Constraining the 22 Ne( α , γ ) 26 Mg and 22 Ne( α ,n) 25 Mg reaction rates using sub-Coulomb α -transfer reactions
H. Jayatissa, G.V. Rogachev, V.Z. Goldberg, E. Koshchiy, G. Christian, J. Hooker, S. Ota, B.T. Roeder, A. Saastamoinen, O. Trippella, S. Upadhyayula, E. Uberseder
CConstraining the Ne( α , γ ) Mg and Ne( α ,n) Mg reaction rates usingsub-Coulomb α -transfer reactions H. Jayatissa a,b,1, ∗ , G.V. Rogachev a,b,c, ∗ , V.Z. Goldberg b , E. Koshchiy b , G. Christian a,b,c,2 , J. Hooker a,b,3 , S. Ota b , B.T.Roeder b , A. Saastamoinen b , O. Trippella d , S. Upadhyayula a,b , E. Uberseder b a Department of Physics & Astronomy, Texas A&M University, College Station, TX 77843, USA b Cyclotron Institute, Texas A&M University, College Station, TX 77843, USA c Nuclear Solutions Institute, Texas A&M University, College Station, TX 77843, USA d Department of Physics and Geology, University of Perugia, and Instituto Nazionale di Fisica Nucleare, Secion of Perugia, Via A. Pascoli,06123 Perugia, Italy
Abstract
The Ne( α , γ ) Mg and Ne( α ,n) Mg reactions play an important role in astrophysics because they have significantinfluence on the neutron flux during the weak branch of the s-process. We constrain the astrophysical rates for thesereactions by measuring partial α -widths of resonances in Mg located in the Gamow window for the Ne+ α capture.These resonances were populated using Ne( Li,d) Mg and Ne( Li,t) Mg reactions at energies near the Coulombbarrier. At these low energies α -transfer reactions favor population of low spin states and the extracted partial α -widthsfor the observed resonances exhibit only minor dependence on the model parameters. The astrophysical rates for boththe Ne( α , γ ) Mg and the Ne( α ,n) Mg reactions are shown to be significantly different than the previously suggestedvalues.
Keywords: s-process, reaction rate, Ne( α , γ ) Mg, Ne( α ,n) Mg, sub-Coulomb α -transfer reaction
1. Introduction
The Ne( α ,n) Mg reaction is one of the two main neu-tron sources for the s-process - a slow neutron capture pro-cess that is responsible for the formation of about half ofthe elements beyond Fe [1, 2]. Due to the negative Q-value(-478 keV), this reaction is activated at relatively high tem-peratures ( > Ne( α ,n) Mg re-action dominates the neutron production. These highermass stars are expected to be the sites for the so calledweak s-process, which produces isotopes with mass up toA=90.The effectiveness of the Ne( α ,n) Mg reaction asa neutron source is influenced by the Ne( α , γ ) Mgradiative capture process. This reaction has a pos-itive Q-value, which enables it to be active duringthe entire He-burning phase, and thus it reduces the ∗ Corresponding authors
Email addresses: [email protected] (H. Jayatissa), [email protected] (G.V. Rogachev) Present address: Physics Division, Argonne National Labora-tory, Argonne, IL 60439, USA Present address: Department of Astronomy & Physics, SaintMary’s University, Halifax, NS B3H 3C3 Canada Present address: Department of Physics & Astronomy, Univer-sity of Tennessee, Knoxville, TN 37996, USA amount of Ne, that is mostly produced through the N( α , γ ) F( β + , ν ) O( α , γ ) Ne reaction sequence, beforethe Ne( α ,n) reaction comes into effect. Hence it is im-portant to constrain the rates for both of these reactions.Uncertainties for the Ne( α ,n) Mg and Ne( α , γ ) Mg reactions at stellar temperatures arestill large and dominated by the uncertainties associatedwith the properties of the resonances located within theGamow window. Several direct measurements of theexcitation functions for the Ne( α ,n) Mg reaction areavailable [3, 4, 5, 6, 7]. Two resonances play particularlyimportant role at temperatures around 0.3 GK, dominat-ing the reaction rate. These are the resonances at 11.32MeV and 11.17 MeV excitation energies in Mg. The( α ,n) strength of the 11.32 MeV resonance was obtainedin several direct experiments, but the results are notconsistent, ranging from ωγ ( α,n ) = 83(24) µ eV [7] to118(11) µ eV in the most recent study [4], to 234(77) µ eVin [3]. On the contrary, direct measurements of the ( α , γ )strength for the 11.32 MeV resonance produced consistentresults. Resonance strengths of 36(4) µ eV was obtainedin [8] and 46(12) µ eV in [9], with a weighted average of37(4) µ eV. The situation with 11.17 MeV resonance (orresonances) is even more complicated. A resonance at11.15 MeV was suggested in [3], but it was not observedin [4] and the upper limit for its resonance strength isgiven instead ( <
