  In this work, Na isotopes with mass varying from $A=$ 20 to 31 have been
studied using DJ16A, JISP16 and N3LO microscopic effective interactions in the
$sd$-shell. These effective interactions are derived for $sd$-shell using
no-core shell model wavefunctions and a unitary transformation method. We have
also performed calculation with IMSRG effective interactions targeted for a
particular nucleus. The studies include a detailed analysis of ground state
binding energy, low-lying spectra, and electromagnetic properties such as
reduced electric quadrupole transition strengths, quadrupole and magnetic
dipole moments of the Na chain. The results obtained from these microscopic
effective interactions were compared with the experimental data as well as with
the results of phenomenological interaction USDB. The charge radii of Na
isotopes are evaluated using shell model harmonic oscillator wave functions. In
addition to charge radii, matter radii and neutron skin thickness in the Na
chain are discussed with a focus on neutron-deficient Na isotopes.
