Proton abundance distribution artificially inserted during the post-processing in our models to simulate the formation of a ¹³C pocket after the 12th TP (left panel) and a PIE event during TP13 (right panel). Left panel: the thin line represents the standard exponentially decreasing proton distribution (pocket_case1) and the thick line the case where the proton abundance Y_p is set to constantly equal 1.05 × 10^-4 (pocket_case4). The dotted line represents the depth reached by the TDU. Right panel: the thin and thick lines represent two different proton distributions with a similar total amount of protons ingested: PIE_case1 (thin line) and PIE_case2 (thick line). The dotted line represents the maximum extension of the intershell convective region associated with TP13. The steep proton profile left over by the H-burning shell is also shown in the plot just above 0.638 M_⊙.