What initiates vigorous energy production immediately after core hydrogen depletion for low-mass stars?

Hydrogen fusion ignites in a shell around the helium core

When core hydrogen is exhausted in a star like the Sun, the subsequent dramatic evolutionary change is triggered not by a cessation of fusion, but by a relocation and intensification of fusion activity. As gravity contracts the inert helium core, the temperature in the thin layer of hydrogen-rich material situated immediately surrounding this dense, contracting core increases dramatically. This elevated temperature in the surrounding shell becomes sufficient to initiate vigorous hydrogen fusion there. This shell burning process is intrinsically more energetic than the original core burning was during the main sequence, leading to a massive surge in outward energy production. This excessive energy output then pushes the star’s outer envelope outward, causing the dramatic swelling associated with becoming a red giant.