Background: The ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ reaction plays a crucial role in the proton-proton chain and Big Bang nucleosynthesis, affecting solar neutrino fluxes and primordial element abundances. Experimental data at astrophysical energies remain uncertain due to the extremely low cross sections.

Purpose: This work uses a microscopic potential-model approach to construct the ${}^3\mathrm{He}+\alpha$ potential from the $\text{nucleon}+\alpha$ interaction, aiming to describe low-energy elastic scattering and to calculate the astrophysical $S$ factor of the ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ reaction.

Method: The nucleon-nucleus potential is derived from self-consistent Skyrme Hartree-Fock (HF) calculations extended to the continuum. The ${}^3\mathrm{He}+\alpha$ potential is then obtained by folding the HF potential with the ${}^3\mathrm{He}$ density. A small number of scaling parameters is constrained by elastic-scattering data.

Result: The scaled Skyrme HF potential and folded potential simultaneously reproduce the low-energy $p+\alpha$ and ${}^3\mathrm{He}+\alpha s$-wave phase shifts, respectively. The calculated astrophysical $S$ factor of ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ shows good agreement with experimental data, yielding the recommended value $S_{34}\left(0\right)=0.610\pm 0.024$ keV b. A moderate sensitivity of $S_{34}\left(0\right)$ to the choice of projectile density is also observed in the folding procedure.

Conclusion: The Skyrme HF-based potential provides a unified and predictive microscopic framework for describing both elastic scattering and radiative capture in light nuclei.

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• Elastic scattering reactions
• H & He induced nuclear reactions
• Models & methods for nuclear reactions
• Nuclear astrophysics
• Nuclear reactions
• Radiative capture
• S-factor
• A ≤ 5