60 neV) [4]. It was conclusively demon-strated later that this state cannot contribute to the
Preprint submitted to Elsevier February 12, 2020 a r X i v : . [ nu c l - e x ] F e b -capture reaction because it has unnatural spin-parity1 + [10]. However, new resonances in the vicinity of 11.17MeV have recently been observed [11, 12, 13] and thecontribution of these new states to the α -capture on Nereaction rates is a source of uncertainty.There are many experiments that used indirect meth-ods to obtain information on the properties of the levels in Mg which could contribute to the astrophysically impor-tant Ne( α ,n) and Ne( α , γ ) reactions. The resonancereaction rates of the Ne( α ,n) Mg and Ne( α , γ ) Mgreactions are proportional to the partial α -widths of theresonances in Mg. The Ne( Li,d) α -transfer reactionhas been used in the past to populate the levels of in-terest in Mg [3, 11, 14]. The most recent and verydetailed work [11] utilized a Li beam of 82.3 MeV forthe Ne( Li,d) reaction, along with an α -particle beamof 206 MeV to populate states in Mg using ( α , α (cid:48) ) in-elastic scattering. The authors of Ref. [11] also sum-marize the results of several previous studies. An exten-sive amount of research has been performed previously us-ing other various techniques to obtain data on the reso-nance energies of Mg such as neutron capture studies on Mg (reactions such as Mg( n , γ ) Mg and Mg( n , tot ))[12, 15, 16], Mg(p,p (cid:48) ) Mg [17, 18], Mg(d,d’) Mgmeasurements [18], and Mg( α , α (cid:48) ) Mg measurements[11, 19]. Mg( γ , γ (cid:48) ) Mg measurements [10, 20, 21] havealso been performed using polarized and unpolarized γ rays in order to obtain information on the spin-paritiesof the levels of Mg. The γ -decaying states in Mg werestudied recently in Ref. [13] where the excitation ener-gies of the resonances within the Gamow window havebeen constrained with high precision and spin-parity as-signments were suggested for some states.It is difficult to evaluate the astrophysical importanceof resonances in Mg observed using indirect techniqueswithout knowledge of the spin-parities and the α partialwidths of the populated resonances. The angular distri-butions of the ( Li,d) reactions are not very sensitive tothe transferred angular momentum. Moreover, there is astrong dependence of the spectroscopic factors and angu-lar distributions upon the specific parameters of the op-tical model potentials used in the Distorted Wave BornApproximation (DWBA) analysis of the α -transfer reac-tions at high energies of the Li beam ( ∼
10 MeV/A) [22].The Mg( α , α (cid:48) ) reaction [11] may be used to characterizestates in Mg. However, due to high level density in Mgat excitation energies around 11 MeV, unique identifica-tion of states populated in different reactions is not alwayspossible.The present work explores the Ne( Li,d) and Ne( Li,t) reactions to obtain data on resonances in Mgin the Gamow window. Unlike previous studies, we per-formed these reactions at center-of-mass energies close tothe Coulomb barrier. While angular distributions are evenless sensitive to the transferred angular momentum atthese low energies, we expected to decrease the dependenceof the results on the optical potentials and to inhibit the levels that require large transferred angular momenta - thehigh spin states. Such states usually play a minor role inthe astrophysical processes.The α -transfer reactions at energies close to theCoulomb barrier have been performed previously [23, 24,25, 26]. It was demonstrated that this approach producesreliable results in determining the partial α -width for thenear α -threshold resonances [24].
