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Register a new userFirst Accurate Normalization of the $beta$-delayed $alpha$ Decay of $^{16}$N and Implications for the $^{12}$C$(alpha,gamma)^{16}$O Astrophysical Reaction Rate
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The $^{12}text{C}(alpha,gamma){}^{16}text{O}$ 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 $alpha$ width, $gamma_{11}$, of the bound $1^-$ level in $^{16}$O is particularly important to determine the cross section. The magnitude of $gamma_{11}$ is determined via sub-Coulomb $alpha$-transfer reactions or the $beta$-delayed $alpha$ decay of $^{16}$N, but the latter approach is presently hampered by the lack of sufficiently precise data on the $beta$-decay branching ratios. Here we report improved branching ratios for the bound $1^-$ level [$b_{beta,11} = (5.02pm 0.10)times 10^{-2}$] and for $beta$-delayed $alpha$ emission [$b_{betaalpha} = (1.59pm 0.06)times 10^{-5}$]. Our value for $b_{betaalpha}$ is 33% larger than previously held, leading to a substantial increase in $gamma_{11}$. Our revised value for $gamma_{11}$ is in good agreement with the value obtained in $alpha$-transfer studies and the weighted average of the two gives a robust and precise determination of $gamma_{11}$, which provides significantly improved constraints on the $^{12}$C$(alpha,gamma)$ cross section in the energy range relevant to hydrostatic He burning.
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The ${}^{12}mathrm{C}(alpha,gamma){}^{16}mathrm{O}$ reaction plays a key role in the evolution of stars with masses of $M >$ 0.55 $M_odot$. The cross-section of the ${}^{12}mathrm{C}(alpha,gamma){}^{16}mathrm{O}$ reaction within the Gamow window ($E_textrm{c.m.}$ = 300 keV, $T_textrm9$ = 0.2) is extremely small (about $10^{-17}$ barn), which makes the direct measurement in a ground-based laboratory with existing techniques unfeasible. Up until now, the cross-sections at lower energies can only be extrapolated from the data at higher energies. However, two subthreshold resonances, located at $E_x$ = 7.117 MeV and $E_x$ = 6.917 MeV, make this extrapolation more complicated. In this work, the 6.917 MeV subthreshold resonance in the ${}^{12}mathrm{C}(alpha,gamma){}^{16}mathrm{O}$ reaction was investigated via the ${}^{12}mathrm{C}({}^{11}mathrm{B},{}^{7}mathrm{Li}){}^{16}mathrm{O}$ reaction. The experiment was performed using the Q3D magnetic spectrograph at the HI-13 tandem accelerator. We measured the angular distribution of the ${}^{12}mathrm{C}({}^{11}mathrm{B},{}^{7}mathrm{Li}){}^{16}mathrm{O}$ transfer reaction leading to the 6.917 MeV state. Based on the FRDWBA analysis, we derived the asymptotic normalization coefficient (ANC) of the 6.917 MeV level in $^{16}$O to be (1.10 $pm$ 0.29) $times 10^{10}$ fm$^{-1}$, with which the reduced $alpha$ width was computed to be $18.0pm4.7$ keV at the channel radius of 6.5 fm. Finally, we calculated the astrophysical $S_{E2}(300)$ factor of the ground-state transitions to be 46.2 $pm$ 7.7 keV b. The result for the astrophysical $S_{E2}(300)$ factor confirms the values obtained in various direct and indirect measurements and presents an independent examination of the most important data in nuclear astrophysics.
As suggested in a Comment by Peters, Phys. Rev. C {bf 96}, 029801 (2017), a correction is applied to the $^{13}$C($alpha$,n)$^{16}$O data of Harissopulos {it et al.}, Phys. Rev. C {bf 72}, 062801(R) (2005). The correction refers to the energy-dependent efficiency of the neutron detector and appears only above the ($alpha$,n$_1$) threshold of the $^{13}$C($alpha$,n)$^{16}$O reaction at about $E_alpha approx 5$ MeV. The corrected data are lower than the original data by almost a factor of two. The correction method is verified using recent neutron spectroscopy data and data from the reverse $^{16}$O(n,$alpha$)$^{13}$C reaction.
