First Accurate Normalization of the β-delayed α Decay of 16N and Implications for the 12C(α,γ)16O Astrophysical Reaction Rate

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ First Accurate Normalization of the β-delayed α Decay of 16N and Implications for the 12C(α,γ)16O Astrophysical Reaction Rate © Authors, 2018 Published version Kirsebom, O. S.; Tengblad, O.; Lica, R.; Munch, M.; Riisager, K.; Fynbo, H. O. U.; Borge, M. J. G.; Madurga, M.; Marroquin, I.; Andreyev, A. N.; Berry, T. A.; Christensen, E. R.; Fernández, P. Díaz; Doherty, D. T.; Van Duppen, P.; Fraile, L. M.; Gallardo, M. C.; Greenlees, Paul; Harkness-Brennan, L. J.; Hubbard, N.; Huyse, M.; Jensen, J. H.; Johansson, H.; Jonson, B.; Judson, D. S.; Konki, Joonas; Lazarus, I.; Lund, M. V.; Marginean, N.; Marginean, R.; Perea, A.; Mihai, C.; Negret, A.; Page, R. D.; Pucknell, V.; Rahkila, Panu; Sorlin, O.; Sotty, C.; Swartz, J. A.; Sørensen, H. B.; Törnqvist, H.; Vedia, V.; Warr, N.; De Witte, H. Kirsebom, O. S., Tengblad, O., Lica, R., Munch, M., Riisager, K., Fynbo, H. O. U., Borge, M. J. G., Madurga, M., Marroquin, I., Andreyev, A. N., Berry, T. A., Christensen, E. R., Fernández, P. D., Doherty, D. T., Van Duppen, P., Fraile, L. M., Gallardo, M. C., Greenlees, P., Harkness-Brennan, L. J., . . . De Witte, H. (2018). First Accurate Normalization of the β-delayed α Decay of 16N and Implications for the 12C(α,γ)16O Astrophysical Reaction Rate. Physical Review Letters, 121(14), Article 142701. https://doi.org/10.1103/PhysRevLett.121.142701 2018 First Accurate Normalization of the β-delayed αDecay of 16Nand Implications for the 12Cðα;γÞ16OAstrophysical Reaction Rate O. S. Kirsebom,1,* O. Tengblad,2R. Lica,3,4 M. Munch,1K. Riisager,1H. O. U. Fynbo,1M. J. G. Borge,2,3 M. Madurga,3I. Marroquin,2A. N. Andreyev,5,18 T. A. Berry,6E. R. Christensen,1P. Díaz Fernández,7D. T. Doherty,5 P. Van Duppen,8L. M. Fraile,9M. C. Gallardo,9P. T. Greenlees,10,11 L. J. Harkness-Brennan,12 N. Hubbard,1,5 M. Huyse,8J. H. Jensen,1H. Johansson,7B. Jonson,7D. S. Judson,12 J. Konki,3,10,11 I. Lazarus,13 M. V. Lund,1 N. Marginean,4R. Marginean,4A. Perea,2C. Mihai,4A. Negret,4R. D. Page,12 V. Pucknell,13 P. Rahkila,10,11 O. Sorlin,3,14 C. Sotty,4J. A. Swartz,1H. B. Sørensen,1H. Törnqvist,15,16 V. Vedia,9N. Warr,17 and H. De Witte8 1Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark 2Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain 3CERN, CH-1211 Geneva 23, Switzerland 4Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), RO-077125 Bucharest-Magurele, Romania 5Department of Physics, University of York, York YO10 5DD, United Kingdom 6Department of Physics, University of Surrey, Guildford, GU2 7XH, United Kingdom 7Department of Physics, Chalmers University of Technology, S-41296 Göteborg, Sweden 8KU Leuven, Instituut voor Kernen Stralingsfysica, 3001 Leuven, Belgium 9Grupo de Física Nuclear, Universidad Complutense de Madrid, E-28040 Madrid, Spain 10University of Jyvaskyla, Department of Physics, P.O. Box 35, FI-40014 University of Jyvaskyla, Finland 11Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-00014 Helsinki, Finland 12Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom 13STFC Daresbury, Daresbury, Warrington WA4 4AD, United Kingdom 14GANIL, CEA/DSM-CNRS/IN2P3, Bvd Henri Becquerel, 14076 Caen, France 15Institut für Kernphysik, Technische Universität Darmstadt, Darmstadt, Germany 16GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany 17Institut für Kernphysik, Universität zu Köln, D-50937 Köln, Germany 18Advanced Science Research Centre (ASRC), Japan Atomic Energy Agency (JAEA), Tokai-mura, Ibaraki 319-1195, Japan (Received 9 April 2018; revised manuscript received 22 June 2018; published 3 October 2018) The 12Cðα;γÞ16O reaction plays