  Introducing a new vertex function, Z(E), of an energy variable E, we derive a
new equation for the effective interaction. The equation is obtained by
replacing the Q-box in the Krenciglowa-Kuo (KK) method by Z(E). This new
approach can be viewed as an extension of the KK method. We show that this
equation can be solved both in iterative and non-iterative ways. We observe
that the iteration procedure with Z(E) brings about fast convergence compared
to the usual KK method. It is shown that, as in the KK approach, the procedure
of calculating the effective interaction can be reduced to determining the true
eigenvalues of the original Hamiltonian H and they can be obtained as the
positions of intersections of graphs generated from Z(E). We find that this
graphical method yields always precise results and reproduces any of the true
eigenvalues of H. The calculation in the present approach can be made
regardless of overlaps with the model space and energy differences between
unperturbed energies and the eigenvalues of H. We find also that Z(E) is a
well-behaved function of E and has no singularity. These characteristics of the
present approach ensure stability in actual calculations and would be helpful
to resolve some difficulties due to the presence of poles in the Q-box.
Performing test calculations we verify numerically theoretical predictions made
in the present approach.
