The neutron pairing correlation and the soft dipole excitation in medium mass nuclei near the drip line are investigated from the viewpoint of the di-neutron correlation. Numerical analyses based on the coordinate-space Hartree-Fock-Bogoliubov method and the continuum quasiparticle random phase approximation are performed for even-even O18-24,Ca50-58, and Ni80-86. A clear signature of the di-neutron correlation is found in the ground state; two neutrons are correlated at short relative distances less than or similar to 2 fm with large probability similar to 50%. The soft dipole excitation is influenced strongly by the neutron pairing correlation, and it accompanies a large transition density for pair motion of neutrons. This behavior originates from a coherent superposition of two-quasiparticle configurations [l x (l + 1)](L=1) consisting of continuum states with high orbital angular momenta l reaching an order of l similar to 10. It suggests that the soft dipole excitation under the influence of neutron pairing is characterized by the motion of di-neutron in the nuclear exterior against the remaining A-2 subsystem. Sensitivity to the density dependence of the effective pair force is discussed.
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