a central role in astrophysics, but its cross section at energies relevant for astrophysical applications is only poorly constrained by laboratory data. The reduced αwidth, γ11,of the bound 1−level in 16O is particularly important to determine the cross section. The magnitude of γ11 is determined via sub-Coulomb α-transfer reactions or the β-delayed αdecay of 16N, but the latter approach is presently hampered by the lack of sufficiently precise data on the β-decay branching ratios. Here we report improved branching ratios for the bound 1−level [bβ;11 ¼ð5.02 0.10Þ×10−2] and for β-delayed α emission [bβα ¼ð1.59 0.06Þ×10−5]. Our value for bβα is 33% larger than previously held, leading to a substantial increase in γ11. Our revised value for γ11 is in good agreement with the value obtained in α-transfer studies and the weighted average of the two gives a robust and precise determination of γ11, which provides significantly improved constraints on the 12Cðα;γÞcross section in the energy range relevant to hydrostatic He burning. DOI: 10.1103/PhysRevLett.121.142701 In the hot and dense interior of stars, helium is burned into carbon and oxygen by means of the triple-αreaction and the 12Cðα;γÞreaction. The rates of the two reactions regulate the relative production of carbon and oxygen—a quantity of paramount importance in astrophysics affecting everything from grain formation in stellar winds to the late evolution of massive stars and the composition of type-Ia supernova progenitors [1]. At the temperatures characteristic of hydrostatic He burning, the triple-αreaction is dominated by a single, narrow resonance—the so-called Hoyle resonance—and hence it has been possible to constrain the reaction rate through measurements of the properties of the Hoyle resonance. In contrast, the 12Cðα;γÞ Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. PHYSICAL REVIEW LETTERS 121, 142701 (2018) 0031-9007=18=121(14)=142701(6) 142701-1 Published by the American Physical Society reaction receives contributions from several levels in 16O, which, as it happens, all lie outside the energy window where thermal fusion of αþ12C in the stellar environment is efficient—the so-called Gamow window. This makes the task of determining the 12Cðα;γÞrate rather complex. While the triple-αrate is now considered known within 10% in the energy range relevant to hydrostatic He burning [2], with efforts underway to reduce the uncertainty to 5% [3,4], the uncertainty on the 12Cðα;γÞrate was recently estimated to be at least 20%, which is insufficient for several astrophysical applications [1]. The 12Cðα;γÞcross section has been measured down to center-of-mass energies of ≈1.0MeV, but the rapidly decreasing tunneling probability makes it challenging to extend the measurements to lower energies and practically impossible to reach the Gamow energy of 0.3 MeV. According to current understanding [1], the capture cross section at 0.3 MeV receives its largest single contribution from the high-energy tail of the bound 1−level in 16O, situated at an excitation energy of Ex¼7.12 MeV only 45 keV below the αþ12C threshold. The reduced αwidth of this level, γ11, provides a measure of how strongly the level couples to the αþ12C channel. Therefore, γ11 is a critical quantity in determining the level’s contribution to the capture cross section at 0.3 MeV and, more generally, in constraining the extrapolation of the12Cðα;γÞcross section to the energy range relevant for stellar helium burning. Specifically, the dominant term in the expression for the E1capture cross section [see, e.g., Eq. (6) in Ref. [5]] is proportional to P1γ2 11 where P1is the p-wave penetration factor of the αþ12C channel. The magnitude of γ11 can be determined from the β-delayed αspectrum (βα spectrum) of 16N[6],but currently this approach is hindered by uncertainties in the normalization of the spectrum [7,8] as the inferred value for γ11 is strongly correlated with the assumed βdecay branching ratios (γ2 11 ∝bβα=bβ;11, see Supplemental Material [9]). Furthermore, the spectral form is not well determined experimentally due to small but significant discrepancies between existing measurements. Here, we focus our attention on the two high-precision spectra of Refs. [5,10] while disregarding a handful of other spectra, including those of Refs. [11,12], which all “retain significant experimental effects”[1]. In this Letter, we report on an experimental study of the βα decay of 16N in which the unique radioactive-isotope production capabilities of the ISOLDE facility [13] are exploited to provide the first accurate and precise determination of bβα. We also present a novel R-matrix analysis of the βα spectra of Refs. [5,10], propose a resolution to the discrepancies between the two spectra, and extract an improved value for P1γ2 11 which is in good agreement with the value inferred from sub-Coulomb α-transfer reactions. Finally, we comment on the implications of our findings for the determination of the 12Cðα;γÞcross section at 0.3 MeV. A detailed account of the experimental work and the R-matrix analysis will be published separately [14]. The experiment was performed at the ISOLDE radioactive-beam facility of CERN [13]. Radioactive isotopes were produced by the impact of a 1.4 GeV proton beam on a nanostructured CaO target [15], before being ionized in a cooled plasma ion source and accelerated through an electrostatic potential difference of 30 kV. Ions with the desired mass-to-charge (A=q) ratio were selected in the high-resolution separator and guided to the ISOLDE decay station [16] where their decay was studied. The ions were stopped in a thin (33 3μg=cm2) carbon foil surrounded by five double-sided silicon strip detectors (DSSD) and four high-purity germanium (HPGe) clovers, allowing for the simultaneous detection of charged particles and γrays. Meanwhile, auxiliary detectors were used to check that the beam was being fully transmitted to the center of the setup and stopped in the foil. During five days of data taking, the βα decay of 16N was studied mainly on A=q ¼30 (16N14Nþ) but also on A=q ¼31 (16N14N1Hþ). Additionally, the decays of 17Ne (βγ,βp,βα), 18N(βγ,βα), and 34Ar (βγ) were studied on A=q ¼17, 32, and 34, providing crucial data for the efficiency calibration of the HPGe array and the energy calibration of the DSSD array. Three of the DSSDs were sufficiently thin (40 μm and 60 μm) to allow the αspectrum of 16N to be clearly separated from the βbackground. The other two DSSDs were much thicker (300 μm and 1 mm) and served primarily to detect the βparticles. The distortions of the αspectrum due to βsumming was negligible due to the high granularity of the DSSDs [17]. Figure 1shows the α (MeV) α E 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Counts / 20 keV 1 10 2 10 N present 16 N Ref. [5] 16 N Ref. [21] 17 N present 18 Counts / 10 keV 0 500 1000 1500 FIG. 1. β-delayed αspectra obtained in one of the 60 μm thick DSSDs on A=q ¼30 (black circles) and 32 (red histogram). The two narrow αlines from the βα decay of 18N feature prominently in the spectrum obtained on A=q ¼32, while the spectrum obtained on A=q ¼30 is due almost entirely to the βα decay of 16N except for a ð2.00.4Þ%contamination from the βα decay of 17N (dashed curve) which has been subtracted. The R-matrix fit to the 16N spectrum of Ref. [5] (downscaled and properly corrected for experimental resolution) is also shown (thick, gray curve). PHYSICAL REVIEW LETTERS 121, 142701 (2018) 142701-2 spectrum obtained in