Accurate random-phase approximation calculation of low-lying states on a three-dimensional Cartesian mesh

We present a simple and efficient method for calculating excitation energies and transition probabilities of low-lying states described by Hartree-Fock (HF) plus random-phase approximation (RPA) with Skyrme force. The method employs conjugate gradient method to solve the RPA equations in the mixed representation of coordinate and occupied orbitals, which was proposed recently. To obtain accurate results with coarse mesh (1 fm) calculation, we find a useful prescription. Performing self-consistently three-dimensional Cartesian mesh calculation with Lagrange mesh method in solving HF and RPA equations, we take an average of quantities calculated with even and odd mesh points in one direction. As a demonstration of our method, we show the numerical results of energies for spurious mode of translation of ¹⁶O and the excitation energies and reduced transition probabilities for first 3^- state of ¹⁶O and ²⁰⁸Pb.