UPDATED THM ASTROPHYSICAL FACTOR OF THE $^{19}{\rm F}{{(p,\alpha )}^{16}}{\rm O}$ REACTION AND INFLUENCE OF NEW DIRECT DATA AT ASTROPHYSICAL ENERGIES

1.1. Astrophysical Scenario

1.2. Assessment of Nuclear Data

As reported in Lombardo et al. (2013), the authors performed a very accurate measurement of the $^{19}{\rm F}{{(p,{{\alpha }_{0}})}^{16}}{\rm O}$ cross section in the $0.6\;{\rm MeV}\lesssim {{E}_{{\rm c}.{\rm m}.}}\lesssim 1\;{\rm MeV}$ energy interval. Since the $^{19}{\rm F}{{(p,{{\alpha }_{0}})}^{16}}{\rm O}$ reaction is highly exoenergetic (Q = 8.114 MeV), aluminum foils could be placed in front of the 12 silicon detectors to suppress the elastically scattered protons and keep the background below 1%. Angular distributions were measured at about 10° steps, while energies were changed at about 10 keV steps. A statistical error ranging between 6% and 20% affects the astrophysical factor in Lombardo et al. (2013), while a systematic error of about 7% was estimated by the authors. Close to the ²⁰Ne state at 13.642 MeV, good agreement is found between the data in Lombardo et al. (2013) and the older data from Caracciolo et al. (1974) and Isoya et al. (1958), within the error bars. At lower energies, ${{E}_{{\rm c}.{\rm m}.}}\lt 700$ keV, good agreement is apparent between the data from Lombardo et al. (2013) and those from Breuer (1959), even if the uncertainties are quite large. Both data sets show a smooth increase in S(E) with decreasing energy in the overlapping energy range, possibly linked to the potential existence of ²⁰Ne broad states at about ∼13.22 MeV, as reported in Breuer (1959) and in the indirect measurement in La Cognata et al. (2011). This energy trend is in sharp disagreement with the analysis of Isoya et al. (1958), supporting a significantly lower S(E) with a discrepancy amounting to ∼40%. A discrepancy of the same order is apparent in the $700\;{\rm keV}\lesssim {{E}_{{\rm c}.{\rm m}.}}\lesssim 770\;{\rm keV}$ energy region where the difference reaches about 30%, and above ∼900 keV, that is, the upper part of the investigated energy region. In the these last cases, the error bars are smaller, making the differences more striking.

Regarding the level at 13.642 MeV, Isoya (1958) attributed a spin parity of ${{J}^{\pi }}={{2}^{+}}$ based on an R-matrix analysis of the cross sections and angular distributions of the $^{19}{\rm F}{{(p,{{\alpha }_{0}})}^{16}}{\rm O}$ and $^{19}{\rm F}{{(p,{{\alpha }_{\pi }})}^{16}}{\rm O}$ reaction. The latter corresponds to the case where α is emitted leaving ¹⁶O in its first excited state, which cannot decay to the ground state through one gamma-ray emission due to spin-parity matching. In contrast, Lombardo et al. (2013) analyzed the energy trend of the A_n and B_n coefficients from the decomposition of the differential cross section $\sigma \left( {{\theta }_{{\rm c}.{\rm m}.}} \right)$ in terms of the cosine and Legendre polynomials, respectively. They concluded that the enhancement of the A₀ and B₀ coefficients around 800 keV center-of-mass energy is a clear signature of the occurrence of a ${{J}^{\pi }}={{0}^{+}}$ state in ²⁰Ne at an excitation energy of 13.642 MeV, in agreement with the spin-parity assignment from previous works (Webb et al. 1955; Caracciolo et al. 1974). Table 1 contains a summary of the $^{19}{\rm F}{{(p,{{\alpha }_{0}})}^{16}}{\rm O}$ data relevant in the normalization region. Specifically, the trend of the astrophysical factor below about 600 keV and the minimum center-of-mass energy reached in the experiments are cited. Moreover, for the ²⁰Ne states at 13.529, 13.586, and 13.642 MeV, responsible for the resonances in the normalization region, the total widths and spin-parities are shown, labeled by the superscripts 1, 2, and 3, respectively. The presence of such contradictory results calls for a more detailed analysis, and makes it necessary to have a thorough discussion concerning the THM astrophysical factor normalization because of the significant difference in direct data at the THM normalization energies.

