  The theory of self-consistent effective interactions in nuclei is extended
for a system with a velocity dependent mean potential. By means of the field
coupling method, we present a general prescription to derive effective
interactions which are consistent with the mean potential. For a deformed
system with the conventional pairing field, the velocity dependent effective
interactions are derived as the multipole pairing interactions in
doubly-stretched coordinates. They are applied to the microscopic analysis of
the giant dipole resonances (GDR's) of ${}^{148,154}Sm$, the first excited
$2^+$ states of Sn isotopes and the first excited $3^-$ states of Mo isotopes.
It is clarified that the interactions play crucial roles in describing the
splitting and structure of GDR peaks, in restoring the energy weighted sum
rule, and in reducing the values of $B(E\lambda)$.
