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Primordial deuterium abundance from calculations of $p(n,γ)$ and $d(p,γ)$ reactions within potential-model approach

Nguyen Le Anh, Dao Nhut Anh, Hoang Thai An, Nguyen Gia Huy, Bui Minh Loc

Abstract

The $p(n,γ)$ and $d(p,γ)$ reactions are key nuclear inputs for Big Bang nucleosynthesis. In this work, both reactions are analyzed within a consistent two-body potential framework based on the Malfliet-Tjon interaction, including contributions from both $E1$ and $M1$ transitions. A single scaling factor $λ$ controlling the low-energy scattering dynamics is constrained by the $p(n,γ)$ and propagated consistently to the $d(p,γ)$. The obtained abundance, $\mathrm{D/H} = 2.479^{+0.350}_{-0.177}\times 10^{-5}$, is in good agreement with values inferred from metal-poor damped Lyman-$α$ systems. The modest variations of $λ$ lead to a significant change in the predicted $\mathrm{D/H}$ ratio and light-element abundances.

Primordial deuterium abundance from calculations of $p(n,γ)$ and $d(p,γ)$ reactions within potential-model approach

Abstract

The and reactions are key nuclear inputs for Big Bang nucleosynthesis. In this work, both reactions are analyzed within a consistent two-body potential framework based on the Malfliet-Tjon interaction, including contributions from both and transitions. A single scaling factor controlling the low-energy scattering dynamics is constrained by the and propagated consistently to the . The obtained abundance, , is in good agreement with values inferred from metal-poor damped Lyman- systems. The modest variations of lead to a significant change in the predicted ratio and light-element abundances.
Paper Structure (10 sections, 18 equations, 3 figures, 5 tables)

This paper contains 10 sections, 18 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Potential-model approach
  3. Cross section
  4. Interaction potential
  5. Nuclear reaction rate
  6. Results and discussion
  7. Cross section of $p(n,\gamma)$ reaction
  8. Astrophysical $S$ factor of $d(p,\gamma)$ reaction
  9. Reaction rates and light-element abundances
  10. Conclusions

Figures (3)

  • Figure 1: Cross section of $p(n,\gamma)$ reaction below $1$ MeV. The solid line represents the total calculated cross section, while the dashed and dotted lines show the $E1$ and $M1$ contributions, respectively. Experimental data from Suzuki et al.suzuki1995 (circles) and Nagai et al.nagai1997 (square) are included for comparison. The dashed-dotted curve shows the $\chi$EFT calculation acharya2022. The shaded band shows the theoretical uncertainty obtained by varying the scaling factor $\lambda = 0.734 \pm 0.023$.
  • Figure 2: Astrophysical $S$ factor of $d(p,\gamma)$ reaction below $2$ MeV. The results are compared to experimental data casella2002mossa2020griffiths1963warren1963bailey1970schmid1995ma1997bystritsky2015tisma2019turkat2021 and the ab initio calculation marcucci2016. The scaling factor is $\lambda = 1.470 \pm 0.046$.
  • Figure 3: Primordial deuterium abundance $\mathrm{D}/\mathrm{H}$ as a function of the ratio $\lambda_{\mathrm{dpg}}/\lambda_{\mathrm{png}}$ obtained in the present work. The shaded band indicates the observational constraint from Cooke et al.cooke2018, while the vertical dashed line marks the central value $\lambda_{\mathrm{dpg}}/\lambda_{\mathrm{png}} = 2$.