Shedding light on 17 O(n,α) 14 C reaction at astrophysical energies with Trojan Horse Method and Asymptotic Normalization Coefficient

. Indirect methods have been established in the past as a complementary way of increasing our knowledge about nuclear structure and low-energy cross section measurements. Among these, the neutron induced reaction cross sections appear to be of particular interest because of their role both for unstable and stable beams. In view of this, we report here the combined study of the 17 O(n,α) 14 C reaction accomplished by the Trojan Horse Method (THM) and the Asymptotic Normalization Coefficient (ANC) method. The low lying resonances 8038, 8125, 8213, and 8282 keV in 18 O are studied and Γ n are derived. A comparison with direct data and recent THM experimental data is presented. The independent ANC investigation corroborates our previous THM results, confirms the consistence of the two indirect investigation and shows new frontiers also in view of neutron induced reactions with RIB's.


Introduction
The 17 O(n,α) 14 C reaction is considered in astrophysical models for its role in the relevant "s(slow)-process" since it could act as a possible "neutron poison" for the neutron-induced nucleosynthesis thus influencing the final stellar abundances of some elements such as Ni or Sr [1]. Thus, its reaction rate must be known in the energy region of interest for astrophysics, going from few keV up to about 400 keV. At such energies, the intermediate 17 O+n→ 18 O nucleus presents four excited levels (8038, 8125, 8213 and 8282 keV) affecting the magnitude of the 17 O+n cross section at astrophysical energies because of the 8044 keV threshold for the neutron emission of 18 O. Besides the role of the two 8213 keV (J π =2 + ) and 8282 keV (J π =3 − ) states, already investigated by the direct measurements [2], up-to-now poor information is available about the 8125 keV (J π =5 − ) resonant level, thus requiring a detailed experiment. However, neutron-induced reaction cross section measurements are difficult to be performed due to the practical difficulties of having "easily available" neutron beams. For such a reason, the Trojan Horse Method (THM) has been applied to the 17 O(n,α) 14 C case and discussed in [3,4]. The THM measurements [3,4] show an evident contribution of the 8213 keV and 8282 keV 18 O excited states with an additional contribution of the 8125 keV resonant level, naturally suppressed in the direct measurements because of the large l=3 angular momentum required for its population in the 17 O+n channel. Thanks to our THM investigation, information about the corresponding neutron (Γn) or alpha partial widths (Γα) is now available. To complement such information, mainly deduced by the (modified) R-matrix formalism for THM described in [5], we proposed a new experiment dedicated to the study of these resonant 18 O levels, with particular regard to the measurement of the 8125 keV level by means of the corresponding ANC.

Method and experiment
The ANC is a fundamental nuclear characteristic of importance in nuclear reactions since it corresponds to the amplitude of the overlap function of the bound-state wave functions of the initial and final nuclei. Hence, the ANC method allows one to obtain the cross section of a peripheral direct capture reaction A(a,γ)B in terms of the radial overlap integral of the X and B nuclei of the A(X,Y)B transfer reaction , where the nuclei X and A can be considered as X = Y+a and B = A+a [6]. This method has been widely used in the last 20 years to investigate proton, neutron and α direct captures in stellar environments [7][8][9]. In the present case, in order to extract the ANC for the 18 O resonant states, the 17 O(d,p) 18 O reaction has been studied, using the deuterium for its simple p+n configuration. The experiment was performed at the isochronus cyclotron U-120M of the Nuclear Physics Institute of the Czech Academy of Science (NPI-ASCR) in Rez (Prague). A 16.3 MeV beam was delivered onto a 90% pure 17 O gas target, connected to the beam line with 3μm-thick havar entrance and exit windows. The beam energy was chosen in order to maximize the peripherical contribution of the reaction (see [10] and reference therein). The detection setup, already used in many experiments [11], consisted of 8 standard point-like ∆E-E telescopes, with thicknesses of 500μm and 5000μm, respectively. Three telescopes were placed at fixed angles of 17°, 27° and 37° with respect to the beam line and have been used also as the monitors. Five telescopes were placed on the turntable plate on the opposite side with a relative angular step of 10°. The whole set of five telescopes could measure reaction products in the range of θLAB from 6° to 67°.

Data analysis and conclusions
After the performed detector calibrations and uncertainties evaluations, the next stage of the present analysis has been the extraction of the angular distribution for both, the elastic scattering 17 O+d and the reaction 17 O(d,p) 18 O. This is a standard procedure followed elsewhere [12] and focuses first on extracting the optical parameters from DWBA calculation on the 17 O+d elastic scattering angular distributions and then the ANC for the resonant 18  (1) where Er is the resonance energy (in MeV), μ is the reduced mass (in MeV), ħc=197 MeV fm and |Cl| 2 is in fm -1 . Then, considering also the Γα as reported in [4], it is possible to calculate the cross section and compare it with the direct and inverse data [2,14,15]. This comparison is reported in Fig.  1 where the red line represents the cross section calculated as described before while the red band is the error associated to the Γn of about 20%. Light blue points are data taken from the work of [2], blue points from [14] while black points are the inverse data of [15] converted using the detailed balance. From Fig.1 it is clear the presence of a quite good agreement between the ANC calculation and the direct data at the energy region above 150 keV. Below this region the direct measurements present a very big scatter distribution, while the ANC calculation decrease a lot due to the absence of a proper evaluation of the subthreshold level.

Figure 1 -ANC cross section compared with available direct data (see text for details)
Moreover, with the same parameters it is possible to compare also the THM data [4], as reported in Fig. 2. Again, red line and red band are used to highlight the cross section calculated from the Γn derived from the ANC data while the black points represent the THM data.
Not yet included is the subthreshold level centered at -7 keV since for this level the analysis is still ongoing. In both cases the results are in good agreement, confirming the possibility to use independent ANC investigation to corroborate THM results and thus opening new frontiers also in view of neutron induced reactions with RIBs, where there is still a lack of direct measurements due to practical problems in the simultaneous production of neutron and radioactive beams.  Table I compare the Γ values for the 18 O level state available in the literature, as a final cross-check of the good agreement between the methods and to underline once more that the combined study presented here allows us to measure for the first time the resonance parameters of the 8125 keV (J π =5 − ) level state, suppressed in direct measurement due to the centrifugal barrier.