Session RD: Nuclear Astrophysics V

Monte-Carlo simulations of multi-specie relativistic thermalization and Analysis of Boltzmann Equation for Big bang nucleosynthesis

A fundamental assumption in BBN is that the nuclear velocity distributions obey Maxwell-Boltzmann (MB) statistics as they do in stars. Specifically, the BBN epoch is characterized by a dilute baryon plasma for which the velocity distribution of nuclei is mainly determined by the dominant Coulomb elastic scattering with mildly relativistic electrons. One must therefore deduce the momentum distribution for reacting nuclei from the multi-component relativistic Boltzmann equation. However, the full multi-component relativistic Boltzmann equation has only recently been analyzed and its solution has only been worked out in special cases. Moreover, a variety of schemes have been proposed that introduce non-thermal components into the BBN environment which can alter the thermal distribution of reacting nuclei. Here, we construct the relativistic Boltzmann equation in the context of BBN. We also perform relativistic Monte-Carlo simulations which clarify the baryon distribution during BBN and can be used to analyze any relaxation from a non-thermal injection. We will discuss the development and application of this simulation to explore the thermalization process in a relativistic multi-component environment. As an illustration we simulate the fully relativistic three-dimensional Brownian-motion-like solution to the thermalization of a high mass particle in a bath of relativistic low-mass particles. We follow the thermalization and ultimate equilibrium distribution of the Brownian-like particle as can happen in the cosmic plasma during Big bang nucleosynthesis. We show by these analyses that the thermalization process leads to a nuclear distribution function that remains very close to MB statistics even during the most relativistic environment relevant to BBN.~   

Lithium destruction in metal-poor halo stars and the cosmological lithium problem

The cosmological lithium problem refers to a shortcoming in the otherwise-successful theory of Big Bang nucleosynthesis (BBN); specifically, while BBN accurately predicts the primordial abundance of light elements such as H and He, the theory predicts there to be about three times more primordial $^7$Li than is actually observed. A possible explanation of this deficit is an insufficient understanding of stellar convective mechanisms in which $^7$Li could be destroyed via thermonuclear processes. We are specifically exploring convective overshoot and microturbulence in simulations of metal-poor halo stars as possible means of reproducing the predicted uniform factor of 3 reduction in primordial $^7$Li abundance.   

Measurement of highly excited states in ${}^9B$ for Big Bang Nucleosynthesis

The relative abundance of ${}^7Li$ to Standard Big Bang Nucleosynthesis (SBBN) calculations remains one of the major questions about the formation of the light elements. SBBN overestimates the abundance by a factor of 3 to 4, therefore channels of mass-7 destruction must be investigated. Of particular interest is the ${}^7Be+d \rightarrow {}^9B$ reaction channel, where the compound nucleus ${}^9B$ is unstable and decays to $2\alpha + p$. Using the ${}^{10}B({}^3He, \alpha){}^9B$ reaction with the Super Enge SplitPole Spectrograph (SESPS) at Florida State University, a high resolution measurement of the excited states in ${}^9B$ at BBN relevant energies was performed to better understand this system. The ${}^9B$ decay products were detected in coincidence by the Silicon Array for Branching Ratio Experiments (SABRE). Results and impact on BBN will be discussed.   

Elastic scattering of $^{\mathrm{3}}$He$+^{\mathrm{4}}$He with SONIK

Elastic scattering of $^{\mathrm{3}}$He$+^{\mathrm{4}}$He is important for a theoretical and phenomenological understanding of $^{\mathrm{4}}$He($^{\mathrm{3}}$He,$\gamma )^{\mathrm{7}}$Be, a key reaction in big bang nucleosynthesis and solar neutrino physics. The astrophysical S factor for this reaction is a dominant source of uncertainty in the prediction of $^{\mathrm{7}}$Be and $^{\mathrm{8}}$B solar neutrino flux using standard solar model. The elastic scattering measurements reported in the literature do not extend to low energies and lack proper uncertainty quantification. A new measurement of $^{\mathrm{4}}$He($^{\mathrm{3}}$He,$^{\mathrm{3}}$He)$^{\mathrm{4}}$He elastic scattering has been measured for 0.72 $\le $ E[$^{\mathrm{3}}$He] $\le $ 5.48 MeV using Scattering of Nuclei in Inverse Kinematics (SONIK) scattering chamber, a windowless, extended gas target surrounded by an array of 30 doubly-collimated silicon charged particle detectors situated at TRIUMF. Experimental techniques and the results from the experiment will be discussed. The results from the R-matrix analysis of the elastic scattering data will be presented.   

