  We examine the mode entanglement and correlation of two fermionic particles.
We study the one- and two-mode entropy and a global characteristic, the
one-body entanglement entropy. We consider not only angular momentum coupled
states with single configuration but use the configuration interaction method.
With the help of the Slater decomposition, we derive analytical expressions for
the entanglement measures. We show that when the total angular momentum is zero
specific single configurations describe maximally entangled states. It turns
out that for a finite number of associated modes the one- and two-mode
entropies have identical values. In the shell model framework, we numerically
study two valence neutrons in the $sd$ shell. The one-body entanglement entropy
of the ground state is close to the maximal value and the associated modes have
the largest mutual information.
