 MeV, is produced by the recoil of 12Cand16O from the target. In Fig. 7, we observe the 16O contaminant that, in addition to the 12C (main target component) and according to the simulations of SIMNRA [44] should (both) contribute to such a wide peak. Figure 9b shows a two-dimensional (2D) spectrum (E+E)ofthe6Li+12C reaction, measured at 6.00 MeV and 35.0◦. Here, different spots (areas) can be identified. Most of the identified spots are (energy) correlated with alpha particles coming from the 12C(6Li,4He)14N∗reaction. Figure 9c shows one-dimensional (1D) spectrum of 6Li+12C reaction, measured at 6.00 MeV and 35.0◦(the same as in Fig. 9a). In addition, superimposed on it, we present the projection of alpha particles, observed in Fig. 9b, on the total energy (E+E)axis. Thus, we were able to energetically correlate the spots (areas) of Fig. 9b with identified peaks of Fig. 9a. It is worth mentioning that higher energy alphas are not visible in the 2D spectrum because they deposit a negligible amount of energy in E, which is below the threshold. Therefore, with MARS, in single or telescope configuration, we can discriminate several peaks related to the 12C(6Li,4He)14N nuclear reaction. As an example, in the single (1D) spectrum of Fig. 9, the resolution obtained from the peak related to the 12C(6Li,4He)14Ng.s. (alpha particles correlated with the 14N ground state as output reaction channel) is 2.1%. Further measurements have been carried out, which allow obtaining excitation functions for 6Li+12C nuclear reactions. The complete set of measurements consists of 13 bombarding energies: 4.00, 4.50, 5.00, 5.50, 5.75, 6.00, 6.25, 6.50, 6.75, 7.00, 7.25, 7.50, 7.75 MeV; with detectors mounted at 8 angles: 35.0, 40.0, 65.0, 70.0, 110.0, 115.0, 140.0, and 145.0◦. Due to collimation and the respective solid angles, two consecutive angles are compatible within the angular precision (θ±2.5◦). The nuclear effects are supposed to be pronounced at the rear angles. Figure 10 shows a 1D spectrum related to 6Li+12C reactions, measured at 6.00 MeV, with the detector at 110.0◦. A quite similar resolution pattern is observed when comparing the single spectra obtained at the forward angle (35.0◦) and at the backward angle (110.0◦). In both cases, the 12C(6Li,4He)14Ng.s.peak is very well resolved, without background. Due to this resolution pattern and to detect high-energy alpha particles, measurements were carried out with the 8 thicker (500 µm) Si detectors, in a single configuration. Thus, we investigate the 12C(6Li,4He)14Ng.s.reaction and its respective cross section, as a function of the bombarding energy. Data were taken with the aim of reducing the statistical uncertainties below 123 Eur. Phys. J. Plus (2025) 140:367 Page 9 of 12 367 Fig. 9 1D and 2D spectra for the 6Li+12C reaction measured at 6.00 MeV and 35.0◦ 5%. Thus, the number of counts (N) related to the 12C(6Li,4He)14Ng.s.peak, for all angles and energies, is mainly greater than 500 counts (see, for example, Figs. 9and 10). The statistical error is then calculated as a function of 1/√N, resulting in the error bars presented in Fig. 11. There is also an angular uncertainty related to the detectors’ position. However, it decreases with the angle of scattering (according to the Rutherford scattering dependence with 1/sin4(θc.m./2)), and it is negligible compared to the statistical uncertainty at the backward angles. Figure 11 shows two excitation functions obtained at two angles (110.0◦and 140.0◦). For both excitation functions, we observe a continuous increase in the 12C(6Li,4He)14Ng.s.reaction cross section, from the bombarding energies around the Coulomb barrier (Vlab B∼4.5 MeV). A pronounced increase in the reaction cross sections is observed, from ∼6.00 MeV (vertical dashed line) to a peak at ∼6.75 MeV. In fact, a variation of one order of magnitude is observed from below the Coulomb barrier (Vlab B∼4.5 MeV) to Eop b∼6.75 MeV. This effect is better observed at 110.0◦,where12C(6Li,4He)14Ng.s.is resolved for the complete set of energies. The optimal energy (Eop b), of 6Li dissociation, is in good agreement with our prediction Eop b≥VB+|Qbu|,where,VBis the Coulomb barrier of the system (Vlab B∼4.5 MeV); and |Qbu|is the module of the Q-value for the dissociation of 6Li into its 123