Determination of alpha spectroscopic factors for unbound 17O states

Abstract. It has been recently suggested that hydrogen ingestion into the helium shell of massive stars could lead to high 13C and 15N excesses when the blast of a core collapse supernova (ccSN) passes through its helium shell. This prediction questions the origin of extremely high 13C and 15N abundances observed in rare presolar SiC grains which is usually attributed to classical novae. In this context the 13N(α,p)16O reaction plays an important role since it is in competition with 13N β-decay to 13C. As a first step to the determination of the 13N(α,p)16O reaction rate, we present a study aiming at the determination of alpha spectroscopic factors of 17O states which are the analog ones to those in 17F, the compound nucleus of the 13N(α,p)16O reaction.


Introduction
Primitive meteorites hold several types of dust grains that condensed in stellar winds or ejecta of stellar explosions. These grains carry isotopic anomalies which are used as a signature of the stellar environment in which they formed. As such, extreme excesses of 13 C and 15 N in rare presolar SiC grains have been considered as a diagnostic of an origin in classical novae [1], however an origin in ccSNe has also been recently proposed [2]. In the context of ccSNe, explosive He shell burning can reproduce the high 13 C and 15 N abundances if H was ingested into the He shell and not fully destroyed before the explosion [3]. The supernova shock will then produce an isotopic pattern similar to the hot-CNO cycle signature obtained in classical novae. It has been shown that a variation of a factor of five for the 13 N(α,p) 16 O reaction rate induces several orders of magnitude uncertainty in the production of 13 N which β + -decays to 13 C.
Currently the 13 N(α,p) 16 O reaction rate is calculated using a statistical model or the time reverse reaction and these determinations have large uncertainties. The goal of this work is to put the 13 N(α,p) 16 O reaction rate on a firmer basis. Given that the alpha emission threshold (S α = 5.819 MeV) is much higher than the proton emission threshold (S p = 0.600 MeV) in the compound nucleus 17 F, the resonance strength of individual resonances is directly proportional to their alpha e-mail: deserevi@ipno.in2p3.fr widths. We report on the analysis of 13 C( 7 Li,t) 17 O data populating the analog states of the states of interest in 17 F. After a DWBA analysis of the measured differential cross sections, alpha spectroscopic factors are extracted and alpha widths are deduced.

Data reduction
An analysis of existing data from the alpha-transfer 13 C( 7 Li,t) 17 O experiment performed at the Tandem-ALTO facility in Orsay, France, was undertaken. All the experimental details can be found in Ref. [4] which focused on the study of the sub-threshold state at 6.356 MeV in 17 O relevant for the 13 C(α,n) 16 O reaction and its role in the main s-process. Tritons from the 13 C( 7 Li,t) 17 O reaction were momentum analyzed by an Enge Split-Pole magnetic spectrometer, and detected and identified at the focal plane. Figure 1 shows the triton focal-plane position spectrum obtained in the case of a spectrometer angle of 7°covering 17 O excitation energies between 6.2 and 7.4 MeV. Calibration of the focal-plane position detector at the same magnetic field using the natural carbon target and known 16 O levels populated through the 12 C( 7 Li,t) 16 O reaction was used to identify the 17 O states. The best least-square fit of the triton spectrum for states above the α+ 13 C threshold (S α = 6.359 MeV) is also represented in Fig. 1 together with the individual contribution of each 17 O state. While narrow states were described by a skewed Gaussian function needed to account for the low energy tail of each triton peak, a Voigt function was used for the broad 17 O state at 7.202 MeV (Γ = 280 (30) keV [5]). Since most of the levels have a natural width much smaller than the experimental width, a common width was taken for each Gaussian function describing 17 O states in the fitting procedure. A width of ≈ 60 keV (FWHM) is obtained which reflects the experimental resolution. The previous procedure has been repeated for each of the eleven spectrometer angles where the measurement was performed.

Angular distributions and DWBA analysis
The differential cross sections corresponding to 17 O states were obtained by normalizing the number of tritons determined at each detection angle to the target thickness, solid angle and accumulated charge.
As an example, the differential cross section of the 7.382 MeV (5/2 − ) state is displayed in Fig. 2.
Finite-range DWBA calculations were performed with the FRESCO code [6]. if the spread on the normalization factor accounts for ±20%. The best compromise for describing all differential cross sections at the same time is with potential III from Schumacher et al. [7] for the entrance channel and with potential I f7/2 from Garrett et al. [8] for the exit channel, in line with the study of the sub-threshold 6.356 MeV state [4].   Assuming that the overlap between the 7 Li and α+t systems is equal to one (see discussion in Ref. [4]), the normalization factor between the experimental and DWBA differential cross sections is the 17 O alpha spectroscopic factor (C 2 S α ). The procedure to extract C 2 S α for unbound 17 O states follows the prescription from Ref. [9]. For low transferred angular momentum ( < 2) such as for the 17 O state at 7.202 MeV, the alpha spectroscopic factor is determined at several binding energies and extrapolated at the actual α-separation energy (BE = -844 keV) as shown in Fig. 3. For higher transferred angular momentum, C 2 S α is determined for an hypothetical 17 O state bound by 100 keV since the α-cluster is quasi-bound due to the large centrifugal barrier. Alpha spectroscopic factor of 0.40 is obtained in the case of the 7.202 MeV broad state. Concerning the experimentally unresolved doublet including 17 O states at 7.379 and 7.382 MeV, alpha spectroscopic factors are 0.28 and 0.42, respectively, assuming all the strength is on one or the other state.
The alpha spectroscopic factor can be used to derive the corresponding partial width in case of unbound states using the following formula [10]: Γ α = 2P l (r, E) 2 r 2µ C 2 S α |φ(r)| 2 , where P l (r, E) is the penetrability for transferred angular momentum , and |φ(r)| is the radial part of the α+ 13 C wave function. This formula should be evaluated at the interaction radius r where the α+ 13 C wave function reaches an asymptotic behavior. This radius was determined by comparing the alpha reduced width γ 2 α with the corresponding Whittaker function (see Fig. 4) and a value of r = 6.5 fm is obtained. This procedure was done for all states and a similar radius was obtained. Alpha widths obtained for the 7.202 MeV and 7.379 MeV states are 6.5 × 10 −2 and 7.8 × 10 −3 keV, respectively. This is in very good agreement (within a factor of two) with alpha widths of 0.07 and 0.01 keV, respectively, reported in the literature [5].

Conclusions
Data from the 13 C( 7 Li,t) 17 O reaction were analysed with the goal to determine the alpha spectroscopic factors of 17 O states relevant for the study of the 13 N(α,p) 16