The elastic scattering $^{16}$O$+^{12}$C angular distributions at $^{16}$O bombarding energies of 100.0, 115.9 and 124.0 MeV and their optical model description including the $alpha$-particle exchange contribution calculated in the Coupled Reaction Channel approach are presented. The angular distributions show not only the usual diffraction pattern but also, at larger angles, intermediate structure of refractive origin on which finer oscillations are superimposed. The large angle features can be consistently described including explicitly the elastic $alpha$-transfer process and using a refractive optical potential with a deep real part and a weakly absorptive imaginary part.
It has been suggested that hydrogen ingestion into the helium shell of massive stars could lead to high $^{13}$C and $^{15}$N excesses when the shock of a core-collapse supernova passes through its helium shell. This prediction questions the origin of extremely high $^{13}$C and $^{15}$N abundances observed in rare presolar SiC grains which is usually attributed to classical novae. In this context $^{13}$N($alpha$,p)$^{16}$O the reaction plays an important role since it is in competition with $^{13}$N $beta^+$-decay to $^{13}$C. The $^{13}$N($alpha$,p)$^{16}$O reaction rate used in stellar evolution calculations comes from the CF88 compilation with very scarce information on the origin of this rate. The goal of this work is to provide a recommended $^{13}$N($alpha$,p)$^{16}$O reaction rate, based on available experimental data. Unbound nuclear states in the $^{17}$F compound nucleus were studied using the spectroscopic information of the analog states in $^{17}$O nucleus that were measured at the Alto facility using the $^{13}$C($^7$Li,t)$^{17}$O alpha-transfer reaction, and spectroscopic factors were derived using a DWBA analysis. This spectroscopic information was used to calculate a recommended $^{13}$N($alpha$,p)$^{16}$O reaction rate with meaningful uncertainty using a Monte Carlo approach. The present $^{13}$N($alpha$,p)$^{16}$O reaction rate is found to be within a factor of two of the previous evaluation, with a typical uncertainty of a factor 2-3. The source of this uncertainty comes from the three resonances at $E_r^{c.m.} = 221$, 741 and 959 keV. This new error estimation translates to an overall uncertainty in the $^{13}$C production of a factor of 50. The main source of uncertainty on the re-evaluated $^{13}$N($alpha$,p)$^{16}$O reaction rate currently comes from the uncertain alpha-width of relevant $^{17}$F states.
The $^{15}{rm N}(p,gamma)^{16}{rm O}$ reaction provides a path from the CN cycle to the CNO bi-cycle and CNO tri-cycle. The measured astrophysical factor for this reaction is dominated by resonant capture through two strong $J^{pi}=1^{-}$ resonances at $E_{R}= 312$ and 962 keV and direct capture to the ground state. Recently, a new measurement of the astrophysical factor for the $^{15}{rm N}(p,gamma)^{16}{rm O}$ reaction has been published [P. J. LeBlanc {it et al.}, Phys. Rev. {bf C 82}, 055804 (2010)]. The analysis has been done using the $R$-matrix approach with unconstrained variation of all parameters including the asymptotic normalization coefficient (ANC). The best fit has been obtained for the square of the ANC $C^{2}= 539.2$ fm${}^{-1}$, which exceeds the previously measured value by a factor of $approx 3$. Here we present a new $R$-matrix analysis of the Notre Dame-LUNA data with the fixed within the experimental uncertainties square of the ANC $C^{2}=200.34$ fm${}^{-1}$. Rather than varying the ANC we add the contribution from a background resonance that effectively takes into account contributions from higher levels. Altogether we present 8 fits, five unconstrained and three constrained. In all the fits the ANC is fixed at the previously determined experimental value $C^{2}=200.34$ fm${}^{-1}$. For the unconstrained fit with the boundary condition $B_{c}=S_{c}(E_{2})$, where $E_{2}$ is the energy of the second level, we get $S(0)=39.0 pm 1.1 $ keVb and normalized ${tilde chi}^{2}=1.84$, i.e. the result which is similar to [P. J. LeBlanc {it et al.}, Phys. Rev. {bf C 82}, 055804 (2010)]. From all our fits we get the range $33.1 leq S(0) leq 40.1$ keVb which overlaps with the result of [P. J. LeBlanc {it et al.}, Phys. Rev. {bf C 82}, 055804 (2010)]. We address also physical interpretation of the fitting parameters.
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