one of the thin DSSDs on A=q ¼30 during 32 hours of measurement at an average 16N implantation rate of 2×104ions=s. The two narrow peaks at Eα¼1081 1and 1409 1keV in the βα spectrum of 18N[18,19] obtained on A=q ¼32 were used to determine the detector response and energy calibration. The energy resolution was 30 keV (FWHM) for the two 60 μm DSSDs and 70 keV for the 40 μm DSSD. The top panel of Fig. 2shows the γ-ray spectrum measured in the HPGe clovers. The spectrum exhibits the characteristic γrays from the decay of 16N[20], most notably the prominent lines at 2.74, 6.13, and 7.12 MeV. Additionally, the spectrum provides evidence for only one other β-delayed particle emitter, namely, 17N, present at a level of 1.3% relative to 16N, as inferred from the observation of its 0.871 MeVand 2.18 MeV γrays. Based on the known βα branching ratio of 17Nofð2.50.4Þ×10−5 [21], we determine the level of 17N contamination in our α spectrum to be ð2.00.4Þ%. In order to convert the observed γ-ray yields to intensity ratios, it is necessary to correct for the energy dependent detection efficiency of the HPGe array. An absolutely calibrated 152Eu source was used to determine the detection efficiency at low energies, while βγ,γγ, and pγcoincidence data were used to extend the efficiency calibration to higher energies. A GEANT 4 simulation [22], normalized only to the 152Eu data, was used to validate the efficiency calibration. As seen in Fig. 2(c), there is excellent agreement across the entire energy range. Particular attention was paid to the 6.13 MeV γray since it is used for the overall normalization. Using the γγ coincidences due to the 8.87 →6.13 →g:s:cascade [Fig. 2(b)] and βγ coincidences, the detection efficiency at 6.13 MeV was determined with a precision of 1.4%. After correcting the observed γγ coincidence yield for the known angular correlation [23], the two approaches (γγ and βγ) gave fully consistent results. Based on the relative γ-ray yields, we determine the β-decay branching ratio to the 7.12 MeV level in 16O to be bβ;11 ¼ð5.02 0.10Þ×10−2in agreement with Refs. [10,20,24–26], but with a reduced uncertainty due to the precise efficiency calibration and high energy resolution of the present study. Based on the number of detected αparticles, the measured 6.13 MeV γ-ray yield, and the known relative intensity of the 6.13 MeV γ-ray line (0.670 0.006 [20,27,28]), we determine the branching ratio for αemission to be bβα ¼ð1.59 0.06Þ×10−5with the following error budget: α-particle detection efficiency, 3.0%; γ-ray detection efficiency, 1.4%; α-particle counting uncertainty, 1.3%; tabulated intensity of the 6.13-MeV γray, 0.9%; and subtraction of the 17N contamination, 0.4%. When added in quadrature these uncertainties combine to give the quoted total uncertainty of 3.8% on bβα. Our value for bβα is significantly larger than the literature value of ð1.200.05Þ×10−5[20,29], but consistent with the less precise values of ð1.30.3Þ×10−5obtained by Ref. [30] and ½1.490.05ðstatÞþ0.0 −0.10ðsysÞ×10−5obtained by us in a previous study using a different experimental technique [31]. In order to parametrize the shape of the αspectrum, we adopt an R-matrix model similar to that of Refs. [5,10], consisting of two physical p-wave levels at Ex¼7.12 and 9.59 MeV, two physical f-wave levels at Ex¼6.13 and 11.60 MeV, and a p-wave background pole at higher energy. The R-matrix model of Refs. [5,10] additionally includes an f-wave background pole with zero feeding, but we find that the inclusion of such a pole only gives a marginal improvement of χ2and a slightly worse χ2=N and hence we do not include it. On the other hand, we allow the feeding of the 11.60 MeV level, which was also set to zero in Refs. [5,10], to vary freely. Our analysis