Determining the low-energy parameters for $^4$He($^3$He,$^3$He)$^4$He scattering using Bayesian methods

Measuring the cross-section for elastic scattering $^4$He($^3$He,$^3$He)$^4$He at solar energies; roughly between 20 to few hundred keV's has not been possible yet because the reaction is exponentially suppressed at this range. So, the solar model is shaped by extrapolating the results of data available at higher energies to solar energies. We employ Effective Field Theory(EFT) up to next-to-leading order(NLO) to model s- and p-waves. We employ Bayesian methods to extract the EFT parameters for these partial waves from the data published in Ref. [1] and from unpublished data recently taken using SONIK at TRIUMF [2]. We analyze the data up to a lab energy of 4.0 MeV after imposing a prior on the p-wave ANCs derived from data on the capture reaction $^3$He$(\alpha,\gamma)^7$Be. I will discuss our results for effective-range-theory parameters and compare them to a recent R-matrix analysis of the same data set [2]. I will also discuss methods to include EFT uncertainties in the Bayesian inference. [1] A. C. L. Barnard, C. M. Jones, and G. C. Phillips, “The scattering of $^3$He by $^4$He,”Nuclear Physics, vol. 50, pp. 629–640. [2] Somnath Paneru's talk, APS Meeting of Divison of Nuclear Physics, Fall 2020.   

Phenomenological R-Matrix Theory and Bayesian Inference

For many years, $\chi^2$ minimization has been the tool of choice for applying the phenomenological $R$-matrix theory. The need for comprehensive error estimates, more flexible statistical models, and the inclusion of prior information has driven progress in applying Bayesian inference to the $R$-matrix. While those projects have included sophisticated statistical models, they are limited to fairly simple $R$-matrix approximations. I will discuss recent efforts to expand the reach of Bayesian inference to much more complex $R$-matrix calculations. This has been achieved by coupling a Markov Chain Monte Carlo sampler to a high-performance $R$-matrix code, AZURE2. I will present the results of a benchmark calculation of $^{12}\rm{C}(p,\gamma)$ as well as recent developments in the analysis of $^3\rm{He}-^4\rm{He}$ scattering and capture. In particular, I will emphasize the usefulness and scope of the implementation as well as the importance of statistical modeling.   

A Bayesian R-matrix analysis of low-energy dt fusion

The dt fusion reaction ${}^2$H + ${}^3$H $\rightarrow$ ${}^4$He + n is important for nuclear fusion applications. It is also part of the BBN chain. There are several precise measurements of this cross section in the energy range 5-250 keV. These data sets are, however, not consistent with one another. We report on the use of Bayesian methods to analyze this data set, in the spirit of Ref. [1] . Employing the quoted point-to-point and common-mode errors from the original publications and a single-level R-matrix parameterization we find $S(40~{\rm keV})=26.57 \pm 0.06$ MeV $\cdot$ b, but with a poor $\chi^2$ per degree of freedom. We find that the point-to-point errors on some data sets must be inflated to obtain a statistically consistent data base. Different possibilities for the inflation yield consistent results for $S(40~{\rm keV})$, as does a three-level R-matrix parameterization. Our preliminary result is $S(40~{\rm keV})=25.48 \pm 0.17$ MeV $\cdot$ b, which is a lower central value and bigger error bar than Ref. [1]. The use of parallel tempering, and the elimination of redundant variables in the R-matrix parameterization allowed us to fully sample the posterior parameter probability density. \newline [1] R. S. de Souza {\it et al.}, Phys. Rev. C {\bf 99}, 014619 (2019)   

Reanalysis of $^{13}$N($p,\gamma $)$^{14}$O reaction and its role in stellar CNO cycle.

Within the framework of the modified potential cluster model with forbidden states, the $^{13}$N($p,\gamma $)$^{14}$O reaction rate and the astrophysical $S$-factor are considered. It is shown that the first $p^{13}$% N resonance determines the $S$-factor and contributions of the $M1$ and $E2$ transitions are negligible at energies $E<1$ MeV, but are significant at high energies. The $S$-factor strongly depends on the $^{3}S_{1}$ resonance parameters. The influence of the width of the $^{3}S_{1}$ resonance on $S$% -factor is demonstrated. Results of our calculations for the $^{13}$N($p,\gamma )^{14}$O reaction rate provide the contribution to the steadily improving reaction rate database libraries. Our calculations of the $^{13}$N($p,\gamma )^{14}$O reaction rate along with results for the rates of $^{14}$N($p,\gamma )^{15}$O and $^{12}$C$(p,\gamma )^{13}$N processes provide the temperature range $0.13 [Preview Abstract]

Using the 23Na(3He,d)24Mg Reaction to Reexamine Sodium Production in Globular Clusters

Globular clusters are gravitationally bound, compact collections of hundreds of thousands of stars. Our current theories of stellar evolution, however, cannot account for the observed anticorrelation between sodium and oxygen in cluster stars. While the astrophysical site of these so called abundance anomalies is still unknown, this chemical signature indicates the processing of stellar material by hydrogen burning at temperatures of $50 \text{-} 100$ MK. Unfortunately, many key thermonuclear reaction rates suffer from large uncertainties at these temperatures, including the critical sodium destroying reaction $^{23}$Na$(p, \gamma)^{24}$Mg. Using the Split-pole Spectrograph at Triangle Universities Nuclear Laboratory, we have measured the $^{23}$Na$(^3$He$,d)^{24}$Mg transfer reaction. Excited states in the astrophysical region of interest were observed and their energies deduced. Making use of novel analysis techniques, we were able to put constrains on level spins and extract spectroscopic factors with statistically rigorous uncertainties. These results indicate that the $^{23}$Na$(p, \gamma)$ reaction rate is significantly stronger than previously reported, increasing the destruction rate of sodium in stellar material.