  The finite amplitude method (FAM), which we have recently proposed (T.
Nakatsukasa, T. Inakura, and K. Yabana, Phys. Rev. C 76, 024318 (2007)),
simplifies significantly the fully self-consistent RPA calculation. Employing
the FAM, we are conducting systematic, fully self-consistent response
calculations for a wide mass region. This paper is intended to present a
computational scheme to be used in the systematic investigation and to show the
performance of the FAM for a realistic Skyrme energy functional. We implemented
the method in the mixed representation in which the forward and backward RPA
amplitudes are represented by indices of single-particle orbitals for occupied
states and the spatial grid points for unoccupied states. We solve the linear
response equation for a given frequency. The equation is a linear algebraic
problem with a sparse non-hermitian matrix, which is solved with an iterative
method. We show results of the dipole response for selected spherical and
deformed nuclei. The peak energies of the giant dipole resonance agree well
with measurements for heavy nuclei, while they are systematically
underestimated for light nuclei. We also discuss the width of the giant dipole
resonance in the fully self-consistent RPA calculation.