differs from those of Refs. [5,10] in a few significant respects: first and most importantly, the analyses of Refs. [5,10] were aimed at determining the capture cross section at 0.3 MeV and therefore involved the simultaneous fitting of βα-decay data, α-scattering data, and α-capture data. Our analysis, on the other hand, is aimed at determining the constraints imposed on γ11 by the βα-decay data alone and at resolving the discrepancies between Refs. [5,10], and hence we restrict our attention to the βα-decay data. We also (MeV) γ E Counts / keV 1 10 2 10 3 10 4 10 5 10 6 10 (a) 6.13→8.87 gs→6.13 gs→7.12 (MeV) γ E 2.72 2.74 2.76 (MeV) γ E 6.1 6.12 6.14 6.16 (b) (MeV) γ E 012345678910 Absolute photopeak efficiency (%) 1 10 Ar 34 Eu 152 βγAr 34 γNe p 17 βγN 16 γγN 16 GEANT4 (c) FIG. 2. (a) γ-ray spectrum from the βdecay of 16N with main transitions indicated. (b) γγ coincidence spectrum zoomed in on the 8.87 →6.13 →g:s:cascade. (c) Experimentally determined and simulated γ-ray detection efficiency. PHYSICAL REVIEW LETTERS 121, 142701 (2018) 142701-3 adopt our improved values for bβ;11 and bβα, and we fix the asymptotic normalization coefficient (ANC) of the 6.13 MeV level to the rather precise value of C¼ 139 9fm−1=2inferred from sub-Coulomb transfer reactions [32].AllR-matrix calculations have been performed with the code ORM [33]. Further details are provided in the Supplemental Material [9]. Following Refs. [5,10] we ignore the four data points in the vicinity of the narrow 2þlevel at Ex¼9.68 MeV. Allowing the channel radius to vary, we obtain a very good fit to the spectrum of Ref. [5] (χ2=N ¼94.3=79 ¼1.19, Pχ2>94.3¼0.116, Fig. 3left panel) yielding P1γ2 11 ¼5.17 0.75ðstatÞ0.54ðsysÞμeV;ð1Þ (with P1evaluated at 0.3 MeV) and a preferred channel radius of 6.35 fm. The largest contribution to the systematic uncertainty comes from the energy calibration (3.8%) with smaller contributions from bβα (2.7%) and bβ;11 (2.0%) and even smaller contributions from the subtraction of 17N and 18N impurities (1.0%), the ANC of the 6.13 MeV level (0.4%), and the energy resolution (0.3%). Using the old branching ratio of bβα ¼1.20 ×10−5[20,29], we obtain P1γ2 11 ¼3.92 0.57ðstatÞμeV with no change in fit quality. Thus, our revised value for bβα leads to a 32% increase in P1γ2 11. The precise effect on the E1capture cross section is difficult to determine since it requires a simultaneous fit to the βα spectrum, α-capture data, and α-scattering data, which is beyond the scope of the present study. An accurate estimate can, however, be obtained by adopting the best-fit parameters of Ref. [5] and only modify the value of γ11. Doing so, one finds a 24% increase in the E1capture cross section at 0.3 MeV, implying an upward shift of the best estimate of the astrophysical Sfactor from SE1ð0.3Þ¼ 79 keV b [5] to SE1ð0.3Þ¼98 keV b. We are unable to obtain a satisfactory fit to the spectrum of Ref. [10] (χ2=N ¼114.9=79 ¼1.45,Pχ2>114.9¼0.005, Fig. 3right panel). Also, the channel radius preferred by the fit is significantly smaller (5.35 fm). Yet, we obtain P1γ2 11 ¼6.82 0.65ðstatÞμeV in fair agreement with Eq. (1). Given the discrepancies between the two spectra [34], it is a little surprising that we obtain almost agreeing values for P1γ2 11. As seen in Fig. 4, the dip around Eα¼ 1.0MeV is less pronounced in the spectrum of Ref. [10], and the main peak is slightly wider and shifted by −6keV relative to the spectrum of Ref. [5]. However, a detailed analysis reveals the agreement to be little more than a lucky coincidence: the less pronounced dip favors a larger γ11 value, but the downward energy shift has the opposite effect on γ11, so the two differences almost cancel out. (arb. units) α E/dNd 4− 10 3− 10 2− 10 1− 10 1-matrix fitR