  By applying the angular-momentum projection (AMP) to the self-consistent
axial mean-field solutions with the semi-realistic effective Hamiltonian
M3Y-P6, the pairing effects on the pure rotational energy of nuclei,
\textit{i.e.}, the rotational energy at a fixed intrinsic state, have been
investigated. While it was shown at the Hartree-Fock (HF) level that the
individual terms of the Hamiltonian contribute to the rotational energy with
ratios insensitive to nuclides except for light or weakly-deformed nuclei, the
pair correlations significantly change the contributions, even for the
well-deformed heavy nuclei. The contribution of the interaction to the
rotational energy is found to correlate well with the degree of proximity
between nucleons, which is measured via the expectation value that two nucleons
exist at the same position. While the nucleons slightly spread as the angular
momentum increases at the HF level, accounting for the positive (negative)
contribution of the attractive (repulsive) components of the interaction, the
pair correlations reduce or invert the effect.