Table 1.  Summary of $^{19}{\rm F}{{(p,{{\alpha }_{0}})}^{16}}{\rm O}$ Data Relevant in the Normalization Region

Reference	Low-energy Behavior	Emin (keV)	${\Gamma }_{{\rm tot}}^{1}$	$J_{1}^{\pi }$	${\Gamma }_{{\rm tot}}^{2}$	$J_{2}^{\pi }$	${\Gamma }_{{\rm tot}}^{3}$	$J_{3}^{\pi }$
Webb et al. (1955)	non-resonant	550	⋯	⋯	⋯	⋯	23	${{0}^{+}}$
Isoya et al. (1958)	non-resonant	598	63	2+	10	2+	22	2+
Breuer (1959)	resonant	461	35	2+	10	⋯	25	0+
Caracciolo et al. (1974)	non-resonant	760	⋯	⋯	⋯	⋯	23a	0+
Lorentz-Wirzba (1978)	non-resonantb	⋯	⋯	⋯	⋯	⋯	⋯	⋯
Herndl et al. (1991) c	non-resonant	150	63	2+	9	2+	17	2+
Yamashita & Kudo (1993) c	non-resonant	⋯	⋯	⋯	⋯	⋯	⋯	⋯
Tilley et al. (1998)	resonant	400	61	2+	9 ± 1	2+	17 ± 1	0+
Angulo et al. (1999) d	non-resonant	⋯e	⋯f	⋯f	⋯f	⋯f	⋯f	⋯f
La Cognata et al. (2011)	resonant	0g	⋯h	2+	⋯h	2+	⋯h	2+
Lombardo et al. (2013)	resonant	600	⋯	2+	9	2+	22	0+
Present work	resonant	⋯i	65 ± 7	2+	17 ± 12	2+	22 ± 3	2+
Present work—AZURE	resonant	⋯i	57	2+	13	2+	20	2+

Notes. For each reference, the trend of the astrophysical factor below about 600 keV, the minimum center-of-mass energy reached in the experiments (E_min), and the total widths and spin-parities of the resonances due to the ²⁰Ne states at 13.529, 13.586, and 13.642 MeV, responsible for the resonances in the normalization regions, are shown, labeled by the superscripts 1, 2, and 3, respectively.

^aSame as in Ajzenberg-Selove (1972). ^bDeduced from the NACRE compilation (Angulo et al. 1999). ^cUsing data from Lorentz-Wirzba (1978). ^dNACRE compilation. ^eSame as in Breuer (1959). ^fThe authors used the data by Isoya et al. (1958) and by Caracciolo et al. (1974; in the range of 0.760–0.817 MeV). ^gIndirect measurement using THM. ^hWidths were fixed to the values in Tilley et al. (1998). ⁱSame as in Lombardo et al. (2013).

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Following the procedure in La Cognata et al. (2011, 2012, 2013) and Tribble et al. (2014), we performed an R-matrix fit of the astrophysical factor in Lombardo et al. (2013) to determine the p-and α-reduced widths to be introduced in the generalized R-matrix fitting of the THM data (La Cognata et al. 2011). In our calculation, we took the non-resonant background from the NACRE compilation (Angulo et al. 1999) and the channel radii from La Cognata et al. (2011). At first, we fixed ${{J}^{\pi }}={{2}^{+}}$ for the three resonances under consideration, that is, we assumed the same conditions as in La Cognata et al. (2011). In Figure 1, we show the astrophysical factor from Lombardo et al. (2013, solid symbols), together with the R-matrix fit performed using the same R-matrix code as in La Cognata et al. (2011), based on Lane & Thomas (1958, red line), and the R-matrix fit obtained using the more advanced multi-level, multi-channel AZURE computer code (blue line, Azuma et al. 2010). Interference effects were fully taken into account and justify the sharp drop in the astrophysical factor in the energy region below about 0.66 MeV and above about 0.82 MeV. In the former fit, the resonance energies were fixed to those obtained in the AZURE fit, namely, 697, 739, and 807 keV (corresponding to the ²⁰Ne states at 13.529, 13.586, and 13.642 MeV). Very good agreement is found between the two fits, as is also clear from the computed ${{\chi }^{2}}$ per degree of freedom, 0.3 and 0.5, respectively (the number of degree of freedom, hereafter ndf, is 14 and 18, respectively). Slightly smaller widths, still in agreement within our uncertainties (∼10%), were obtained in the AZURE fit, giving ${{{\Gamma }}_{{\rm tot}}}=57$, 13, and 20 keV for the three resonances mentioned above, respectively. Our fit instead provided ${{{\Gamma }}_{{\rm tot}}}=65\pm 7$, 17 ± 12, and 22 ± 3 keV. The resonance energies and widths are in good agreement with those reported by Lombardo et al. (2013) and, taking into account the differences in the astrophysical factor between Lombardo et al. (2013) and Isoya (1958), also agree with this latest data set. The main difference between our widths and those cited in the literature (Isoya 1958) resides in the width of the resonance at 739 keV, ${{{\Gamma }}_{{\rm tot}}}=10$ keV (Isoya 1958); however, this value is well within the large uncertainty affecting this width in our calculation. The widths obtained through the fitting procedures described so far are reported in Table 1, together with the resonance parameters in the literature.

