Astrophysical ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ and ${}^3\mathrm{H}(\alpha ,\gamma {)}^7\mathrm{Li}$ direct capture reactions in a potential model approach

Abstract

The astrophysical ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ and ${}^3\mathrm{H}(\alpha ,\gamma {)}^7\mathrm{Li}$ direct capture processes are studied in the framework of the two-body model with the potentials of a simple Gaussian form, which describe correctly the phase-shifts in the s-, p-, d-, and f-waves, as well as the binding energy and the asymptotic normalization constant of the ground $p_{3/2}$ and the first excited $p_{1/2}$ bound states. It is shown that the E1-transition from the initial s-wave to the final p-waves is strongly dominant in both capture reactions. On this basis the s-wave potential parameters are adjusted to reproduce the new data of the LUNA collaboration around 100 keV and the newest data at the Gamov peak estimated with the help of the observed neutrino fluxes from the Sun, $S_{34}$(23${}_{-5}^{+6}$ keV)=0.548$\pm$0.054 keV b for the astrophysical S-factor of the capture process ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$. The resulting model describes well the astrophysical S-factor in low-energy Big Bang nucleosynthesis region of 180-400 keV, however has a tendency to underestimate the data above 0.5 MeV. Two-body potentials, adjusted on the properties of the ${}^7$Be nucleus, ${}^3\mathrm{He}+\alpha$ elastic scattering data and the astrophysical S-factor of the ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ direct capture reaction, are able to reproduce the properties of the ${}^7$Li nucleus, the binding energies of the ground 3/2${}^{-}$ and first excited 1/2${}^{-}$ states, and phase shifts of the ${}^3\mathrm{H}+\alpha$ elastic scattering in partial waves. Most importantly, these potential models can successfully describe both absolute value and energy dependence of the existing experimental data for the mirror astrophysical ${}^3\mathrm{H}(\alpha ,\gamma {)}^7\mathrm{Li}$ capture reaction without any additional adjustment of the parameters.

22 pages, 8 figures, 2 tables

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Cited by in corpus (7)

• ${}^7$Be and ${}^7$Li nuclei within the no-core shell model with continuum
• Theoretical study of the direct $\alpha +d$ $\to$ ${}^6$Li + $\gamma$ astrophysical capture process in a three-body model II. Reaction rates and primordial abundance
• Solar fusion III: New data and theory for hydrogen-burning stars
• Analysis of the ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ and ${}^3\mathrm{H}(\alpha ,\gamma {)}^7\mathrm{Li}$ astrophysical direct capture reactions in a modified potential-model approach
• New Theoretical Results for Radiative 3H(p, γ)4He, 3He(2H, γ)5Li, 4He(2H, γ)6Li, 4He(3H, γ)7Li, and 4He(3He, γ)7Be Captures At Astrophysical Energies
• Astrophysical S factor and rate of ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ direct capture reaction in a potential model
• ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ and ${}^3\mathrm{H}(\alpha ,\gamma {)}^7\mathrm{Li}$ reaction rates and the implication for Big Bang nucleosynthesis in the potential model