New measurement of 12 C+ 12 C fusion reaction at astrophysical energies
W. P. Tan, A. Boeltzig, C. Dulal, R. J. deBoer, B. Frentz, S. Henderson, K. B. Howard, R. Kelmar, J. J. Kolata, J. Long, K. T. Macon, S. Moylan, G. F. Peaslee, M. Renaud, C. Seymour, G. Seymour, B. Vande Kolk, M. Wiescher, E. F. Aguilera, P. Amador-Valenzuela, D. Lizcano, E. Martinez-Quiroz
NNew measurement of C+ C fusion reaction at astrophysicalenergies
W. P. Tan, ∗ A. Boeltzig, C. Dulal, R. J. deBoer, B. Frentz, S. Henderson, K.B. Howard, R. Kelmar, J. J. Kolata, J. Long, K. T. Macon, S. Moylan, G. F.Peaslee, M. Renaud, C. Seymour, G. Seymour, B. Vande Kolk, and M. Wiescher
Department of Physics and Institute for Structure and Nuclear Astrophysics (ISNAP),University of Notre Dame, Notre Dame, Indiana 46556, USA
E. F. Aguilera, P. Amador-Valenzuela, D. Lizcano, and E. Martinez-Quiroz
Departamento de Aceleradores, Instituto Nacional de Investigaciones Nucleares,Apartado Postal 18-1027, Codigo Postal 11801, Mexico, D.F., Mexico (Dated: May 8, 2020)
Abstract
Carbon and oxygen burning reactions, in particular, C+ C fusion, are important for the un-derstanding and interpretation of the late phases of stellar evolution as well as the ignition andnucleosynthesis in cataclysmic binary systems such as type Ia supernovae and x-ray superbursts.A new measurement of this reaction has been performed at the University of Notre Dame usingparticle- γ coincidence techniques with SAND (a silicon detector array) at the high-intensity 5UPelletron accelerator. New results for C+ C fusion at low energies relevant to nuclear astro-physics are reported. They show strong disagreement with a recent measurement using the indirectTrojan Horse method. The impact on the carbon burning process under astrophysical scenarioswill be discussed. a r X i v : . [ nu c l - e x ] M a y NTRODUCTION
The main nucleosynthesis products of stellar helium burning are the C and O isotopes.For massive enough stars, the subsequent phases of stellar evolution are dictated by fusionreactions such as C+ C and C+ O [1–3]. The cross sections of both fusion reactionsare characterized by significant uncertainties associated with the possible emergence of lowenergy resonances but also a significant suppression due to the so-called hindrance effectwhich is suggested to reduce the cross section due to the incompressibility of nuclear matterin the collision event [4]. A dramatic increase in the fusion rate of C+ C as suggestedrecently [5] may significantly change the abundance distribution in oxygen-neon white dwarfsand in the burning patterns of massive stars in their evolution to core collapse supernovae[3].Type Ia supernovae (SN) are interpreted as the consequence of explosive carbon burningignited near the core of the white dwarf star in a binary system [6]. The C+ C fusionprocess is supposed to be the dominant energy source for pre-ignition processes such ascarbon simmering and the ignition itself [7]. However the C+ O reaction may also play asignificant role depending on the associated fusion rates [8] and the environmental conditionssuch as O abundance, temperature, and density [4, 7]. Recent studies showed indeed thatthe C+ O rate is expected to have an unusually large effect on the calcium and sulfuryields in SN Ia, e.g., the higher C+ O rate suppresses the alpha-particle abundance, whichin turn decreases the Ca/S ratio [7].X-ray superbursts, another phenomenon involving binary compact star systems, arethought to be ignited by the carbon fusion reactions in the burning ashes of accumulatedhydrogen and helium on the surface of accreting neutron stars [9, 10]. For such an igni-tion condition of unstable burning, the mass fraction of C has to be at least above 10%in the ocean of heavy ashes accumulated from previous rp-process burning of X-ray bursts[11]. However, X-ray burst models could not produce a high enough carbon abundance withknown nuclear physics [12, 13]. The uncertainty of the rate of the X-ray burst trigger reac-tion O( α, γ ) [14] may reduce the tension a little but certainly not enough [15]. To makesuperburst models work, a hypothetical resonance at 1.5 MeV of the center of mass fusionenergy of C+ C was suggested [16].In the following sections, we will discuss first the status of the C+ C fusion cross section2ata followed by a presentation of the new experimental data obtained at the University ofNotre Dame in comparison with previous results.