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In the comparison between the analysis in Lombardo et al. (2013) and Isoya (1958), two main differences have to be noted if we focus on the energy region close to the 800 keV resonance. The first difference is the spin-parity assignment for the 13.642 MeV ²⁰Ne state, as discussed above. Moreover, based on the anomalies affecting the A₂ and B₂ terms at ${{E}_{p}}\sim 825$ keV, the presence of a ${{J}^{\pi }}={{1}^{-}}$ ²⁰Ne state at 13.626 MeV with a width ${{{\Gamma }}_{{\rm tot}}}=30$ keV is deduced, in agreement with the results in Caracciolo et al. (1974). Using the parameters obtained in the previous case as initial values for the ${{J}^{\pi }}={{2}^{+}}$ resonances and the values provided in Lombardo et al. (2013) for the ${{J}^{\pi }}={{1}^{-}}$ and 0⁺ resonances, the AZURE code was used to perform a fit for the astrophysical factor in Lombardo et al. (2013) following the discussion contained therein. The resulting fitting curve is provided in Figure 2 (blue line), superimposed on the Lombardo et al. (2013) data. Even if a very good reproduction of the data were achieved (the ${{\chi }^{2}}$ per degree of freedom is 0.15, ndf = 12), the resonance parameters deviate from those mentioned above and generally accepted for the resonances under investigation. In particular, while ${{{\Gamma }}_{{\rm tot}}}=26\pm 4$ keV was calculated for the ${{J}^{\pi }}={{1}^{-}}$ state, as indicated in Lombardo et al. (2013), ${{{\Gamma }}_{{\rm tot}}}\sim 40\pm 7$ keV was obtained for the other three resonances, which does not match the values reported, for instance, by Lombardo et al. (2013). The present findings necessitate more direct measurements of the $^{19}{\rm F}{{(p,\alpha )}^{16}}{\rm O}$ reaction and, in particular, a new measurement of the ${{\alpha }_{\pi }}$ contribution, since the present considerations stem from the data of Isoya (1958). Based on such an analysis, we chose to normalize the THM data to the astrophysical factor of Lombardo et al. (2013), still assuming a spin-parity assignment of ${{J}^{\pi }}={{2}^{+}}$ for the 13.642 MeV ²⁰Ne state.

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As briefly discussed in the Introduction and at length in La Cognata et al. (2012, 2013), normalization was attained by extending the THM measurement up to 1 MeV to guarantee an overlap with the direct astrophysical factor. A standard R-matrix routine was used to compute the reduced widths necessary to reproduce the direct data, where available. Since the same reduced widths appear in the THM cross section ${{d}^{2}}\sigma /d{{E}_{{\rm c}.{\rm m}.}}d{{{\Omega }}_{n}}$ as in the direct S(E) factor, with the essential difference between the two being the absence of any Coulomb or centrifugal penetration factor in the entrance channel (Mukhamedzhanov 2011; La Cognata et al. 2013), such parameters were fixed to those previously obtained. After folding ${{d}^{2}}\sigma /d{{E}_{{\rm c}.{\rm m}.}}d{{{\Omega }}_{n}}$ with a Gaussian having an FWHM of 60 keV to account for the energy resolution (La Cognata et al. 2011), as calculated from beam spot size and divergence, energy loss in the ΔE detectors, target and dead layers, and detectors intrinsic angular and energy resolution, we superimposed the calculated THM cross section onto the experimental one, leaving a scaling factor as the only free parameter. This is necessary to match the theoretical ${{d}^{2}}\sigma /d{{E}_{{\rm c}.{\rm m}.}}d{{{\Omega }}_{n}}$ to the experimental data; it was found by comparing the two above 600 keV, but the same normalization factor was then used over the whole energy region covered by the experimental THM data. In this way, we fixed the relative normalization of the low-energy region, below 600 keV, to that at higher energies, 0.6 MeV ≲ E_c.m.. The ≲ 0.8 MeV data and calculated THM cross section are both given in arbitrary units. This means that the resonance parameters of the ²⁰Ne states at excitation energies below about 13.5 MeV are normalized to those of the states at 13.529, 13.586, and 13.642 MeV. A normalization error of +12%–8% was determined.

