  The S-matrix which satisfies the unitarity, giving the poles as RPA excited
states, is derived using the extended Jost function within the framework of the
RPA theory. An analysis on the correspondence between the component
decomposition of the RPA strength function by the eigenphase shift obtained by
diagonalisation of the S-matrix and the S- and K-matrix poles was performed in
the calculation of the $^{16}$O quadrupole excitations. The results show the
possibility that the states defined by the eigenphase shift can be expressed as
RPA-excited eigenstates corresponding to the S-matrix poles in the continuum
region.