CURRENT STATUS OF C+ C Extensive efforts, both experimentally and theoretically, have been invested in the deter-mination of the C+ C reaction rate for all associated reaction channels. Despite theseefforts, large uncertainties remain in the reaction rate especially when extrapolating the datainto the astrophysically important energy range (the Gamow window) [3]. The predictedrates depend sensitively on adopted model parameters, hindrance effects, and the possibilityof cluster, dynamic or molecular resonances at relevant energies [4, 17–19].Extending and improving the quality of experimental data towards lower energies istherefore crucial for reducing the uncertainties, giving more robust extrapolation towardslower energies, and ultimately providing more reliable reaction rates for the study of carbonburning in stars and other stellar environments.Astrophysically, the most important energy range for the carbon fusion cross sectionis about 1 − C( C,p) Na ( Q = 2 .
241 MeV), C( C, α ) Ne ( Q = 4 . C( C,n) Mg ( Q = − .
598 MeV) reactions can populate the ground state orexcited states in the respective residual nuclei that subsequently decay by gamma emissionto the ground state.Earlier direct measurement of the n-emission channel near astrophysically relevant ener-gies conducted at Notre Dame demonstrated that this channel contributes less than 5% tothe total reaction rate [20], similar to the case of the Si+n channel in the C+ O fusionreaction [8].Most of the early experimental efforts following the observation of resonances in carbonfusion cross sections by the Chalk River experiment [21] are direct singles measurementswith detection of either charged particles [22–25] or gamma radiation [26–32], which areshown in Fig. 1. Such an approach may suffer background issues at low energies dueto the rapidly declining cross section. For this reason coincidence techniques between theparticle and subsequent γ transitions have been applied for better identification of the specific3ecay patterns of the Mg compound system. The most important channels for coincidencemeasurements are the p transition (emission of protons to the first excited state in Nafollowed by the 440 keV γ transition to the ground state) as well as the α transition(emission of alpha particles to the first excited state in Ne with its subsequent groundstate decay via the 1634 keV γ transition).An early test experiment using the particle- γ coincidence technique for the C+ Creaction was conducted at Argonne National Laboratory [33]. Similar techniques were thenused to measure the cross sections at a few points with energies below E cm ≤
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV] Becker198110
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV] Aguilera200610
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV] High197710
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV] Patterson196910
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV]Barrón-Palos200610
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV]10
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV]Spillane200710
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV]10
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV] STELLA201910
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV]10
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV]Jiang201810
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV]Mazarakis197310
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV]This work10
2 2.5 3 3.5 4 4.5 5 5.5 S * ( E ) [ M e V ba r n ] E cm [MeV] FIG. 1. The total S ∗ ( E ) factor for this work is shown and compared with previous directmeasurement data [22–24, 26, 27, 29, 32, 34, 36]. See the electronic version for better presentationof the details. A more recent measurement using the indirect Trojan Horse method (THM) provided anadditional set of data for the low energy range of the C+ C fusion process [5]. It extracteda number of resonances between E cm = 0 . − . C+ C reaction crosssections based on the particle- γ coincidence technique and a target approach that allows usto determine the yield from thin target layers through a differential thick target analysisthat can potentially address some of the uncertainties present in previous experiments. EXPERIMENTAL SETUP
