Session CD: Nuclear Astrophysics: Reaction Rates of Light Nuclei

Reaction Rate Uncertainties using R-matrix: 3He(a,g) and 12C(a,g)

Many of the reaction rates involving light nuclei in the $pp$ chains and the CNO cycles are heavily influenced by short lived nuclear states. These states manifest as broad resonance structures observed in the cross sections of low energy reaction data. Because of the Coulomb repulsion between the two charged particles, the low energy cross section is often too small to be measure directly in the laboratory. For this reason, experimental measurements are made at higher energies, and then extrapolated down to the energy region of astrophysical interest. The energy dependence of the experimentally measured cross sections may be described using $R$-matrix theory. While $R$-matrix theory has proved to be quite successful, it is often difficult to extract uncertainties from the mathematically complicated framework. To illustrate these points, $R$-matrix analysis for the reactions $^3$He$(\alpha,\gamma)^7$Be and $^{12}$C$(\alpha,\gamma)^{16}$O will be described. A Monte Carlo uncertainty analysis is performed in order to extract statistically meaningful uncertainties. To find the total rate uncertainty, the $R$-matrix MC analysis can be combined with an MC analysis for the narrow resonance contributions using, for example, the Starlib code RatesMC.   

New Triple-\boldmath$\alpha$ Reaction Rates from the Second \boldmath$J^\pi=2^+$ State in \boldmath${}^{12}\mathrm{C}$

The second $J^\pi = 2^+$ state in ${}^{12}\mathrm{C}$, recently identified near 10~MeV in the ${}^{12}\mathrm{C}$($\gamma$,$\alpha$)${}^{8}\mathrm{Be}$ reaction [1], can affect the triple-$\alpha$ reaction rates at high temperatures. These rates can determine the outcome of nucleo\-synthesis during supernovae and other explosive astrophysical scenarios. We present new high-temperature triple-$\alpha$ reaction rates calculated by including the $2^+$ state near 10~MeV\@. Simulations of explosive nucleo\-synthesis which include the $\nu p$ process are being performed to investigate the possible implication of these new rates on the production of heavy elements during core-collapse supernovae.\\[4pt] [1] W.~R.~Zimmerman \emph{et al.}, Phys.\ Rev.\ Lett.\ \textbf{110}, 152502 (2013)   

Direct Measurements of the $^{23}$Na($\alpha$,p)$^{26}$Mg reaction cross section at energies relevant for the production of galactic $^{26}$Al

In the convective C/Ne burning shell of massive pre-supernova stars, the $^{23}$Na($\alpha$,p)$^{26}$Mg reaction is one of the main sources of protons for the $^{25}$Mg(p,$\gamma$)$^{26}$Al reaction, which is the primary direct process for $^{26}$Al production in this environment. A recent study found that a factor of 10 increase in the $^{23}$Na($\alpha$,p)$^{26}$Mg reaction rate corresponds to a factor of 3 change in the final abundance of $^{26}$Al for this particular scenario. No reliable experimental information exists at appropriate astrophysical energies. The recommended rate is based on a statistical model. We have performed a direct measurement of the $^{23}$Na($\alpha$,p)$^{26}$Mg reaction cross section using inverse kinematics with a $^{23}$Na beam from ATLAS, a cryogenic $^4$He gas target, and an array of Double Sided Silicon Detectors. Integrated cross sections for the reactions $^{23}$Na($\alpha$,p$_{0}$)$^{26}$Mg and $^{23}$Na($\alpha$,p$_{1}$)$^{26}$Mg$^{*}$ have been extracted for the first time at astrophysically relevant energies(E$_{cm}$ = 1.84 MeV to 2.63 MeV). The corresponding stellar reaction rate has been recalculated and compared with the statistical model recommended rate.   

($\alpha$,p) Measurements with ANASEN

Certain ($\alpha$,$p$) reaction rates are important for understanding energy generation and light curves of X-Ray bursts. Only two ($\alpha$,$p$) reactions, $^{14}$O($\alpha$,$p$) and $^{18}$Ne($\alpha$,$p$), have had direct experimental investigation. Some investigations have measured inverse ($p$,$\alpha$) reactions which measure the ground state branch of the ($\alpha$,$p$) rate. Other reactions have provided information on resonance parameters using stable beam transfer reactions. However large uncertainties remain on ($\alpha$,$p$) reaction rates. ANASEN (The Array for Nuclear Astrophysics and Structure with Exotic Nuclei) is an extended gas target charged particle detector array. ANASEN has demonstrated the capability to directly measure the excitation functions of ($\alpha$,$p$) reactions in inverse kinematics with a stable beam test, and we have performed our first experiment with radioactive beam of $^{18}$Ne at FSU. In this talk the performance of ANASEN will be presented along with preliminary results.   

