  Energy levels of nitrogen-vacancy centers in diamond were investigated using
optically detected magnetic-resonance spectroscopy near the electronic
ground-state level anticrossing (GSLAC) at an axial magnetic field around
102.4~mT in diamond samples with a nitrogen concentration of 1~ppm and 200~ppm.
By applying radiowaves in the frequency ranges from 0 to 40 MHz and from 5.6 to
5.9 GHz, we observed transitions that involve energy levels mixed by the
hyperfine interaction. We developed a theoretical model that describes the
level mixing, transition energies, and transition strengths between the
ground-state sublevels, including the coupling to the nuclear spin of the NV
center\textquotesingle s $^{14}$N and $^{13}$C atoms. The calculations were
combined with the experimental results by fitting the ODMR spectral lines based
on a theoretical model, which yielded information about the polarization of
nuclear spins. This study is important for the optimization of experimental
conditions in GSLAC-based applications, e.g., microwave-free magnetometry and
microwave-free nuclear-magnetic-resonance probes.