In this work both charged particles (i.e., protons and alphas) and γ -rays emitted fromthe C+ C fusion process were measured simultaneously. A beam of C and C ions(up to about 13 particle µ A) with E cm = 2 . − µ A) heavy ion beams, up to Ar. The targetwas a highly ordered pyrolytic graphite (HOPG) [39], which has a layered structure ofmultiple thin graphene sheets [40]. The advantage of using HOPG as target material is itssuperior purity compared to natural graphite. Impurity of hydrogen and deuterium in thetarget can cause background in charged particle spectra [41, 42] while impurity of Na canseverely affect the gamma spectra as discussed later. The HOPG target with a dimensionof 2 cm × × ◦ to 146 ◦ and 151 ◦ to 170 ◦ in the laboratory frame. Eachwedge-shaped YY1 is segmented into 16 strips on the front junction side with six YY1detectors forming a “lampshade” configuration. The CD-shaped S2 detector is double-sidedand has 48 rings on the front junction side and 16 segments on the back ohmic side. Thesolid angle covered by the detectors is 4.1% of 4 π for each YY1, and 5.4% of 4 π for the S2, asdetermined from measured and design dimensions in addition to an alpha source calibration.For the measurement of the γ rays, a HPGe detector with relative efficiency of 109% (relativeto that of 3” ×
3” NaI at 1.33 MeV) was placed in a 10-cm thick lead castle and positionedright behind the target to maximize the detection efficiency of γ rays. Radioactive sourcesof Be, Co, Co, Ga,
Ba,
Cs, and
Eu were used to calibration the HPGe detectorfor an energy range of 0 . − . γ peak efficiency was determinedto be 2.30% at 440 keV and 1.22% at 1634 keV with an uncertainty of about 5%. Thedata were collected by the VMUSB data acquisition system implemented at NSL, where 160channels of signals from the silicon detector array were processed via an ASIC (ApplicationSpecific Integrated Circuit) readout system. The core component of the system is HINP16C,a 16-channel ASIC specifically developed for readout of silicon strip detectors used in low-and intermediate-energy heavy-ion reaction experiments [44]. The HPGe detector was readout by a 13-bit high resolution ADC (MADC-32) from Mesytec [45]. More details of thesetup can be seen in the earlier study on the C+ O reaction [8].
DATA ANALYSIS AND RESULTS
Cross sections for various exit channels in the C+ C fusion reaction were obtainedfrom the thick-target yields for γ transitions associated with the different decay channels andprotons/alpha-particles in coincidence. The same analysis procedure for all beam energiesis presented as follows.The thick-target reaction yield is obtained from the number of events detected per incidentcarbon nucleus on the target for a given reaction channel. It includes the production yieldfor reactions not only at the incident beam energy, but also in the energy range below dueto the energy loss of beam particles in the thick HOPG target. The cross section at theincident energy can then be obtained from the derivative dY /dE of the thick-target yieldsmeasured in multiple small energy steps of 50 keV in the center of mass [46]. This makes our6ffective target thickness ∼
50 keV in contrast to a few hundred keV of typical “thin” targetexperiments. The value of dY /dE at a given energy was determined by fitting the yield atthis energy together with the yields detected for the two neighboring energy steps using asecond-order polynomial of logY vs. E [46]. Whereas this treatment is not possible at theedge of an energy range, a linear fit from one side is applied and results in larger uncertaintiesfor dY /dE . The partial cross sections are derived from the extracted differential yield dY /dE for each of the observed particle groups using the thin target equation, σ ( E ) = 1 ε M T f N A dEd ( ρX ) dYdE (1)where ε is the detection efficiency of measured γ rays and charged particles in coincidence, f is the molecular fraction of target nucleus, N A is the Avogadro constant, M T is the molecularweight of the target, and dE/d ( ρX ) is the stopping power calculated with SRIM [47].Coincidence data between charged particles and γ -rays are shown in Fig. 2 for a typicalrun at E beam =8.9 MeV where E (Ge) is the energy of γ -rays detected in HPGe and E ∗ ( p ) isthe excitation energy of the residual nucleus calculated from the particle energy in