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Study of 16O(12C,α20Ne)α for the investigation of carbon-carbon fusion reaction via the Trojan Horse Method

Carbon-carbon fusion reaction represents a nuclear process of great interest in astrophysics, since the carbon burning is connected with the third phase of massive stars (M > 8 M☉) evolution. In spite of several experimental works, carbon-carbon cross section has been measured at energy still above the Gamow window moreover data at low energy present big uncertainty. In this paper we report the results about the study of the 16O(12C,α20Ne)α reaction as a possible three-body process to investigate 12C(12C,α)20Ne at astrophysical energy via Trojan Horse Method (THM). This study represents the first step of a program of experiments aimed to measure the 12C+12C cross section at astrophysical energy using the THM.


Introduction
The 12 C+ 12 C reaction is of great interest both in nuclear physics, producing the first evidence of nuclear molecular phenomena, as well as in astrophysics. In particular in this last field Carbon burning is connected with the third phase of massive star evolution in stars with M > 8 M [1]. 12 C+ 12 C reaction rate is a fundamental parameter to determine the so-called M up , that is, the minimum mass of a star for carbon ignition. Stars with M up evolve into CO White dwarf, while stars with M > M up conclude their life as core-collapse Supernovae [2]. The core carbon burning takes place in a temperature range of T = 0.5 -1.0 GK. For a temperature of 0.5 GK, the corresponding Gamow energy for the 12 C+ 12 C fusion is E G = 1.5 ± 0.3 MeV. Accurate determination of the carbon burning reaction rate requires very precise measurement of the 12 C+ 12 C cross section down to this energy, well below the Coulomb barrier. In spite of the key role of carbon fusion reactions in understanding stellar evolution, experimental data available ( [3] and references therein) cover down to carbon-carbon center of mass energy E cm = 2 MeV, that is at the higher edge of the Gamow peak. Moreover experimental data below E cm = 3 MeV are rather uncertain [2]. Up to now people calculate the reaction rate by means of the from data at higher energy, but this procedure can lead to wrong result since the 12 C+ 12 C excitation function is characterized by resonant structures also at the low energy of astrophysical interest  [3] . In this framework new and accurate experimental data, down to the astrophysical energies, are strongly required. A possible way to measure 12 C+ 12 C excitation function down to astrophysical energies, overcoming the problems connected to the direct measurement, mainly the strong suppression of the cross section due to the Coulomb barrier, is by using indirect methods. Among of them the Trojan Horse Method (THM) [5,6,7] is a consolidated method applied successfully for the study of nuclear reaction of astrophysical interest. In this paper we report on the measurement of the 16 O( 12 C, α 20 Ne)α in quasi-free kinematic condition to study the possibility to apply the THM to this three-body reaction for the indirect study of the 12 C( 12 C, 20 Ne) α reaction, that is the alpha channel of the carbon-carbon fusion. This represent the first measurement of a experimental program devoted to the study of the carbon-carbon fusion reaction via THM.

The Trojan Horse Method
The THM is a powerful technique that allows to extract a two-body reaction cross section, A + x → c + C , down to the low energies of astrophysical interest by selecting the quasi-free break-up channel of a suitable three-body reaction A+a → c+C +s. Nucleus a is selected to have an high probability for a cluster configuration x ⊕ s. The A + a interaction induces the nucleus a breakup into x and s. Selecting the quasi-free kinematic condition it is assumed that s acts as a spectator while x interacts with the nucleus A leading to the astrophysically relevant two-body reaction. The A + a reaction is induced at energies higher than the Coulomb barrier, in this way the breakup can take place inside the nuclear field and accordingly the A + x interaction takes place without suffering the Coulomb barrier suppression and the electron screening. Moreover thanks to x ⊕ s inter-cluster motion, the THM allows to measure the two-body cross section in a wide energy using a single beam energy. THM has been widely applied to study nuclear reaction involved in several astrophysical scenario including reactions induced by unstable nuclei and by neutrons [8,9,10,11,13,14].

