  This study provides accurate results for the electronic stopping
cross-sections of H, He, N, and Ne in silicon in low to intermediate energy
ranges using various non-perturbative theoretical methods, including real-time
time-dependent density functional theory, transport cross-section, and
induced-density approach. Recent experimental findings [Ntemou \textit{et al.},
Phys. Rev. B {\bf 107}, 155145 (2023)] revealed discrepancies between the
estimates of density functional theory and observed values. We show that these
discrepancies vanish by considering the nonuniform electron density of the
silicon deeper bands for ion velocities approaching zero ($v \to 0$). This
indicates that mechanisms such as ``elevator'' and ``promotion,'' which can
dynamically excite deeper-band electrons, are active, enabling a localized free
electron gas to emulate ion energy loss, as pointed out by [Lim \textit{et
al.}, Phys. Rev. Lett. {\bf 116}, 043201 (2016)]. The observation and the
description of a velocity-proportionality breakdown in electronic stopping
cross-sections at very low velocities are considered to be a signature of the
deeper-band electrons' contributions.
