Fully self-consistent QRPA solver for deformed nuclei using Skyrme EDF and Lanczos diagonalization

One of the current projects at the Department of Physics, University of Jyvaeskylae is the creation of an efficient Quasiparticle Random Phase Approximation (QRPA) computer program designed for deformed nuclei. The aim is to create a tool that would allow for a rapid determination of giant-resonance and beta-decay properties for nuclei across the mass chart. The QRPA equations are based on the same Energy Density Functional (EDF) as the ground state solution, including all terms of the standard Skyrme EDF plus approximate or exact Coulomb exchange and are therefore fully self-consistent. This ensures that the spurious QRPA solutions are controlled and that imaginary eigenvalues (RPA collapse) may occur only near phase transitions. We express the EDF in the spherical-tensor formalism of Ref [1]. Within this formalism the handling of the full Skyrme EDF in QRPA becomes straightforward. It also allows us to extend the EDF to include higher orders of density derivatives, if desired. To solve the large-dimensional QRPA equations for deformed nuclei, a variant of Lanczos diagonalization method is adapted for QRPA. This methods builds upon the so-called finite amplitude method recently proposed in Ref. [2]. Two calculation strategies will be used: either a few lowest RPA phonons can be accurately calculated by using restarted Lanczos method, or strength functions can be calculated by using Lanczos moments method. Spherical code working on the harmonic-oscillator basis is being constructed first for testing and benchmarking purposes. All codes developed within this project will be rapidly published and made available to other researchers.(author)