SANDafter kinematic corrections for the proton channel. The gated p (left) and α (right) channelprojections and corresponding Doppler effects are also shown in the middle panels for thesame energy and in the top panels for E cm =2.2 MeV of Fig. 2, respectively.After applying the differential thick target method as presented in Eq. 1, we can obtainthe p cross section. For better comparison and presentation, it is customary to calculatethe so-called S ( E ) factor that removes removes the strong energy dependence caused by theCoulomb barrier. In particular, a special S ∗ ( E ) factor for C+ C commonly used in theliterature [48] is defined as follows, S ∗ ( E ) = σ ( E ) · E · exp(87 . / √ E + 0 . E ) (2)where E is the center-of-mass energy in unit of MeV. Fig. 3 shows the p channel S ∗ ( E )factor for this work in comparison with previous work [5, 23, 34]. Other data that do notprovide separate information on the p channel are not shown. The error bars of our datashown in Fig. 3 are statistical. The additional systematic errors are about 5% from thestopping powers and up to about 10% from efficiency calibration and summing effects. Weassume isotropic distributions in our measurement which can incur uncertainties of about7
500 1000 1500 2000 2500 3000 3500 4000 4500
E (Ge) [keV] E * ( p ) [ k e V ]
350 400 450 500 550 C oun t / k e V C oun t / k e V
350 400 450 500 550
E (Ge) [keV]0.51 C oun t / k e V E (Ge) [keV] 0.51 C oun t / k e V FIG. 2. A coincidence spectrum (bottom) for a typical run at E beam =8.9 MeV between chargedparticles and gamma-rays is shown. The middle panels show the projections to the γ energiesand the Doppler effects for the p (left) and α (right) channels, respectively, where the bump justoutside the α shaded region is contributed from the p channel. The top panels present the similarprojections for the lowest energy at E beam =4.4 MeV.
10% for p and 30% for α based on previous measurements of angular distributions [23].However, extreme cases and effects of possible correlations could significantly increase theuncertainties (e.g., about 20% for p and 60% for α assuming an angular distribution of ∝ cos ( θ )).The THM data (solid line) [5] show about an order of magnitude higher values comparedto our low energy data as can be seen in Fig. 3. The trend towards lower energies seems toincrease, which could be related to the mistreatment of Coulomb interactions as suggestedby Ref. [38]. In particular, the THM-predicted resonance at E cm = 2 . > < .
2 2.5 3 3.5 4 4.5 5 p channel S * ( E ) [ M e V ba r n ] E cm [MeV] Becker198110
2 2.5 3 3.5 4 4.5 5 p channel S * ( E ) [ M e V ba r n ] E cm [MeV] Jiang201810
2 2.5 3 3.5 4 4.5 5 p channel S * ( E ) [ M e V ba r n ] E cm [MeV] Tumino201810
2 2.5 3 3.5 4 4.5 5 p channel S * ( E ) [ M e V ba r n ] E cm [MeV] This work10
2 2.5 3 3.5 4 4.5 5 p channel S * ( E ) [ M e V ba r n ] E cm [MeV] FIG. 3. The p channel S ∗ ( E ) factor for this work is shown and compared with previous work[5, 23, 34]. Similarly, the α channel S ∗ ( E ) factor for this work is presented in Fig. 4 in comparisonwith previous work [5, 23, 34]. The lowest data point at E cm = 2 . p data, the α channel is more proneto background contamination even for coincidence measurements as shown in Fig. 2. As amatter of fact, the background level outside the coincidence gate is very similar to that withinthe gate suggesting that all the observed coincidence events may stem from background. Ifso, the estimate of the upper limit at the lowest energy can be much lower and may be closeto the value of the p channel. As such, our p and α data sets have shown similar S ∗ ( E )values throughout the energy range.The 1634 keV γ -ray peak from the α channel may potentially be contaminated by the1636 keV γ -rays from either the p channel or inelastic scattering of Na contaminationwithin the target or anywhere the scattered beam can reach. This can cause severe back-ground issues at low energies in measurements using the “thin” target approach. Previousdata sets for the proton and alpha-particle channels have similar S ∗ ( E ) factors at higher en-ergies ( (cid:38) (cid:46) C and α clusterresonances as suggested by the THM data or they could be simply due to the contaminationas mentioned above. For example, the previously claimed resonance at E cm = 2 .
