Self-consistent calculation of nuclear photoabsorption cross sections: Finite amplitude method with Skyrme functionals in the three-dimensional real space

Abstract

The finite amplitude method (FAM), which we have recently proposed [T. Nakatsukasa, T. Inakura, and K. Yabana, Phys. Rev. C 76, 024318 (2007)], significantly simplifies the fully self-consistent calculation of the random-phase approximation (RPA). This article presents a computational scheme of FAM suitable for systematic investigation and shows its performance for realistic Skyrme energy functionals. We adopt the mixed representation in which the forward and backward RPA amplitudes are represented by index of hole orbitals and of the spatial grid points for the three-dimensional real space. We solve a linear algebraic problem with a sparse non-Hermitian matrix, using an iterative method. We show results of the dipole response for selected spherical and deformed nuclei. The calculated peak energies of the giant dipole resonance well agree with experiments for heavy nuclei. However, they are systematically underestimated for light nuclei. We also discuss the width of the giant dipole resonance in the fully self-consistent RPA calculation.