N Ref. [5] 16 (a) (MeV) α E 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Norm. residual 10− 5− 0 5 10 (b) -matrix fitR N Ref. [10] 16 (c) (MeV) α E 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 (d) FIG. 3. (a), (c) Rmatrix fits to the βα spectra of Refs. [5,10]. (b), (d) Normalized residuals. (MeV) α E 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 (arb. units) α E/dNd 3− 10 2− 10 1− 10 1 Ref. [5] Ref. [10] (a) 1.6 1.7 1.8 1.9 (b) FIG. 4. (a) Comparison of the R-matrix distributions determined from the βα spectra of Refs. [5,10]. (b) Zoom in on the maximum of the distribution. PHYSICAL REVIEW LETTERS 121, 142701 (2018) 142701-4 The spectrum obtained in the present work contains significantly fewer counts (1.07 ×104) than the spectra of Refs. [5,10] (1.03 ×106and 2.75 ×105), and hence does not impose any useful constraints on P1γ2 11. Our spectrum does, however, impose useful constraints on the position of the maximum of the R-matrix distribution. Taking into account the uncertainty on the energy calibration, the maximum is found to be consistent with Ref. [5], but shifted by 63keV relative to Ref. [10]. Apart from this small shift, our spectrum is consistent with both previous spectra as the level of statistics is insufficient to reveal the small discrepancies in the region around Eα¼1.0MeV. Thus, our analysis shows that the spectrum of Ref. [5] is both supported by the better fit quality and in better agreement with the energy calibration of the present spectrum. Sub-Coulomb α-transfer reactions provide an alternative route to determining P1γ2 11 by constraining the ANC of the 7.12 MeV level, which is related to γ11 via Eq. (44) in Ref. [1]. Adopting the most recent and most precise ANC value of ð4.39 0.59Þ×1028 fm−1[32] and assuming the channel radius to be 6.32 0.27 fm (the 68.3% confidence interval determined from the β-decay data, see the figure in the Supplemental Material [9]), we obtain P1γ2 11 ¼4.44  0.70 μeV in good agreement with Eq. (1). The weighted average of the two is 4.71 0.56 μeV, when statistical and systematic uncertainties are combined in quadrature, yielding a relative uncertainty of 12%. We note that the less precise ANCs obtained in three previous α-transfer studies are in good agreement with that of Ref. [32]. In conclusion, we have obtained the first accurate normalization of the β-delayed αspectrum of 16N and resolved a significant discrepancy between two previous high-precision measurements of the spectral shape. The branching ratio for β-delayed αemission is found to be 33% larger than previously held and the value of P1γ2 11 inferred from the βα spectrum is increased by the same factor. Our value for P1γ2 11 is in good agreement with the value inferred from sub-Coulomb α-transfer studies and has comparable precision. The weighted average of the two has an uncertainty of 12%. Since the dominant term in the expression for the E1capture cross section is proportional to P1γ2 11, our result implies that indirect measurements alone now constrain the E1capture cross section to within close to 12%, a remarkable result considering the large variability in the SE1ð0.3Þvalues reported over the last 60 years (Table IV of Ref. [1]). By further including direct measurements of the capture cross section as well as αscattering data it may be possible to reduce the uncertainty even further. Considering the progress made in recent years in constraining the other components of the 12Cðα;γÞcross section, it may finally be possible to bring the uncertainty on the total cross section at 0.3 MeV below 10%. We are grateful to the ISOLDE technical staff for providing excellent running conditions during the experiment, and thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the