14 MeV [26](shown in Fig. 1) has a significantly larger contribution from the alpha-particle channels.The recent coincident measurement by the STELLA collaboration [36] shows similar S ∗ ( E )9actors for both channels above E cm = 3 MeV while dramatically higher values in the α channel at energies below 3 MeV. In particular, the STELLA data provide a p upper limitat E cm = 2 . α S ∗ ( E )factor at the same energy. We do not concur with that result.On the contrary, the Na contamination effect is largely canceled out in our differentialthick target approach. In addition, the Doppler effect can shift the p gamma rays by morethan 30 keV as shown in the middle right panel of Fig. 2, which makes α and p gamma raysbetter separated in our setup. Fig. 4 shows that our α data agree fairly well with existingdata at high energies. Similar to the p case, the differences at energies just below E cm = 3MeV could stem from the uncertainties of angular distributions and / or the integrativeeffects of target thickness. Again, the data (solid line) from the indirect THM measurementare much higher than what our data show.
2 2.5 3 3.5 4 4.5 5 α channel S * ( E ) [ M e V ba r n ] E cm [MeV] Becker198110
2 2.5 3 3.5 4 4.5 5 α channel S * ( E ) [ M e V ba r n ] E cm [MeV] Jiang201810
2 2.5 3 3.5 4 4.5 5 α channel S * ( E ) [ M e V ba r n ] E cm [MeV] Tumino201810
2 2.5 3 3.5 4 4.5 5 α channel S * ( E ) [ M e V ba r n ] E cm [MeV] This work10
2 2.5 3 3.5 4 4.5 5 α channel S * ( E ) [ M e V ba r n ] E cm [MeV] FIG. 4. The α channel S ∗ ( E ) factor for this work is shown and compared with previous work[5, 23, 34]. To compare our results with more of the available data on total S ∗ ( E ) factor, we renor-malized our data using the linear fit of the p -to- p total and α -to- α total ratios from the fairlycomplete data set of Becker et al. [23], which should be less sensitive to the above-discussedadverse effects. Unfortunately, such a normalization procedure translates to an uncertaintyof up to a factor of two due to large fluctuations of the ratios in the data of Becker etal. [23]. Nevertheless, our renormalized total S ∗ ( E ) factor data (solid circles) without theadditional normalization uncertainties are shown in Fig. 1 in comparison with other avail-able data. The above discussions for the p and α channels can be applied here as well.The upper limit at the lowest energy can be lowered by more than a factor of two if we10onsider all the coincident counts observed in the α channel as background. Our low energydata are lower than most of the previous works possibly due to significant contaminationin the α channel of the previous measurements. Meanwhile, our data, consistent with thepublished thick-target yield of Zickefoose et al. [25], agree with the singles measurementfrom Zickefoose’s unpublished thesis work using the thick target approach [49], which wasunfortunately hindered by much larger uncertainty and therefore not shown in Fig. 1. CONCLUSIONS