2. Experiment
The Ne( Li,d) and Ne( Li,t) reactions were mea-sured using a 1.0 MeV/u Ne beam delivered by the K150cyclotron at the Texas A&M University Cyclotron Insti-tute. It corresponds to the Ne+ Li center-of-mass en-ergy of 4.7 MeV and 5.3 MeV for the Ne+ Li, whichis below the Coulomb barrier of ∼ ∼ µ g/cm thickness on ∼ µ g/cm Carbon back-ing, enriched to 95% of the Li isotope, and the Li targetswere made using natural Li. The energy loss of the Nebeam in the targets were mainly responsible for the finalenergy resolution of 95 keV in the deuteron and tritonspectra.We used the Multipole-Dipole-Multipole (MDM) spec-trometer [27] to observe deuterons scattered at 5 ◦ in thelab frame. The detection, identification and tracking oflight recoils (deuterons and tritons), filtered by the MDM,is provided by the modified Oxford focal plane trackingdetector [28] with the CsI(Tl) scintillator array installedat the end of Oxford detector for this experiment for betterparticle identification.A silicon detector, collimated to have an opening of 0.5 ◦ was placed in the target chamber at an angle of 31 ◦ relativeto the beam direction. It was used for absolute normal-ization, to monitor the possible target degradation, and tomeasure overall efficiency of the MDM spectrometer andthe focal plane detector. Using the Ne+ Li elastic scat-tering and also elastic scattering of 8 MeV deuteron beamon gold target, it was established that the efficiency of thesetup was 87%.
3. Results
Fig. 1 shows a deuteron energy spectrum from the Ne( Li,d) Mg reaction and a triton energy spectrumfrom the Ne( Li,t) Mg reaction measured at 5 ± ◦ lab.angle. The fields of the MDM spectrometer were set tomagnetic rigidity of deuteron/triton ions with energiesthat correspond to population of states in the Gamow en-ergy window for the Ne( α ,n) and Ne( α , γ ) reactions,2 .4 6.6 6.8 7 7.2 7.4 7.6 7.8Lab. Energy, MeV051015202530354045 C oun t s Mg (a) Li,d) Ne( C oun t s Mg (b) Li,t) Ne( Figure 1: Energy spectrum of (a) deuterons and (b) tritons from the Ne( Li,d) Mg and Ne( Li,t) Mg reactions respectively. between 10.7 and 11.5 MeV of Mg excitation. The tri-ton missing mass spectrum from the Ne( Li,t) Mg re-action was obtained with the aim of a general compari-son with the higher statistics deuteron spectrum from the Ne( Li,d) Mg reaction. Using the reconstructed ener-gies and angles of the deuteron/triton particles, the Q-value of the reaction was calculated and converted to theexcitation energies of Mg (Fig. 2).Four states have been observed in the missing massdeuteron spectrum from the Ne( Li,d) Mg reaction.The triton spectrum is consistent, while the countingstatistics are worse due to shorter measurement. The exci-tation energies, center-of-mass cross sections (at 5 ◦ in thelab.) and the extracted partial α -width (depending on theassumed spin-parity assignment) for the observed statesare given in Table 1.The Mg excitation energy spectra from both ( Li,d)and ( Li,t) reactions shows a similar dominance of a res-onance at 11.32 MeV and serves as an indication of thedominance of the same α -cluster transfer reaction mecha-nism. Out of the 4 resonances observed within the Gamow C oun t s = . a Q = . n Q Figure 2: The excitation energy spectrum of Mg reconstructedfrom the missing mass deuteron energy spectrum observed in Ne( Li,d) Mg reaction. The α and neutron decay thresholds areshown with vertical dashed lines. window, only the state at 11.32 MeV is above the neutrondecay threshold.The dominance of the 11.32 MeV peak withinthe Gamow window agrees with the most recent Ne( Li,d) Mg data [11]. In contrast, there is no evi-dence for the 11.17 MeV resonance that was observed asan equally strong state in Ref. [11]. A peak at 11.32 MeVwas also observed in Ne( Li,d) Mg at 32 MeV of Libeam [3], but the 11.17 MeV resonance is also absent. Weprovide a stringent upper limit for the partial α -width ofthe 11.17 MeV state in this work.The state at 11.08 MeV from the present study has beenpreviously reported by Talwar et. al [11] at 11.085(8)MeV. The 10.95 MeV state was also present in both ofthe previously mentioned ( Li,d) studies at 10.95 MeV in[3] and 10.951(21) MeV in [11], as well as in Ref. [14] at E x =10.953(21) MeV.The state at 10.83 MeV from the present study has alsobeen seen in two previous ( Li,d) studies, in Ref. [14] at E x = 10.808(20) MeV and in Ref. [11] at 10.822(10) MeV.
