  Starting from realistic nuclear forces, the chiral N$^3$LO and JISP16, we
have applied many-body perturbation theory (MBPT) to the structure of
closed-shell nuclei, $^4$He and $^{16}$O. The two-body N$^3$LO interaction is
softened by a similarity renormalization group transformation while JISP16 is
adopted without renormalization. The MBPT calculations are performed within the
Hartree-Fock (HF) bases. The angular momentum coupled scheme is used, which can
reduce the computational task. Corrections up to the third order in energy and
up to the second order in radius are evaluated. Higher-order corrections in the
HF basis are small relative to the leading-order perturbative result. Using the
anti-symmetrized Goldstone diagram expansions of the wave function, we directly
correct the one-body density for the calculation of the radius, rather than
calculate corrections to the occupation propabilities of single-particle orbits
as found in other treatments. We compare our results with other methods where
available and find good agreement. This supports the conclusion that our
methods produce reasonably converged results with these interactions. We also
compare our results with experimental data.
