Implication of the proton-deuteron radiative capture for Big Bang Nucleosynthesis

TL;DR

The predicted theoretical value for ^{2}H/H is in excellent agreement with its experimental determination, using the most recent determination of the baryon density of the Planck experiment, and with a standard number of relativistic degrees of freedom N_{eff}=3.046 during primordial nucleosynthesis.

Abstract

The astrophysical $S$-factor for the radiative capture $d(p,γ)^3$He in the energy-range of interest for Big Bang Nucleosynthesis (BBN) is calculated using an {\it ab-initio} approach. The nuclear Hamiltonian retains both two- and three-nucleon interactions - the Argonne $v_{18}$ and the Urbana IX, respectively. Both one- and many-body contributions to the nuclear current operator are included. The former retain for the first time, besides the $1/m$ leading order contribution ($m$ is the nucleon mass), also the next-to-leading order term, proportional to $1/m^3$. The many-body currents are constructed in order to satisfy the current conservation relation with the adopted Hamiltonian model. The hyperspherical harmonics technique is applied to solve the $A=3$ bound and scattering states. A particular attention is used in this second case in order to obtain, in the energy range of BBN, an uncertainty on the astrophysical $S$-factor of the order or below $\sim$1 %. Then, in this energy range, the $S$-factor is found to be $\sim$10 % larger than the currently adopted values.Part of this increase (1-3 %) is due to the $1/m^3$ one-body operator, while the remaining is due to the new more accurate scattering wave functions. We have studied the implication of this new determination for the $d(p,γ)^3$He $S$-factor on deuterium primordial abundance. We find that the predicted theoretical value for $^2$H/H is in excellent agreement with its experimental determination, using the most recent determination of baryon density of Planck experiment, and with a standard number of relativistic degrees of freedom $N_{\rm eff}=3.046$ during primordial nucleosynthesis.

Figures (2)

• Figure 1: (Color online) The astrophysical $S$-factor obtained in the present work (magenta up-triangles) is plotted together with the available experimental data of Refs. Gri62Sch96Ma97LUNA02, the calculation of Ref. Mar05 (solid black line), and the quadratic best fit to the data of Ref. Ade11 (green band). The inset shows the astrophysical $S$-factor in the 0-300 keV energy range, of relevance for BBN.
• Figure 2: (Color online) The likelihood contours (68, 95 and 99 % C.L.) in the $\Omega_b h^2$-$N_{\rm eff}$ plane from $^2$H/H, with the Planck 2015 prior on $\Omega_b h^2$, a free $N_{\rm eff}$ and using the experimental result of Ref. Coo14. The triangle is the best fit value of Planck 2015 results for these parameters, with corresponding 68% C.L. error bars Planck2015.