4. Analysis
Analysis of the α -transfer reaction cross sections wasperformed using Distorted Wave Born Approximation(DWBA) with code FRESCO [29]. We used global opticalpotentials taken from [30] for the Ne+ Li channel andfrom [31] for the Mg+d channel (shown in Table 2). Thepotential parameters for the α +d form factor were takenfrom Ref. [32]. The Ne+ α wave function was generatedby the Woods-Saxon potential with the shape parametersgiven in Table 2, and the depth was fit to reproduce thebinding energies of the states (see discussion below).To satisfy the Pauli exclusion principle, the minimum2 N + L values for the α -cluster in Mg are 8 and 9 forpositive and negative parity states respectively, where N is the number of radial nodes and L is the relative angular3 able 1: Excitation energies, adopted excitation energies, adopted resonances energies in center-of-mass, measured Ne( Li,d) Mg crosssections and partial α widths for the states in Mg observed in this work. The widths are given for 0 + ,1 − , and 2 + spin-parity assignments.The preferred spin-parity assignments are boldfaced (see text). Expt. column gives the power of ten. The statistical (first) and systematic(second) uncertainties are given for cross sections and partial α widths. a Adopted from the most recent direct measurement of Ne( α , γ ) by Hunt et. al [9] b The partial widths are the weighted averages between the ( Li,d) and ( Li,t) measurements from the present work. c Adopted from Lotay, et. al. [13] d Experimental cross section is normalized to Ne( Li, Li) elastic scattering at 31 ◦ lab. (118 ◦ c.m.) which was calculated using globaloptical model potential given in Table 2 (70 mb/sr, 70% of Rutherford). Uncertainty associated with the specific choice of optical modelpotentials is included into the systematic error budget. E ex Adopted E ex E r Exp. CS d J π Γ α Expt.(MeV) (MeV) (keV) ( µ b/sr) (eV)11.30(2) 11.3195(25) a a ± +13 − + ± ± b -51 − ± ± b -52 + ± ± b -611.17 11.1717(30) c c < . + < − < + < c c ± +4 − + ± ± − ± +0 . − . -10 + ± +1 . − . -1110.95(2) 10.9491(8) c c ± +6 − + ± +0 . − . -13 − ± +0 . − . -142 + ± +1 . − . -1510.83(2) 10.8226(30) c c ± +4 − + ± +1 . − . -211 − ± +0 . − . -21 + ± ± Table 2: Optical model parameters used in the FRESCO calculations for the Ne( Li,d) Mg reaction. The radii r x are given such that R x = r x × A / T . Reaction V r r a r W s W D r I a I r C V so r so a so Ref.Channel (MeV) (fm) (fm) (MeV) (MeV) (fm) (fm) (fm) (MeV) (fm) (fm) Ne+ Li 109.5 1.326 0.811 51.307 1.534 0.884 1.30 [30] Mg+d 93.293 1.149 0.756 1.394 1.339 0.559 1.303 [31]” 10.687 1.385 0.715 3.557 0.972 1.011 Ne+d 79.5 1.25 0.8 10.0 1.25 0.8 1.25 6.0 1.25 0.8 [31] α +d 85.0 1.25 0.68 1.25 [32] Ne+ α N + L =12 and 11 for positive and negative spin-parityassignment respectively, but the final partial α width ofthe states in Mg is insensitive to this choice. The spe-cific shape parameters for the form factor potentials alsohave little influence on the partial widths. This insensi-tivity to the parameters of the form-factor potentials is arather evident consequence of a peripheral nature of the α -transfer reaction at sub-Coulomb energy. Another conse-quence of sub-Coulomb energy is rather weak dependenceof the extracted partial width on the parameters of the op-tical model potentials, especially when absolute normaliza-tion is performed as a ratio to the elastic scattering crosssection.Note that all of the Mg states discussed in this workare above the α -decay threshold. Therefore, DWBA calcu-lations of the α -transfer to the continuum are, in principle,required. We use the bound-state approximation instead.The same approach was used in Ref. [24] and demon-strated to work well. For a bound state, an α -particleAsymptotic Normalization Coefficient ( C ) can be intro-duced. It is related to the reduced width as in Eq. 1a,where µ is a reduced mass, R is a channel radius, W is aWhittaker function, S ≡ S (cid:96) ( kR ) is a shift function, and P ≡ P (cid:96) ( kR ) is a penetrability function. Eq. 1a is evalu-ated at certain small binding energy