  We report on the measurements of the superconducting order parameter in the
nonmagnetic borocarbides LuNi$_2$B$_2$C and YNi$_2$B$_2$C. Andreev conductance
spectra are obtained from nanoscale metallic junctions on single crystal
surfaces prepared along three major crystallographic orientations: [001],
[110], and [100]. The gap values extracted by the single-gap
Blonder-Tinkham-Klapwijk model follow the BCS predictions as a function of
temperature and magnetic field and exhibit a small anisotropy. These
observations are robust and reproducible among all the measurements on two
different sets of LuNi$_2$B$_2$C crystals and one set of YNi$_2$B$_2$C
crystals. We suggest possible explanations for the small gap anisotropy based
on the recent detailed gap measurements by angle-resolved photoemission
spectroscopy and the tunneling cone effect. Our results provide a consistent
picture of the superconducting gap structure in these materials, addressing the
controversy particularly in the reported results of point-contact Andreev
reflection spectroscopy.