New measurements of the C+ C fusion reaction were conducted at Notre Dame usingparticle- γ coincidence and differential thick target techniques which help to minimize pos-sible contamination effects at low energies and reduce the uncertainty of target thicknessintegration due to the large energy loss associated with the large stopping power of lowenergy carbon beams. The new data provide a more reliable cross section and S ∗ ( E ∗ [email protected]
1] F. Hoyle, Astrophys. J. Suppl. Ser. , 121 (1954).[2] M. Wiescher, F. K¨appeler, and K. Langanke, Annu. Rev. Astron. Astrophys. , 165 (2012).[3] M. Pignatari, R. Hirschi, M. Wiescher, R. Gallino, M. Bennett, M. Beard, C. Fryer, F. Herwig,G. Rockefeller, and F. X. Timmes, Astrophys. J. , 31 (2013).[4] L. R. Gasques, E. F. Brown, A. Chieffi, C. L. Jiang, M. Limongi, C. Rolfs, M. Wiescher, andD. G. Yakovlev, Phys. Rev. C , 035802 (2007).[5] A. Tumino, C. Spitaleri, M. L. Cognata, S. Cherubini, G. L. Guardo, M. Gulino, S. Hayakawa,I. Indelicato, L. Lamia, H. Petrascu, and others, Nature , 687 (2018).[6] W. Hillebrandt and J. C. Niemeyer, Annu. Rev. Astron. Astrophys. , 191 (2000).[7] H. Mart´ınez-Rodr´ıguez, C. Badenes, H. Yamaguchi, E. Bravo, F. X. Timmes, B. J. Miles,D. M. Townsley, A. L. Piro, H. Mori, B. Andrews, and S. Park, Astrophys. J. , 35 (2017).[8] X. Fang, W. P. Tan, M. Beard, R. J. deBoer, G. Gilardy, H. Jung, Q. Liu, S. Lyons, D. Robert-son, K. Setoodehnia, and others, Phys. Rev. C , 045804 (2017).[9] E. F. Brown and L. Bildsten, Astrophys. J. , 915 (1998).[10] E. F. Brown, Astrophys. J. Lett. , L57 (2004).[11] A. Cumming and L. Bildsten, Astrophys. J. Lett. , L127 (2001).[12] H. Schatz, L. Bildsten, A. Cumming, and M. Wiescher, Astrophys. J. , 1014 (1999).[13] R. H. Cyburt, A. M. Amthor, A. Heger, E. Johnson, L. Keek, Z. Meisel, H. Schatz, andK. Smith, Astrophys. J. , 55 (2016).[14] W. P. Tan, J. L. Fisker, J. G¨orres, M. Couder, and M. Wiescher, Phys. Rev. Lett. , 242503(2007).[15] J. L. Fisker, W. Tan, J. G¨orres, M. Wiescher, and R. L. Cooper, Astrophys. J. , 637(2007).[16] R. L. Cooper, A. W. Steiner, and E. F. Brown, Astrophys. J. , 660 (2009).[17] N. Cindro, Ann. Phys. Fr. , 289 (1988).[18] C. L. Jiang, K. E. Rehm, B. B. Back, and R. V. F. Janssens, Phys. Rev. C , 015803 (2007).[19] A. Diaz-Torres and M. Wiescher, Phys. Rev. C , 055802 (2018).[20] B. Bucher, X. D. Tang, X. Fang, A. Heger, S. Almaraz-Calderon, A. Alongi, A. D. Ayangeakaa,M. Beard, A. Best, J. Browne, and others, Phys. Rev. Lett. , 251102 (2015).[21] E. Almqvist, D. A. Bromley, and J. A. Kuehner, Phys. Rev. Lett. , 515 (1960).[22] J. R. Patterson, H. Winkler, and C. S. Zaidins, Astrophys. J. , 367 (1969).
23] H. W. Becker, K. U. Kettner, C. Rolfs, and H. P. Trautvetter, Z Physik A , 305 (1981).[24] M. G. Mazarakis and W. E. Stephens, Phys. Rev. C , 1280 (1973).[25] J. Zickefoose, A. Di Leva, F. Strieder, L. Gialanella, G. Imbriani, N. De Cesare, C. Rolfs,J. Schweitzer, T. Spillane, O. Straniero, and F. Terrasi, Phys. Rev. C , 065806 (2018).[26] T. Spillane, F. Raiola, C. Rolfs, D. Sch¨urmann, F. Strieder, S. Zeng, H.-W. Becker, C. Bor-deanu, L. Gialanella, M. Romano, and J. Schweitzer, Phys. Rev. Lett. , 122501 (2007).