Many-channel microscopic cluster model of ${}^8$Be: S-factors

Abstract

We investigate low--energy astrophysical $S$ factors for reactions proceeding through the ${}^8$Be compound system with entrance channels $p+{}^7$Li, $n+{}^7$Be, and $d+{}^6$Li. Using the same microscopic many--channel three--cluster framework as in our previous study of the high--lying ${}^8$Be spectrum, we calculate $S(E)$ for ${}^7$Li($p,\alpha {)}^4$He, ${}^7$Be($n,\alpha {)}^4$He, ${}^7$Be($n,p{)}^7$Li, ${}^6$Li($d,\alpha {)}^4$He, ${}^6$Li($d,p{)}^7$Li, and ${}^6$Li($d,n{)}^7$Be in the energy range relevant for primordial and stellar nucleosynthesis. For the mirror pair ${}^7$Li($p,\alpha {)}^4$He / ${}^7$Be($n,\alpha {)}^4$He and for ${}^7$Be($n,p{)}^7$Li the calculated $S$ factors reproduce both the absolute scale and the low--energy trends of the experimental data within their quoted uncertainties, whereas the absolute $S$ factors for the deuteron--induced channels on ${}^6$Li are underestimated at low energy, consistent with the shifted ${}^6$Li+$d$ threshold and the absence of a broad subthreshold $2^{+}$ structure in the present implementation. A partial--wave analysis identifies the dominant $J^{\pi }$ contributions in each channel and relates them to specific ${}^8$Be resonances, while demonstrating that cluster polarization, previously shown to be crucial for the ${}^8$Be spectrum, is likewise essential for the normalization and energy dependence of several $S$ factors. Evaluating $S(E)$ at appropriate Gamow energies, we obtain a hierarchy of reaction channels that quantifies the relative importance of neutron-- and deuteron--induced processes for the production and destruction of ${}^7$Li and ${}^7$Be.

Comments: 40 pages, 16 figures, 9 tables. Submitted to Phys.Rev.C