Experimental set-up
In the present case 16 O( 12 C, α 20 Ne)α had been selected as possible three-body reaction for the indirect study of the 12 C( 12 C, 20 Ne)α reaction via THM. For the first time 16 O has been selected as Trojan Horse nucleus for is possible 12 C ⊕ α configuration. The experiment took place at the Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH) Bucharest, Romania. The 9 MV Tandem accelerator provided a 25 MeV 16 O beam with a spot size on the target of about 2 mm and an intensity of about 8 nA. A natural carbon target, 100 µg/cm 2 thick, was used to induce the 16 O+ 12 C reaction. Energy and position of the outgoing particles were detected using six charge-partition position sensitive silicon detectors (PSD) in a symmetric configuration to double the number of collected events. PSDs 1,2,3 covered the angular rages 13 • -26 • , 41 • -55 • and 65 • -80 • respectively; PSDs 4,5,6 were placed on the other side with respect to the beam axis, covering the same angular ranges. Particle identification was carried out with ∆E-E technique. In particular two ionization chambers (IC) filled by P10 (average pressure 23 mb) placed in front of PSD1 and PSD4. The two telescopes (IC-PSD) were devoted to the neon detection and identification. The experimental set-up described above had been set to measure the 12 C( 12 C,α 20 Ne) excitation function in a wide range 0-3 MeV, including the Gamov region. Signals produced by detectors were processed through standard electronic. The trigger signal was produced by the coincidence between PSD1 (PSD4) and the total OR between PSD4-5-6 (PSD1-2-3). For the energy calibration we used a 12 C beam on Au target to get carbon from elastic scattering, 12 C beam on carbon target to get alphas for the 20 Ne+α exit channel and a standard alpha source.

Data Analysis
To identify the reaction channel 16 O( 12 C, α 20 Ne)α of our interest we performed the study of ∆E-E matrices. In fig.1 typical experimental result is shown. We can identified three loci related to oxygen (mainly due to the beam scattering) neon and magnesium. To select data of our interest a graphical cut was made around the neon locus. The experimental q-value for the three-body process was reconstructed considering alpha particles detected on PSD5-6 (PSD2-3) and assuming that the third undetected particle is an alpha particle. The experimental values obtained -2.66 MeV, -4.23 MeV, corresponds with good approximation to the theoretical q-value of the 16 O( 12 C, α 20 Ne)α reaction with 20 Ne at g.s and 1 st excited state respectively. This result confirm the correct selection of the reaction channel. For the following analysis we selected events related to 20 Ne at g.s. In fig.1 we can observe also that magnesium partially overlap the neon locus. This is partially due to the resolution of the detection system, on the other hand the loci are overlapped since we are in a energy range corresponding to the Bragg pick region. In particular the contamination is evident for events corresponding to a kinematic region with high probability for the quasi-free process. For this reason we applied a procedure in order to remove spurious events avoiding to put sharp cuts. In order to study the reaction mechanism populating our three-body channel, we reconstructed the relative energy matrices. In particular in fig.2 we have 20 Ne-alpha relative energy (E20 N eα ) versus alpha-alpha relative energy (E αα ). The vertical locus for a fix alpha-alpha relative energy corresponds to the formation of the 8 Be g.s. It means that our exit channel is populated by a sequential process 16 O + 12 C −→ 20 Ne + 8 Be * −→ 20 Ne+ α +α. The horizontal loci for fix E20 N eα energy correspond to the population of 24 Mg excited states. Due to the l = 0 12 C-α intercluster motion inside the 16 O, the region where we aspect to have the highest probability for the quasi-free process corresponds to low values for momentum of the alpha particle spectator (p s ) (lass than 100 MeV/c.) The study of the 20 Ne-alpha relative energy as function of p s indicates that the quasi-free region shows a very low statistic, moreover there is no evidence of 24 Mg excited states. We have to say that this region corresponds to low-energy 20 Ne area where we had the strong contamination of spurious events. So the low-statistic could be due to wrong selection of the events in this region. On the other hand the 24 Mg excited states are populated in correspondence of high momenta. This result indicates that these levels are populated by a sequential mechanism 16 O + 12 C −→ 24 Mg * + α −→ 20 Ne+ α +α. In fig.3 the spectrum of the 24 Mg exited states populated is shown. We can seen five levels. The experimental data did not . allow to make J π assignment, on the other hand this energy range shows a very high density of 24 Mg levels. In tab.1 we report a comparison between our data and the results obtained by E. Goldberg et al. [15] where the 24 Mg levels were observed via 20 Ne-alpha resonant scattering.

Conclusion
In the framework of the study carbon-carbon fusion reaction at astrophysical energy via THM, we have studied the 16 O( 12 C, α 20 Ne)α using for the first time the 16 O as Trojan Horse nucleus. Experimental results obtained, in the experimental conditions described, have shown that threebody exit channel is mainly populated by sequential decay mechanism while no clear evidence of quasi-free process has been observed. The strong contamination of spurious events in the quasifree energy region could be the reason of wrong selection of quasi-free events. 24 Mg excited states have been populated and compared with data present in literature. On the basis of this results a new experimental run has been performed with a different experimental set-up in order to increase the resolution and avoid the contaminations problems. Moreover we performed a experimental run where THM have been applied to the 14 N( 12 C, α 20 Ne) 2 H three-body reaction using for the first time 14 N ( 12 C ⊕ d cluster configuration) as Trojan Horse nucleus.