[27] E. F. Aguilera, P. Rosales, E. Martinez-Quiroz, G. Murillo, M. Fern´andez, H. Berdejo, D. Liz-cano, A. G´omez-Camacho, R. Policroniades, A. Varela, and others, Phys. Rev. C , 064601(2006).[28] L. J. Satkowiak, P. A. DeYoung, J. J. Kolata, and M. A. Xapsos, Phys. Rev. C , 2027(1982).[29] M. D. High and B. ˇCujec, Nuclear Physics A , 181 (1977).[30] K. U. Kettner, H. Lorenz-Wirzba, and C. Rolfs, Z Physik A , 65 (1980).[31] B. Dasmahapatra, B. ˇCujec, and F. Lahlou, Nuclear Physics A , 257 (1982).[32] L. Barr´on-Palos, E. F. Aguilera, J. Aspiazu, A. Huerta, E. Mart´ınez-Quiroz, R. Monroy,E. Moreno, G. Murillo, M. E. Ortiz, R. Policroniades, A. Varela, and E. Ch´avez, NuclearPhysics A , 318 (2006).[33] C. L. Jiang, K. E. Rehm, X. Fang, X. D. Tang, M. Alcorta, B. B. Back, B. Bucher, P. Collon,C. M. Deibel, B. DiGiovine, and others, Nuclear Instruments and Methods in Physics ResearchSection A: Accelerators, Spectrometers, Detectors and Associated Equipment , 12 (2012).[34] C. L. Jiang, D. Santiago-Gonzalez, S. Almaraz-Calderon, K. E. Rehm, B. B. Back, K. Auranen,M. L. Avila, A. D. Ayangeakaa, S. Bottoni, M. P. Carpenter, and others, Phys. Rev. C ,012801(R) (2018).[35] M. Heine, S. Courtin, G. Fruet, D. G. Jenkins, L. Morris, D. Montanari, M. Rudigier, P. Ad-sley, D. Curien, S. Della Negra, and others, Nuclear Instruments and Methods in PhysicsResearch Section A: Accelerators, Spectrometers, Detectors and Associated Equipment ,1 (2018).[36] STELLA collaboration, G. Fruet et al. , Phys. Rev. Lett. (2020).[37] W. A. Fowler, C. C. Lauritsen, and T. Lauritsen, Rev. Mod. Phys. , 236 (1948).[38] A. M. Mukhamedzhanov, D. Y. Pang, and A. S. Kadyrov, Phys. Rev. C , 064618 (2019).[39] C. Soldano, A. Mahmood, and E. Dujardin, Carbon , 2127 (2010).
40] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva,S. V. Dubonos, and A. A. Firsov, Nature , 197 (2005).[41] L. Morales-Gallegos, M. Aliotta, C. G. Bruno, R. Buompane, T. Davinson, M. D. Cesare,A. D. Leva, A. D’Onofrio, J. G. Duarte, L. R. Gasques, and others, Eur. Phys. J. A , 132(2018).[42] J. Zickefoose, J. Schweitzer, T. Spillane, F. Strieder, H.-W. Becker, C. Rolfs, A. Di Leva,M. De Cesare, N. De Cesare, F. Terrasi, L. Gialanella, D. Sch¨urmann, Y. Guan, G. Imbriani,and B. Limata, in Proceedings of 11th Symposium on Nuclei in the Cosmos — PoS(NIC XI) (Sissa Medialab, Heidelberg, Germany., 2011) p. 019.[43] “Micron semiconductor,” .[44] G. L. Engel, M. Sadasivam, M. Nethi, J. M. Elson, L. G. Sobotka, and R. J. Charity, Nucl.Instrum. Methods Phys. Res. Sect. A , 418 (2007).[45] “Mesytec,” .[46] M. Notani, H. Esbensen, X. Fang, B. Bucher, P. Davies, C. L. Jiang, L. Lamm, C. J. Lin,C. Ma, E. Martin, K. E. Rehm, W. P. Tan, S. Thomas, X. D. Tang, and E. Brown, Phys.Rev. C , 014607 (2012).[47] “Srim code,” .[48] C. A. Barnes, S. Trentalange, and S.-C. Wu, in Treatise on Heavy-Ion Science: Volume 6:Astrophysics, Chemistry, and Condensed Matter , Vol. 6, edited by D. A. Bromley (SpringerUS, Boston, MA, 1985) pp. 1–60.[49] J. Zickefoose, C+ C Fusion: Measurement and Advances Toward the Gamow Energy , Ph.Ddissertation, University of Connecticut (2011)., Ph.Ddissertation, University of Connecticut (2011).