{
  "id": "2310.20255",
  "version": "v1",
  "published": "2023-10-31T08:20:46.000Z",
  "updated": "2023-10-31T08:20:46.000Z",
  "title": "New ANCs for $α+ {}^{12}{\\rm C}$ synthesis obtained using extrapolation method and the $S$-factor for ${}^{12}{\\rm C}(α,γ){}^{16}{\\rm O}$ radiative capture",
  "authors": [
    "A. M. Mukhamedzhanov",
    "R. J. deBoer",
    "B. F. Irgaziev",
    "L. D. Blokhintsev",
    "A. S. Kadyrov",
    "D. A. Savin"
  ],
  "categories": [
    "nucl-th",
    "astro-ph.SR"
  ],
  "abstract": "Background: The $^{12}{\\rm C}(\\alpha,\\gamma)^{16}$O reaction, determining the survival of carbon in red giants, is of interest for nuclear reaction theory and nuclear astrophysics. Numerous attempts to obtain the astrophysical factor of the $^{12}{\\rm C}(\\alpha,\\gamma)^{16}$O reaction, both experimental and theoretical, have been made for almost 50 years. The specifics of the $^{16}$O nuclear structure is the presence of two subthreshold bound states, (6.92 MeV, 2$^+$) and (7.12 MeV, 1$^-$), dominating the behavior of the low-energy $S$-factor. The strength of these subthreshold states is determined by their asymptotic normalization coefficients (ANCs) which need to be known with high accuracy. Recently, using the model-independent extrapolation method, Blokhintsev {\\it et al.} [Eur. Phys. J. A {\\bf 59}, 162 (2023)] determined the ANCs for the three subthreshold states in $^{16}$O. Purpose: In this paper, using these newly determined ANCs, we calculated the low-energy astrophysical $S$-factors for the $^{12}{\\rm C}(\\alpha,\\gamma)^{16}$O radiative capture. Method: The $S$-factors are calculated within the framework of the $R$-matrix method using the AZURE2 code. Conclusion: Our total $S$-factor includes the resonance $E1$ and $E2$ transitions to the ground state of $^{16}$O interfering with the corresponding direct captures and cascade radiative captures to the ground state of $^{16}$O through four subthreshold states: $0_2^+,\\,3^-,\\, 2^+$ and $1^-$. Since our ANCs are higher than those used by deBoer {\\it et al.} [Rev. Mod. Phys. {\\bf 89}, 035007 (2017)], the present total $S$-factor at the most effective astrophysical energy of 300 keV is 174 keVb versus 137 keVb of that work. Accordingly, our calculated reaction rate at low temperatures ($T_{9} < 2$) is higher than the one given in the aforesaid paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-31T08:20:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "radiative capture",
      "subthreshold states",
      "ground state",
      "subthreshold bound states",
      "model-independent extrapolation method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}