  Pre-stellar cores represent a critical evolutionary phase in low-mass star
formation. We aim to unveil the detailed thermal structure and density
distribution of three early-stage cores, starless core L1517B, and prestellar
core L694-2 and L429, with the high angular resolution observations of the
NH$_{3}$ (1,1) and (2,2) inversion transitions obtained with VLA and GBT. In
addition, we explore where/if NH$_{3}$ depletes in the central regions.
Applying the mid-infrared extinction method to the $\textit{Spitzer}$ 8$~\mu$m
map we obtain a high angular resolution hydrogen column density map, and derive
the gas density profile to assess the variation of NH$_{3}$ abundance as a
function of gas volume density. The measured temperature profiles of L429 and
L1517B show a minor decrease towards the core center, dropping from $\sim$9\~K
to below 8\~K, and $\sim$11 K to 10 K, while L694-2 has a rather uniform
temperature distribution around $\sim$9 K. Among the three cores, L429 has the
highest central gas density, close to sonic velocity line-width, and largest
localised velocity gradient, all indicative of an advanced evolutionary stage.
We resolve that the abundance of NH$_{3}$ becomes two times lower in the
central region of L429, occurring around a gas density of
4.4$\times$10$^{4}$$~cm^{-3}$. Compared to Ophiuchus/H-MM1 which shows an even
stronger drop of the NH$_{3}$ abundance at 2$\times$10$^{5}$$~cm^{-3}$, the
abundance variations of the three cores plus Ophiuchus/H-MM1 suggest a
progressive NH$_{3}$ depletion with increasing central density of the core.