Letter. This work has been supported by the European Research Council under the ERC starting Grant Long Beamtime Experiments in Nuclear Astrophysics, No. 307447, the Horizon 2020 Research and Innovation Programme under Grant Agreement No. 654002, the Spanish Ministry of Economy and Competitiveness through Projects No. FPA2015-64969P, FPA2015-65035-P, and FPA2017-87568-P, the Romanian Institutul de Fizica Atomica Grant CERN/ISOLDE, the United Kingdom Science and Technology Facilities Council, the Fonds voor Wetenschappelijk OnderzoekVlaanderen (Belgium) and GOA/2010/010 (Bijzonder OnderzoeksFonds KU Leuven), the German Federal Ministry of Education and Research under Contract No. 05P15PKCIA (ISOLDE) and Verbundprojekt 05P2015. B. J. acknowledges support from The Royal Society of Arts and Sciences in Gothenburg and OSK from the Villum Foundation through Project No. 10117. *Corresponding author. [email protected] [1] R. J. deBoer et al.,Rev. Mod. Phys. 89, 035007 (2017). [2] H. O. U. Fynbo and C. A. Diget, Hyperfine Interact. 223, 103 (2014). [3] C. Tur et al.,Nucl. Instrum. Methods Phys. Res., Sect. A 594, 66 (2008). [4] T. Kib´edi, A. E. Stuchbery, G. D. Dracoulis, and K. A. Robertson, EPJ Web Conf. 35, 06001 (2012). [5] R. E. Azuma et al.,Phys. Rev. C 50, 1194 (1994). [6] F. C. Barker, Aust. J. Phys. 24, 771 (1971). [7] J. Humblet, B. W. Filippone, and S. E. Koonin, Phys. Rev. C 44, 2530 (1991). [8] L. Buchmann, G. Ruprecht, and C. Ruiz, Phys. Rev. C 80, 045803 (2009). [9] SeeSupplementalMaterialathttp://link.aps.org/supplemental/ 10.1103/PhysRevLett.121.142701 for details on the experimental resolution of the αspectrum, the Rmatrix parametrization, and the confidence limits analysis. [10] X. D. Tang et al.,Phys. Rev. C 81, 045809 (2010). [11] H. Hättig, K. Hünchen, and H. Wäffler, Phys. Rev. Lett. 25, 941 (1970). [12] R. H. France III, E. L. Wilds, J. E. McDonald, and M. Gai et al.,Phys. Rev. C 75, 065802 (2007). [13] R. Catherall et al.,J. Phys. G 44, 094002 (2017). [14] O. S. Kirsebom et al. (to be published). [15] J. Ramos et al.,Nucl. Instrum. Methods Phys. Res., Sect. B 320, 83 (2014). [16] H. Fynbo, O. S. Kirsebom, and O. Tengblad, J. Phys. G 44, 044005 (2017). [17] O. S. Kirsebom et al.,Phys. Rev. C 83, 065802 (2011). [18] K. I. Hahn, C. R. Brune, and P. R. Wrean, Phys. Rev. C 48, 914 (1993). [19] D. Tilley, H. Weller, and C. Cheves, Nucl. Phys. A564,1 (1993). [20] D. Tilley, H. Weller, C. Cheves, and R. Chasteler, Nucl. Phys. A595, 1 (1995). PHYSICAL REVIEW LETTERS 121, 142701 (2018) 142701-5 [21] M. Dombsky et al.,Phys. Rev. C 49, 1867 (1994). [22] C. Sotty and R. Lica (to be published). [23] W. J. Vermeer and A. R. Poletti, J. Phys. G 8, 743 (1982). [24] C. H. Millar, G. A. Bartholomew, and B. B. Kinsey, Phys. Rev. 81, 150 (1951). [25] B. J. Toppel, Phys. Rev. 103, 141 (1956). [26] D. E. Alburger, A. Gallmann, and D. H. Wilkinson, Phys. Rev. 116 (1959) 939. [27] E. K. Warburton, D. E. Alburger, and D. J. Millener, Phys. Rev. C 29, 2281 (1984). [28] A. R. Heath and G. T. Garvey, Phys. Rev. C 31, 2190 (1985). [29] W. Kaufmann and H. Wäffler, Nucl. Phys. 24, 62 (1961). [30] Z. Zhao, R. H. France, K. S. Lai, M. Gai, E. L. Wilds, R. A. Kryger, J. A. Winger, and K. B. Beard, Phys. Rev. C 48, 429 (1993). [31] J. Refsgaard et al.,Phys. Lett. B 752, 296 (2016). [32] M. L. Avila, G. V. Rogachev, E. Koshchiy, L. T. Baby, J. Belarge, K. W. Kemper, A. N. Kuchera, A. M. Mukhamedzhanov, D. Santiago-Gonzalez, and E. Uberseder, Phys. Rev. Lett. 114, 071101 (2015). [33] M. Munch, O. S. Kirsebom, and J. Refsgaard, 2018, DOI: 10.5281/zenodo.1174079. [34] Possible reasons for the discrepancies between the βα spectra of Refs. [5,10] are discussed in Ref. [8]. PHYSICAL REVIEW LETTERS 121, 142701 (2018) 142701-6