The resulting calculation is shown in Figure 3. The solid symbols demonstrate the THM data as in La Cognata et al. (2011). The middle red line is the best-fit curve (${{\chi }^{2}}$ per degree of freedom 3.6, ndf = 8) while the upper and lower red lines highlight the upper and lower limits due to statistical and normalization uncertainties. The black arrows mark the ²⁰Ne states introduced into the calculation. The reduced widths of the states at 13.529, 13.586, and 13.642 MeV are fixed to the values from the standard R-matrix fitting of the Lombardo et al. (2013) data. The resonance parameters of the other levels at 12.957, 13.048, and 13.226 MeV are instead adjusted to reproduce the trend of the experimental THM ${{d}^{2}}\sigma /d{{E}_{{\rm c}.{\rm m}.}}d{{{\Omega }}_{n}}$. In the region around 400 keV, a single resonance is considered as in La Cognata et al. (2011), the one with the largest spin (${{J}^{\pi }}={{3}^{-}}$), as states with higher spin are preferentially populated in the THM reaction yield (La Cognata et al. 2011, 2013; Mukhamedzhanov 2011). Other resonances are present, due to the ²⁰Ne states at 13.224 MeV (${{J}^{\pi }}={{1}^{-}}$) and 13.222 MeV (${{J}^{\pi }}={{0}^{+}}$), which are less enhanced in the THM measurement than the ${{J}^{\pi }}={{3}^{-}}$ state, due to the ${{J}^{\pi }}$ dependence of the THM cross section (La Cognata et al. 2011, 2013; Mukhamedzhanov 2011). Therefore, based on the THM data, we can state that around 400 keV, a resonance is present in the direct data, in agreement with the conclusions drawn in La Cognata et al. (2010, 2011), Lombardo et al. (2013), and Breuer (1959). However, the THM data do not allow us to provide quantitative information on the resonance parameters since the mentioned resonances cannot be resolved. As in La Cognata et al. (2011), the most important result of this work is the determination of the occurrence of a resonance at 113 keV in the $^{19}{\rm F}$–p center-of-mass system. Even if the resolution were better than 60 keV, the three resonances could be hardly resolved as they are located 2 keV apart. Guidance from direct data is necessary for more accurate indirect results.

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An important characteristic clearly featured by the THM data set is the possible presence of a shift of about 25 keV in the energy scale. This is the radix of the ${{\chi }^{2}}$ per degree of freedom which is larger than that in La Cognata et al. (2011). Its origin is associated with the contributions from the resonances at 685 and 742 keV in Lombardo et al. (2013), which are more prominent than those in Isoya (1958). When the generalized R-matrix calculation is folded with a Gaussian curve to account for the energy resolution (La Cognata et al. 2009), the resonances above 600 keV cannot be resolved and a single peak shows up, whose position is set by the weighted average of the resonance energies. Since the peaks at 685 and 742 keV are fed with a larger probability than in Isoya (1958; the astrophysical factor is about 30% larger in Lombardo et al. 2013), and the contribution of the 798 keV resonance remains constant, the centroid of the folded ${{d}^{2}}\sigma /d{{E}_{{\rm c}.{\rm m}.}}d{{{\Omega }}_{n}}$ is shifted toward lower energy. This might signal the presence of a systematic error in the energy calibrations which has to be taken into account in the forthcoming analysis. It is worth noting that such a shift is apparent at energies above 600 keV while it is not evident at lower energies, especially at the energies of astrophysical interest.

