  Mixed modes observed in red giants allow for investigation of the stellar
interior structures. One important feature in these structures is the buoyancy
spike caused by the discontinuity of the chemical gradient left behind during
the first dredge-up. The buoyancy spike emerges at the base of the convective
zone in low-luminosity red giants and later becomes a glitch when the g-mode
cavity expands to encompass the spike. Here, we study the impact of the
buoyancy spike on the dipolar mixed modes using stellar models with different
properties. We find that the applicability of the asymptotic formalisms for the
coupling factor, q, varies depending on the location of the evanescent zone,
relative to the position of the spike. Significant deviations between the value
of q inferred from fitting the oscillation frequencies and either of the
formalisms proposed in the literature are found in models with a large
frequency separation in the interval 5 to 15 microHz, with evanescent zones
located in a transition region which may be thin or thick. However, it is still
possible to reconcile q with the predictions from the asymptotic formalisms, by
choosing which formalism to use according to the value of q. For stars
approaching the luminosity bump, the buoyancy spike becomes a glitch and
strongly affects the mode frequencies. Fitting the frequencies without
accounting for the glitch leads to unphysical variations in the inferred q, but
we show that this is corrected when properly accounting for the glitch in the
fitting.