Measurement and $R$-matrix Analysis of $^{14}$N(p,$\gamma)^{15}$O for the CNO Cycle

The CNO cycle is the primary energy source for stars more massive than the Sun during hydrogen burning. The energy producing cycle uses heavy nuclei as catalysts in order to convert four protons into an alpha particle. $^{14}$N(p, $\gamma)^{15}$O is the slowest reaction in this cycle, thus it governs the time scale and the energy generation rate of the whole cycle. It also plays an important role in the determination of the age of globular clusters. Previous measurements and analysis of this reaction lead to different astrophysical $S$-factors due to the uncertainties in the $R$-matrix fit to the cross section data at higher energies. To better constrain the extrapolation, measurements were made of the excitation functions and angular distribution cross sections over a proton beam energy range from 0.5 MeV to 3.6 MeV. A multichannel $R$-matrix analysis including both the elastic scattering and the $^{14}$N(p, $\gamma)^{15}$O data has been performed using the code AZURE. The new analysis provides better constraints for the extrapolation of the astrophysical $S$-factor towards stellar energies.   

Measurements of interest to $^{18}$F nucleosynthesis with the JENSA gas-jet target

The observation of $^{18}$F decay in novae would provide a direct test of nova models. To interpret such observations, the nuclear reactions that create and destroy $^{18}$F in novae must be understood. The destruction primarily occurs through the $^{18}$F($p,\alpha$)$^{15}$O reaction via resonances from states in $^{19}$Ne. Significant uncertainties remain concerning the properties of these states near the proton threshold at 6411 keV. We will use the JENSA (Jet Experiments in Nuclear Structure and Astrophysics) gas jet target at Oak Ridge National Laboratory to study these levels via the $^{20}$Ne($p,d$)$^{19}$Ne reaction. In the longer term, we plan to study one of the primary reactions for $^{18}$F creation, the $^{17}$F($p,\gamma$)$^{18}$Ne reaction, by bombarding localized $^{3}$He targets in JENSA with radioactive $^{17}$F beams produced at the ReA3 facility at the National Superconducting Cyclotron Laboratory. The ($^{3}$He,d) reaction will be measured on $^{17}$F beams to constrain the $^{17}$F($p,\gamma$)$^{18}$Ne direct capture rate at nova temperatures. The JENSA target along with first results and future plans will be presented.   

Cross Section Measurement of the $^{12}$C($^{6}$Li, d)$^{16}$O Reaction and the $^{12}$C($\alpha $, $\gamma )^{16}$O Reaction

The $^{12}$C($\alpha $, $\gamma)^{16}$O reaction is a very important reaction for the understanding of the helium burning in massive stars. However, despite many experimental studies, the low-energy cross-section of the $^{12}$C($\alpha $, $\gamma )^{16}$O reaction remains highly uncertain. In view of the importance of $^{12}$C($\alpha $, $\gamma )^{16}$O reaction, a new determination of the $^{12}$C($\alpha $, $\gamma )^{16}$O reaction cross-section has been performed via a measurement of the transfer reaction $^{12}$C($^{6}$Li, d)$^{16}$O at the Edwards Accelerator Laboratory at Ohio University. The differential cross-section of the $^{12}$C($^{6}$Li, d)$^{16}$O reaction has been measured to the 0$^{+}$ (6.05 MeV), 3$^{-}$ (6.13 MeV), 2$^{+}$ (6.92 MeV), and 1$^{-}$ (7.12 MeV) states of $^{16}$O with $^{6}$Li beams of 3-, 4-, and 5-MeV. The cross-section measurements were done by detecting the deuterons. The time of flight method was used to separate the different particles.   

$^{25}$Na studied in the $^{9}$Be($^{18}$O,pn) reaction

$^{25}$Na was produced via the $^{9}$Be($^{18}$O,pn) reaction which favored the production of higher spin states. Three new states have been discovered as well as ten new gamma rays and a doublet of states has been resolved through high resolution gamma ray spectroscopy. Observed states have been analyzed using the Doppler shift attenuation method and angular distributions of the gamma decays have been measured leading to new spin assignments. Experimental results have been compared to theoretical results from the Cosmo shell-model code.