From the fitting of the THM data, we obtained the widths of the resonances lying below 600 keV. In detail, we obtained ${{{\Gamma }}_{{\rm tot}}}=50_{-8}^{+14}$, $10_{-6}^{+2}$, and $54_{-9}^{+11}$ keV for the three ²⁰Ne states at 12.957, 13.048, and 13.226 MeV. The cited errors include correlations, as the different sources of uncertainty are clearly not independent. In contrast with La Cognata et al. (2011), these are fitted values and were not fixed in the calculation. The energy and spin parity of these resonances were instead fixed to the values given in the compilation (Tilley et al. 1998; see La Cognata et al. 2011, for more details). These values agree very well with those in La Cognata et al. (2011) and with those reported in the compilation (Tilley et al. 1998). The quite large error bars include the statistical and normalization errors, and reflect the uncertainty due to the possible shift in energy affecting the indirect data. As mentioned above, while the contribution of the 13.226 MeV state is dominant in the indirect measurement as no centrifugal barrier is suppressing its population, in the direct measurement, other levels at 13.224 MeV (${{J}^{\pi }}={{1}^{-}}$) and 13.222 MeV (${{J}^{\pi }}={{0}^{+}}$) might be dominant, and so information about the 13.226 MeV level may be of little interest for astrophysical applications, which is at odds with the 12.957 MeV state whose importance was already pointed out in La Cognata et al. (2011).

The resonance parameters provided by fitting the experimental ${{d}^{2}}\sigma /d{{E}_{{\rm c}.{\rm m}.}}d{{{\Omega }}_{n}}$ cross section were then introduced into a standard R-matrix code (Lane & Thomas 1958) to determine the energy trend of the astrophysical factor of the $^{19}{\rm F}{{(p,\alpha )}^{16}}{\rm O}$ reaction (as stated above, of the more important ${{\alpha }_{0}}$ channel) at low energies. This is possible because in the modified R-matrix approach, the same reduced widths appear as in the on-energy-shell S(E) factor, with the only difference being the absence of any Coulomb or centrifugal penetrability factor in the entrance channel (La Cognata et al. 2011, 2013; Mukhamedzhanov 2011). The S(E) factor calculated with the resonance parameters from the fitting of the THM data below 600 keV is shown in Figure 4. Since the TH cross section yielded the resonance contribution only, the non-resonant part of the cross section was taken from Angulo et al. (1999). However, there is a clear mismatch between the direct contribution recommended by Angulo et al. (1999) and the experimental measurement in Lombardo et al. (2013). New direct measurements are of the utmost importance to obtain a more realistic non-resonant contribution at low energies, since the one given in Angulo et al. (1999) is based on a very simple calculation. The middle red curve depicts the S(E) factor computed using the parameters from the best fit, while the red band arises from the uncertainties on the resonance parameters due to the combined statistical, normalization, and energy shift errors (including correlation). An average error of 20% is obtained. This is different from the result in La Cognata et al. (2011), where only the errors affecting the resonances below 600 keV were reported (no correlations).

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If we focus on the main result of this measurement, that is, the resonance due to 12.957 MeV, then here we stress the very good agreement between the present result, based on the normalization of the THM data to the Lombardo et al. (2013) data, and the data in La Cognata et al. (2011) where the normalization to the older data in Isoya (1958) was carried out. This demonstrates the robustness of the THM approach and the weak dependence on the normalization if this is performed to more than one resonance. In this way, in fact, we reduce the impact of the systematic errors affecting the direct data. In detail, the top value of the resonance at 113 keV obtained in the present work, $29_{-2}^{+1}$ MeVb, should be compared with the previous result (La Cognata et al. 2011), $29_{-3}^{+2}$ MeVb. The smaller uncertainty of the peak value is a consequence of the more thorough treatment of the different sources of uncertainty (statistical, normalization, and energy shift), attributing the uncertainty mostly to the non-resonant part. Indeed, from inspection of Figure 4, it is clear that the main source of uncertainty is our current poor knowledge of the non-resonant contribution, which was neglected in La Cognata et al. (2011). Such a consideration makes it clear that new direct measurements reaching energies lower than 600 keV are mandatory to improve our current understanding of the $^{19}{\rm F}{{(p,\alpha )}^{16}}{\rm O}$ reaction, and such measurement should be aimed at both the ${{\alpha }_{0}}$ and ${{\alpha }_{\pi }}$ channels.