between 0.1 and 1.0MeV. Eq. 1b relates the reduced width to the partial α width and is evaluated at the actual center-of-mass energyof the resonance, keeping the reduced width γ the samein both cases [34]. Partial α -widths are calculated for sev-eral binding energies and then extrapolated linearly to theactual energy of the resonance (to negative binding ener-gies). This extrapolation results in small width correctionthat does not exceed 20%.The partial α widths (Γ α ) for the 4 observed resonanceswere calculated using the Eq. 1b. The reduced widthswere evaluated by the Eq. 1a using the ANC values ( C )which were determined from the ratios of the FRESCODWBA calculations to the experimental cross sections. C = 2 µR (cid:126) W − η,l +1 / (2 kR ) γ γ dSdE (1a)Γ α = 2 γ P γ dSdE (1b)Only the 11.32 MeV resonance contributes to the Ne( α ,n) reaction since it is neutron unbound. For thisstate, the width is taken as a weighted average of the( Li,d) and ( Li,t) measurements. The Γ α found usingthe ( Li,t) measurement for the 11.32 MeV state agreeswithin error bars with the widths obtained for the samestate using the ( Li,d) measurement. The partial α -widthis largest for J π = 0 + spin-parity assignment and decreaseswith increasing transferred angular momentum. Moreover,the resonance strength, calculated by multiplying the par-tial α -width by the spin statistics factor (2J+1), is also largest for the J π = 0 + spin-parity assignment. The sys-tematic errors in Table 1 are dominated by the uncertain-ties associated with absolute normalization and theoreticaluncertainties associated with parametrization choices forthe DWBA calculations.No more than 2 counts can be attributed to a possi-ble state (or states) in the 11.16-11.18 MeV energy rangeobserved in recent experiments [11, 12, 13] (see Fig. 2).Using the resulting experimental cross section of 0.8 µ b/sr,an absolute upper limit for Γ α of the 11.17 MeV state iscalculated as 3 neV, assuming 557 keV c.m. and 0 + spin-parity assignment. Adopting a tentative spin-parity of 2 + [13] for this state would result in a limit of 13 peV.The reaction rates of the Ne( α ,n) Mg and Ne( α , γ ) Mg reactions are proportional to the res-onance strengths that are determined by the Γ α , spinsand the branching ratios of the resonances in Mgin the Gamow window. For low energy resonances(Γ α (cid:28) Γ n , Γ γ ), the resonance strength for neutronunbound states can be written as in Eqs. 2, whereasfor neutron bound states that contribute to the ( α, γ )reaction, the resonance strength is then ωγ ( α,γ ) ≈ (2 J +1)Γ α . ωγ ( α,n ) ≈ (2 J + 1) Γ α γ / Γ n (2a) ωγ ( α,γ ) ≈ (2 J + 1) Γ α n / Γ γ (2b)Combining the results of this work with the new exper-imental data for the ( Li,d) reaction obtained at energiesabove the Coulomb barrier [35] a stringent constraint onthe spin-parity assignment for the 11.32 MeV resonancecan be obtained. The main result of Ref. [35] is the di-rect measurement of the neutron to γ branching ratio forthe 11.32 MeV state - Γ n /Γ γ = 1.14(26) [35]. Using theweighted average between direct Ne( α, γ ) measurements( ωγ ( α,γ ) = 37(4) µ eV), the Γ α of the state can be calcu-lated using Eq. 2b. It is 79(13), 26(4), and 16(3) µ eVfor L = 0, 1 and 2, respectively. The Γ α for the 11.32MeV state from the present study (Table 1) is in agree-ment within error bars (1.1 σ ) with the widths calculatedfrom the direct Ne( α, γ ) measurements but only for the (cid:96) =0 case - yielding the likely 0 + spin-parity assignment forthe 11.32 MeV state. The (cid:96) =1 assignment would produce2.8 σ discrepancy, and the (cid:96) =2 would lead to 5.0 σ discrep-ancy. Therefore, 0 + is the highly favored spin-parity as-signment, but the 1 − still cannot be excluded and all otherspin-parity assignments are safely excluded for the 11.32MeV state in Mg.The weighted average ωγ ( α,γ ) = 37(4) µ eV for the 11.32MeV state from previous direct measurements [8, 9] alongwith Γ n / Γ γ = 1.14(26) from Ref. [35] in Eq. 2, resultsin a neutron decay strength ωγ ( α,n ) = 42(11) µ eV. Thisis within 1.7 σ of the