Alpha clustering in nuclear astrophysics and topology

When we think of clustering in nuclear physics, the astrophysical importance within light nuclei and structural manifestations with classical analogs immediately come to mind. 4He, also known as the alpha particle, is the most abundant nucleus in the Universe, being quite tightly bound for its mass, with a first excited state of over 20 MeV. The nature of the alpha particle places it in a unique position within nuclear astrophysics and structure (including geometry). The plurality of energy release from stellar hydrogen fusion-whether quiescent or explosive-comes from the conversion of hydrogen to helium. Within more complex nuclei, the alpha particles are continuously arranged, leading to fascinating phenomena such as excited rotational bands, Borromean ring ground states, and linear structures. Nuclei with an equal and even number of protons and neutrons are colloquially referred to as "alpha conjugate nuclei," where such special properties are the most pronounced and easiest to spot. However, when a single nucleon or a pair of nucleons is added to the system, alpha clustering not only remains evident but it may also be enhanced. Excited states with large alpha partial widths are a signature of clustering behavior, and these states can have a profound effect on the reaction rates in astrophysical systems when the excitation energy aligns with the so-called Gamow energy-the preferential thermal energy to statistically overcome the Coulomb barrier. In this article, we will consider in detail the specific ramifications of alpha clustering in selected scenarios for both nuclear astrophysics and topology. In particular, we discussed the astrophysical reactions of 7Li (& alpha;, & gamma;), 7Be+& alpha;, 11C (& alpha;, p), and 30S (& alpha;, p), where & alpha;-clusters may increase the reaction rates from 10% to an order of magnitude; large & alpha; resonances make the astrophysical rate of 18F (p, & alpha;) quite uncertain. We also focused on the & alpha; rotational bands of both positive and negative parities of 11B and 11C, and finally on the strongest evidence for the linear-chain cluster state observed in 14C.