  We have done a systematic no-core shell-model study of $^{20-23}$Na isotopes.
The low-energy spectra of these sodium isotopes consisting of natural and
un-natural parity states were reported, considering three realistic
interactions: inside nonlocal outside Yukawa (INOY), charge-dependent Bonn 2000
(CDB2K), and the chiral next-to-next-to-next-to-leading order (N$^3$LO). We
also present the mirror energy differences in the low-energy spectra of $|T_z|$
= 1/2 mirror pair ($^{21}$Na - $^{21}$Ne). Apart from the energy spectra, we
have also reported the electromagnetic transition strengths and moments.
Finally, considering all three realistic interactions, we report the
point-proton radii and neutron skin thicknesses.
