The 13C(α,n)16O cross section measurement at low energies at LUNA

One of the main neutron sources for the astrophysical s-process is the 13C(α,n)16O. This reaction takes place in thermally pulsing asymptotic giant branch (TP-AGB) stars in a stellar environmental with temperature of about 90 MK. To model the nucleosynthesis process connected with the reaction, it is important the cross section reaction evaluation inside the so called Gamow peak, in the energy window 150-240 keV. In this work the results of the first 13C(α,n)16O direct measurement performed by the LUNA collaboration in the underground laboratory of LNGS are presented. The measurement covers the energy range 230-300 keV, being the first direct measurement to reach the s-process Gamow window. Lower uncertainties with respect to previous measurements in literature are provided and this allows to reduce overall uncertainties on reaction rates calculation. Selected stellar models have been computed to estimate the impact of our revised reaction rate. Using the lower reaction rate at -2σ, for stars of nearly solar composition, we find sizeable variations for some isotopes, whose production is influenced by the activation of close-by branching points that are sensitive to the neutron density, in particular 60Fe, 205Pb and and 152Gd.


Introduction and State of the Art
The 13 C(α, n) 16 O reaction is the main neutron source for the s-process in low mass AGB stars [1], The reaction takes place subsequently to complex convective motions in the so-called 13C pocket in a stellar environment of about 1 − 2 • 10 8 K, corresponding to a Gamow window between 1401 and 250 keV, well below the Coulomb potential energy of the reaction.
In the last 25 years, several direct cross section measurements of this reaction have been performed [2,3,4].The lowest energy point, corresponding to E=265 keV, was measured by Drotleff et al. [3] with a 60% uncertainty.From the literature one can see that statistical error is due to the low signal to noise ratio at low energy anda strong source of systematical uncertainty comes from the difficulty to keep under control target properties such as thickness and composition than might change after long irradiations with alpha beam.In addition, the presence of a near threshold resonance at E R = (−3 ± 8) keV, corresponding to E x = 6.356MeV state in 17 O, influences the cross section in the Gamow window, making extrapolations from higher energies complicated.In 2008, Heil et al. [2] performed a direct measurement and a multichannel R-matrix analysis was carried out: the S(E) factor extrapolation uncertainty in the Gamow peak is at least of 20%.
A recent work by deBoer et al. [5] states that one of the main source of uncertainty for of the reaction rate evaluation is due to normalisation uncertainty of the 13 C(α, n) 16 O data, directly connected to systematic uncertainties on different datasets.Also several indirect measurements have been performed using the Asymptotic Normalization Coefficient (ANC) [6] and the Trojan Horse [7] methods.With some hypotesisi, these techniques can enter in the Gamow window because are not affected by Coulomb repulsion or screening effect, but they must be normalized to direct measurements.In this scenario the new LUNA (Laboratory for Underground Nuclear Astrophysics) measurement, whose goal is to reach the Gamow window with a direct measurement with an overall 20% uncertainty at maximum, finds a perfect collocation that allows to constrain the reaction rate for a better development of stellar evolution.