minimum strength for this resonanceobtained in Ref. [7], but certainly disagrees with all other5irect measurements. If the Γ α (for (cid:96) =0) from the presentmeasurement and the Γ n / Γ γ from Ref. [35] are adopted,the ωγ ( α,n ) would be 32(7) µ eV, in good agreement withthe former approach (which results in ωγ ( α,n ) = 42(11) µ eV). However, this new ( α ,n) resonance strength for the11.32 MeV state is lower than previously reported valuesand results in significant reduction of the Ne( α ,n) Mgreaction rate. Ne( a ,n) Mg R a t e / Long l and Temperature, GK Ne( a , g ) Mg R a t e / Long l and Temperature, GK
Figure 3: Ratio of the updated (a) Ne( α ,n) Mg and (b) Ne( α , γ ) Mg reaction rates to the recommended Monte Carlorates of Longland, et al., [36]. The light grey band representsconservative uncertainties, and the dark grey band, shown for the Ne( α , γ ) Mg reaction only (b), corresponds to one σ deviation.See text for details. The overall effect of the new constrains for the partial α -widths of the resonances in the Gamow window on thereaction rates is demonstrated in Fig. 3. We show theratios of the new rates to the recommended rates fromLongland, et al. [36]. For the Ne( α ,n) Mg reaction(Fig. 3a) the dashed curve represents the rate calculatedusing the 11.32 MeV resonance strength of 32 µ eV (for 0 + assignment) and 10% of the upper limit of the resonancestrength for the 11.17 MeV resonance for the 2 + assign-ment suggested as tentative in Ref. [13]. The strength forthe higher lying states were adopted from [4]. The con-servative upper/lower limits (light grey band) correspondto 2 σ up/down deviation for the 11.32 MeV resonancestrength and to the upper limit (if 0 + ) and zero strengthfor the 11.17 MeV resonance respectively (assuming that11.17 MeV resonance decays only by neutron emission). The narrow-resonance approximation was used. For the Ne( α , γ ) Mg reaction we used only the states given inTable 1. Note that the upper limit for the strength of the11.17 MeV resonance obtained in this work is such thatfor the Ne( α , γ ) Mg reaction it makes little difference ifthe state is included or not. It is still true even if we makethe assumption that only γ -decay contributes to the de-excitation of this state. The conservative uncertainty band(grey region) corresponds to 2 σ deviation and simultane-ously extreme assumptions for the spin-parity assignment- all four states are 0 + for the upper limit and all states but11.32 MeV are 2 + states for the lower limit. The weightedaverage of the direct measurements was used for the ( α , γ )strength of the 11.32 MeV state - ωγ ( α,γ ) =37(4) µ eV. It isconsistent (within 1.1 σ ) with the value of 29(6) µ eV thatis obtained using Eq. 2b, the Γ α measured in this workand the Γ n /Γ γ ratio from [35]. The dark grey band in Fig.3(b) is a more realistic, 1 σ uncertainty with spin-parity as-signments for all states except for 11.32 MeV taken from[13] - 2 + /1 − /2 + /0 + for the 10.83/10.95/11.08/11.32 MeVstates respectively. Using the data on the partial α -widthsobtained in this work it becomes possible to tightly con-strain the Ne( α , γ ) Mg reaction rate, provided that thespin-parities of the resonances listed in Table 1 are reliablydefined. This highlights an urgent need to firmly estab-lish the spin-parities of the states in Table 1. The moresophisticated Monte Carlo analysis for the reaction ratesthat takes into account the results of this work, includesthe states observed in other studies, and also provides acomparison to the other “recommended” reaction rates isgiven in [35]. It is generally consistent with the rates shownin Fig. 3, except for the low energy part of the ( α ,n) ratebelow 0.25 GK, where the 11.112 MeV state, observed inRef. [12], potentially dominates the reaction rate. Thisresonance cannot be resolved from the 11.08 MeV state inour work, making it difficult to provide stringent limits onits strength. We do not include this state in our calcula-tions, but one should not forget that this state may playa major role at temperatures below 0.25 GK.
