We present a detailed description of a recently proposed optical theorem formulation of nonresonant low-energy nuclear reactions between two charged nuclei. Based on the optical theorem formulation, we obtain an analytic formula for the reaction cross section σ(E) which exhibits explicitly the energy and charge dependences of σ(E). The formula may provide a physical understanding of the anomalous low-energy enhancement of σ(E) observed in sub-barrier heavy-ion fusions and also in light nuclei fusions relevant for primordial nucleosynthesis and stellar evolution. As examples of its application, the new formulation is used to analyze astrophysical S factors for ${}^7\mathrm{Li}(p,\alpha {)}^4\mathrm{He},$ ${}^6\mathrm{Li}(d,\alpha {)}^4\mathrm{He},$ and ${}^6\mathrm{Li}(p,\alpha {)}^3\mathrm{He}$ reactions.

• Received 16 August 1996

DOI:https://doi.org/10.1103/PhysRevC.55.801