L$ becomes larger than 2, leading to a drastic decrease of the time-step. The subsequent evolution of $L_{\rm H}$ and $L_{\rm He}$ is resolved accurately ($|1-\delta L|<0.5$).

Input physics. {#inphy}
--------------

In order to describe the chemical evolution of the star we follow the abundances of $\mathrm{H}$, $^3$He, $^4$He, $^{12}$C, $^{13}$C, $^{14}$N, $^{15}$N, $^{16}$O, $^{17}$O, without assuming [*a priori*]{} equilibrium compositions for these chemical elements.

Since the metal distribution in our models can show strong deviations with respect to the usually adopted scaled-solar mixture, we decided not to use the most updated equation of state [like OPAL-EOS; @OPEOS], but the Saha-equation for the outer stellar layers, and a simplified equation of state for a degenerate electron gas in the core regions [@KW][^3]. The switching point between these two equations of state is determined by the position where either carbon or helium (in case there is no carbon present) is fully or maximally ionized.

For the radiative opacity we have used, unless stated differently (see below), the tables provided by @OP96 for temperatures above $T>10000$ K, and for low temperatures ($T<8000$ K) those by @Alex. In the intermediate temperature range a smooth transition between the two tables is used. Both opacity 