Final answer:
In the asymptotic giant branch phase, a star features a carbon-oxygen core with no nuclear reactions, surrounded by a helium-fusing shell, and an outer shell where hydrogen fusion occurs.
Step-by-step explanation:
When a star ascends the red-giant branch for the second time in the asymptotic giant branch phase, it has a complex, layered structure. Inside the core, there are no nuclear reactions taking place because it is composed of carbon and oxygen which cannot undergo fusion at the temperatures present in the core of a red giant. Surrounding the inert core is a shell where helium fusion occurs, producing carbon in a process known as the triple-alpha process. Beyond this helium-fusing shell, there is another shell where hydrogen fusion occurs, converting hydrogen into helium. Therefore, the correct answer is that during the asymptotic giant branch phase, a star has no nuclear reactions occurring in the core, but there is hydrogen fusion in a shell outside the core.