5. Conclusion
The Ne( Li,d) Mg and Ne( Li,t) Mg reactionswere studied with an aim to identify states in Mg thatcontribute to the Ne( α ,n) Mg and Ne( α , γ ) Mg reac-tion rates that are important nuclear physics inputs for theweak branch of the s-process. Unlike other similar studies,we explore the reaction at energies close to the Coulombbarrier, thus making the interpretation of the results lessmodel dependent. It was confirmed that the 11.32 MeVlevel in Mg provides the dominant contribution to the Ne( α ,n) Mg reaction rate at temperatures around 0.3GK. The analysis of the data from the present work, com-bined with the new results of Ref. [35] and previous directmeasurements of the Ne( α , γ ) Mg reaction showed thatthe most probable spin-parity assignment for this state is6 + , but 1 − still cannot be excluded. The Γ α values for thisstate were calculated (for spin-parity assignments 0 + , 1 − and 2 + ). While the α -particle reduced width of the 11.32MeV state appears to be large, indicating importance ofthe α -clustering for this α -capture reaction, it is still sig-nificantly smaller than most direct Ne( α ,n) Mg exper-iments indicate. Conversely, the partial α -width for the11.32 MeV state obtained in this work is in good agree-ment with the direct Ne( α , γ ) Mg measurements andthe Γ n /Γ γ ratio obtained in Ref. [35].The partial α -width for three more states within theGamow window for the Ne( α , γ ) Mg reaction - 10.823MeV, 10.949 MeV, and 11.081 MeV were obtained (assum-ing 0 + , 1 − , and 2 + spin-parity assignments). These valuesprovide additional constrains on the Ne( α , γ ) Mg reac-tion rate. Moreover, no evidence for a resonance (or res-onances) in the vicinity of 11.17 MeV has been observed.As a result, a stringent upper limit for a partial α -widthof resonances in this region was obtained. This is impor-tant in the context of recent experiments, in which severalnatural spin-parity resonances have been observed in thevicinity of 11.17 MeV [11, 12, 13]. Detailed discussionof implications for nuclear astrophysics will be presentedelsewhere.Another important result of this work is uncovering ofevident disagreement between the results of this indirectstudy with the direct Ne( α ,n) Mg measurements andconversely good agreement with the direct Ne( α , γ ) Mgmeasurements and the recent branching ratio study of Ref.[35]. This highlights the importance of repeating directstudies of the Ne( α ,n) Mg reaction to resolve this dis-crepancy.
Acknowledgements
The authors are grateful to the cyclotron team at theCyclotron Institute for consistently reliable operationand to Carl Brune (Ohio University) for reading themanuscript and making useful comments and suggestions.This research used targets provided by the Center forAccelerator Target Science at Argonne National Labo-ratory. The authors acknowledge that this material isbased upon their work supported by the U.S. Departmentof Energy, Office of Science, Office of Nuclear Science,under Award No. DE-FG02-93ER40773, and by NationalNuclear Security Administration through the Center forExcellence in Nuclear Training and University Based Re-search (CENTAUR) under grant No. de-na0003841, andthe Nuclear Solutions Institute at Texas A&M University.The authors G.V.R. and H.J. are also supported by theWelch Foundation (Grant No. A-1853). A special thanksgoes out to Dr. I. Thompson, Dr. Pang Yang, Dr. T.Belyaeva, Dr. Shubchintak, and Dr. A. Moro for thevaluable discussions of the FRESCO results.
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