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Study of few $^3$He-induced nuclear fusion reactions using density-dependent double-folding complex potential

N. Mohammad, H. Sultana, Md. R. Islam, Md. A. Khan

TL;DR

The paper addresses sub-barrier fusion cross-sections for light nuclei relevant to primordial nucleosynthesis. It adopts a microscopic density-dependent double-folding potential using the M3Y-Reid nucleon-nucleon interaction within the Selective Resonant Tunnelling Model (SRTM) to compute the astrophysical S-factor $S(E)$ and fusion cross-sections $σ(E)$ for three $^{3}$He-induced reactions: $^{3}$He($^3$He,2p)$^{4}$He, $^{6}$Li($^3$He,d)$^{7}$Be, and $^{10}$B($^3$He,n)$^{12}$N. The results align with experimental data across sub-barrier energies, with adjustable boundary parameters at the matching radius and Woods-Saxon densities underpinning the folding potential. This microscopically grounded framework provides a predictive tool for astronuclear reaction rates and can be extended to heavier systems and more complex reaction channels, improving nucleosynthesis modeling in stars.

Abstract

Nuclear fusion reactions at sub-barrier energies play crucial roles in many aspects of primordial nucleosynthesis in stellar objects. One of the primary aspects that plays a pivotal role in understanding the relationship between stellar evolution and nuclear reaction dynamics is the energy dependence of astronuclear observables, such as the fusion cross-section $σ$. This paper presents the results of a few $^3$He-induced nuclear fusion reactions-$^{3}$He($^3$He,2p)$^{4}$He, $^{6}$Li($^3$He,d)$^{7}$Be and $^{10}$B($^3$He,n)$^{12}$N which are investigated adopting the single-step selective resonant tunnelling model (SRTM). As an improvement over earlier works, the authors have used a microscopically derived density-dependent double-folding potential model, invoking the M3Y-Reid NN interactions, for the numerical computation of the astrophysical S-factor, $S(E)$, and the fusion cross-section, $σ$. The results of the calculations have been compared with those found in the literature. The results obtained in the present studies agree fairly with the experimentally observed results found in the literature.

Study of few $^3$He-induced nuclear fusion reactions using density-dependent double-folding complex potential

TL;DR

The paper addresses sub-barrier fusion cross-sections for light nuclei relevant to primordial nucleosynthesis. It adopts a microscopic density-dependent double-folding potential using the M3Y-Reid nucleon-nucleon interaction within the Selective Resonant Tunnelling Model (SRTM) to compute the astrophysical S-factor and fusion cross-sections for three He-induced reactions: He(He,2p)He, Li(He,d)Be, and B(He,n)N. The results align with experimental data across sub-barrier energies, with adjustable boundary parameters at the matching radius and Woods-Saxon densities underpinning the folding potential. This microscopically grounded framework provides a predictive tool for astronuclear reaction rates and can be extended to heavier systems and more complex reaction channels, improving nucleosynthesis modeling in stars.

Abstract

Nuclear fusion reactions at sub-barrier energies play crucial roles in many aspects of primordial nucleosynthesis in stellar objects. One of the primary aspects that plays a pivotal role in understanding the relationship between stellar evolution and nuclear reaction dynamics is the energy dependence of astronuclear observables, such as the fusion cross-section . This paper presents the results of a few He-induced nuclear fusion reactions-He(He,2p)He, Li(He,d)Be and B(He,n)N which are investigated adopting the single-step selective resonant tunnelling model (SRTM). As an improvement over earlier works, the authors have used a microscopically derived density-dependent double-folding potential model, invoking the M3Y-Reid NN interactions, for the numerical computation of the astrophysical S-factor, , and the fusion cross-section, . The results of the calculations have been compared with those found in the literature. The results obtained in the present studies agree fairly with the experimentally observed results found in the literature.

Paper Structure

This paper contains 4 sections, 27 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction:
  2. Theoretical Framework:
  3. Results and Discussions:
  4. Summary and conclusions:

Figures (4)

  • Figure 1: Coordinates used in double-folding nucleus-nucleus potential of the colliding system.
  • Figure 2: Upper panel: Comparison of computed S-factor data with experimentally observed data reported by Kudomi et. al. (2004)kudomi-2004 Lower panel: Comparison of computed fusion cross-section data with experimentally measured data reported by Kudomi et. al. (2004)kudomi-2004 for $^{3}$He($^3$He,2p)$^{4}$He reaction.
  • Figure 3: Upper panel: Astrophysical S-factor computed by using SRTM formula (Eq.(\ref{['sf']})). Lower panel: Comparison of computed fusion cross-section data with experimentally measured data reported by Barr and Gilmore (1965)barr-1965 for $^{6}$Li($^3$He,d)$^{7}$Be reaction.
  • Figure 4: Upper panel: Astrophysical S-factor computed by using SRTM formula (Eq.(\ref{['sf']})). Lower panel:Comparison of computed fusion cross-section data with experimentally measured data reported by Glass and Peterson (1963)glass-1963 for $^{10}$B($^3$He,n)$^{12}$N reaction.