  Based on the relativistic Hartree-Bogoliubov theory, the influence of the
pairing interaction strength on the di-neutron correlations and the crossover
from superfluidity of neutron Cooper pairs in the $^{1}S_{0}$ channel to
Bose-Einstein condensation of di-neutron pairs is systematically investigated
in the nuclear matter. The bare nucleon-nucleon interaction Bonn-B is taken in
the particle-particle channel with an effective factor to simulate the medium
effects and take into account the possible ambiguity of pairing force, and the
effective interaction PK1 is used in the particle-hole channel. If the
effective factor is larger than 1.10, a di-neutron BEC state appears in the
low-density limit, and if it is smaller than 0.85, the neutron Cooper pairs are
found totally in the weak coupling BCS region. The reference values of several
characteristic quantities which characterize the BCS-BEC crossover are obtained
respectively from the dimensionless parameter $1/(k_{\rm Fn}a)$ with $a$ the
scattering length and $k_{\rm{Fn}}$ the neutron Fermi momentum, the
zero-momentum transfer density correlation function D(0) and the effective
chemical potential $\nu_{\rm n}$.