The experimental setup
For the first time ever, the LUNA collaboration designed and installed a neutron detector at the end of the solid target beamline.Figure 1a shows the experimental setup used for this measurement: it is based on 18 3 He counters with low intrinsic background arranged in two rings (6 in the inner ring, 12 in the outer ring) concentric with respect to the target chamber.The counters are embedded in a polyethylene moderator.The whole setup is surrounded by a 2 inches borated polyethylene absorber to further reduce the environmental background [8].The selection of materials with lower thorium and uranium concentration, in particular the choice of stainless steel case instead of aluminium, reduced the alpha particle intrinsic background of the detector and a pulse shape analysis performed on the signals from counters' preamplifiers allowed a further rejection of remaining alpha signals [9] obtaining a total background in the whole setup of about 1 count/hour [10], 2 orders of magnitude lower with respect to all previous measurements performed in surface laboratories.The moderator can be opened, allowing the insertion of a High-Purity Germanium (HPGe) detector in close geometry for the target monitoring as explained later.Figure 1b shows the absolute neutron detection efficiency of the setup.This was evaluated by means of a Monte Carlo simulation based on Geant4 [11] and validated in two different experimental campaigns: below neutron energy of 1 MeV, the activation measurement of the 51 V(p,n) 51 Cr reaction was used at the Van Dee Graaff accelerator installed at the Institute for Nuclear Research ATOMKI (Debrecen, Hungary); at high energy a certificated AmBe radioactive source was used, whose average energy is at about 4 MeV.The interpolation of experimental data constrained the efficiency in the LUNA region of interest, at E n =2.5 MeV to a value of (38±3)% [8]. 13C targets used during the measurement at LUNA have been produced evaporating 13 C isotopically enriched at 99% on tantalum backings.To check target stoichiometry, depth profile and uniformity immediately after the evaporation, an extensive target characterization was performed by means of Nuclear Resonant Reaction Analysis (NRRA) of the 13 C(p,γ) 14 N reaction at 1.75 MeV at the Tandetron accelerator installed at ATOMKI [12].Shortly, the well known aforementioned resonance is populated in the target deeper and deeper with the increase of the beam energy.From the fit of the excitation function it is possible to evaluate target thickness and stoichiometry.The monitoring of these mentioned quantities are crucial also during the cross section measurement performed at LUNA, where the NRRA technique is not applicable, due to the lack of resonances in the dynamic energy range of the accelerator.For this reason, a new method of analysis was developed and details can be found in the paper by Ciani et al. [13].Data taking at LUNA consisted in long α-beam runs with accumulated charges of ≈ 1 C per run, interspersed by short proton-beam runs at E p = 310 keV with moderator opened and HPGe detector in close geometry, with typical accumulated charges of 0.2 C at most.During the last mentioned proton runs, the target degradation can be checked by the fit of the direct capture de-excitation to the ground state peak of 13 C(p,γ) 14 N reaction with the HPGe detector.

Results and discussion
The big effort performed in the background reduction and in the development of the new analysis for monitoring target degradation, allowed the LUNA collaboration to achieve unprecedented results.Indeed, for the first time ever a direct measurement was performed in the energy range 230 keV <E cm <305 keV, reaching the high energy edge of the Gamow window.Moreover, the points in the whole dataset had a statistical uncertainty lower that 10% [14].
Figure 2 shows the LUNA results compared with other main direct measurements.The beige area indicates the Gamow window.An R Matrix analysis using the code Azure2 [15] was performed using the new LUNA data together with those by Heil, Drotleff and Harissopoulos.Because of a large discrepancy in the data, it was decided to scale up Harissopoulos data by a factor 1.37.A check on potential source of systematic uncertainty due to this choice was performed repeating R-matrix calculation using data by Harissopulos et al. as a reference and a scale down of Heil and Drotleff data.In both cases the cross section evaluation in the Gamow window gave comparable results.As last step, the evaluation of the astrophysical reaction rate R=N A < σv > as a function of stellar temperature was performed using the well-know relation: Thanks to overall low uncertainty of the LUNA dataset, the reaction rate at T= 0.  given to the reaction rate at -95% uncertainty.Assuming this scenario, most of 13 C survives and it is it subsequently burned into a convective shell powered by a subsequent thermal pulse where the temperature is about ∼ 200 MK.This generates a second neutron burst characterised by lower exposure but higher neutron density.
According to simulation performed with FRUITY code, this causes considerable variations of some isotopic abundances (i.e. 60 Fe and 205 Pb and 152 Gd) in stars with simular composition with respect to Sun (Y = 0.27 and Z = 0.02).This is caused by the fact that the mentioned isotopes are close-by branching points that are sensitive to the neutron density.With the installation of the MV accelerator Ion Beam Facility in the hall B of LNGS, that will provide a maximum terminal voltage of 3.5 MV, the LUNA collaboration is planning to extend the measurement of the 13 C(α,n) 16 O up to 1 MeV, having the unique possibility to provide to literature a complete dataset over a wide energy range with better controlled uncertainties [16].

Figure 1 :
Figure 1: (a) The neutron detector array used for the LUNA measurement[8].A detailed description can be found in the text.(b) Simulated (dashed line) and experimental (filled symbols) total efficiency curves [8] of the LUNA setup.Green and blue points (exp.data) and curves (simulation) show the energy dependency of the efficiency related inner and outer rings, respectively.The linear fit of the experimental data (solid yellow line) interpolates the efficiency value in the experimental region of interest (E n =2.4 MeV) (empty diamond).

Figure 2 :
Figure 2: (Colour online) Extrapolation from R-Matrix analysis (red curve) of the astrophysical S(E) factor of 13 C(α,n) 16 O calculated using the new LUNA dataset together with the Heil, Drotleff and Harissopulos data.Figure adapted from [14].