Using the astrophysical factor in Figure 4, we evaluated the variation of the reaction rate with respect to that recommended by NACRE (Angulo et al. 1999) and usually adopted in astrophysical modeling. The reaction rate for the $^{19}{\rm F}{{(p,{{\alpha }_{0}})}^{16}}{\rm O}$ channel was calculated, for the present data set (R) and for that recommended by NACRE (${{R}_{{\rm NACRE}}}$), by means of standard equations (Rolfs & Rodney 1988; Iliadis 2007), that is, by folding S(E) with the Maxwell–Boltzmann energy distribution. The ratio of the THM rate to that calculated using the NACRE data set is given in Figure 5 as a function of ${{T}_{9}}=T/{{10}^{9}}$. As in the previous figures, the middle red line marks the recommended reaction rate ratio based on the best-fit curve in Figure 4. Similarly, the upper and lower red lines provide the uncertainty range. According to the discussion in the Introduction, the NACRE S(E) factor shows a non-resonant behavior from 0.6 MeV downward, which is in sharp disagreement with the THM result. Coherently, the $R/{{R}_{{\rm NACRE}}}$ in Figure 5 significantly deviates from 1 in the temperature range of interest for AGB studies, $0.04\lesssim {{T}_{9}}\lesssim 0.2$ K (see the introductory section for more details). Such deviation, as large as a factor of 1.8, can be  attributed to the presence of the 113 keV peak in the $^{19}{\rm F}{{(p,{{\alpha }_{0}})}^{16}}{\rm O}$ astrophysical factor due to the 12.957 MeV state of ²⁰Ne. This result relies on the assumption that the non-resonant contribution is the same as that assumed in the NACRE compilation. Recently, new data from Lombardo et al. (2013) seem to suggest that such resonant behavior, even if they cannot reach energies of astrophysical relevance, is more realistic than the simple linear extrapolation recommended by NACRE (Angulo et al. 1999). Finally, the reaction rate given here essentially agrees with that from La Cognata et al. (2011), as should be expected since the contribution of the 113 keV resonance is the same in both works. In the present work, larger errors are found because a full error analysis has been performed, as discussed above, while in La Cognata et al. (2011) only the uncertainties affecting the resonances were taken into account. The $R/{{R}_{{\rm NACRE}}}$ ratio given in La Cognata et al. (2011) is shown as a blue band in Figure 5. For astrophysical calculations, the present work rate should be employed using the quoted uncertainties.

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This work was motivated by the recent publication of a new measurement of the $^{19}{\rm F}{{(p,{{\alpha }_{0}})}^{16}}{\rm O}$ channel (Lombardo et al. 2013), which is the most important channel for fluorine destruction in AGB stars (Spyrou et al. 2000). Since the new astrophysical factor departs from that in Isoya (1958), used to normalize the THM S(E) in La Cognata et al. (2011), we have reanalyzed the THM data to verify the dependence of the THM astrophysical factor on normalization in case more than one peak is used. This has important consequences for astrophysics and in the application of the method because it allows us to critically analyze systematic errors affecting the THM S(E) factor. Normalization is, in fact, a critical point in the application of the method and, very often, one of the largest sources of uncertainties. In the present work, it turns out that the new normalization negligibly alters the conclusions of our previous work (La Cognata et al. 2011), although it does show some critical points linked to the energy calibration and energy resolution. Indeed, the new direct data (Lombardo et al. 2013) suggest the presence of a shift in the $^{19}{\rm F}$–p relative energy spectrum. However, the poor energy resolution does not allow us to check the energy calibration since peaks are not resolved. These results call for a new THM measurement with improved energy resolution and better energy calibration.

Regarding direct measurements, this work underscores the importance of direct measurements for the application of indirect approaches. The two methods are strictly complementary and only a synergistic study can lead to an accurate understanding of low-energy nuclear reactions, which are of key importance for astrophysics. This paper has clearly demonstrated the necessity of a more comprehensive analysis of all the channels leading to the population of ²⁰Ne at excitation energies ≳13 MeV to perform a correct attribution of the spin parity of the 13.642 MeV level, of new direct measurements to collect new ${{\alpha }_{\pi }}$ data for a more accurate determination of the resonance parameters, and of new low-energy data to fix the direct contribution. Only a complete picture of ²⁰Ne excitation energies at ∼13 MeV can result in a significant improvement of our understanding of fluorine nucleosynthesis. In this framework, indirect measurements play an important role as they allow us to reach astrophysical energies, which is often impossible due to Coulomb suppression of the cross section and the electron screening effect.

The work was supported in part by the Italian MIUR under grant No. RBFR082838. A.M.M. acknowledges that his work is supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Science, under awards No. DE-FG02-93ER40773 and No. DE-SC0004958. It is also supported by the U.S. Department of Energy, National Nuclear Security Administration, under award No. DE-FG52-09NA29467 and by the US National Science Foundation under award No. PHY-1415656.