Self-consistent RPA calculations with Skyrme-type interactions: The skyrme_rpa program

Abstract

Random Phase Approximation (RPA) calculations are nowadays an indispensable tool in nuclear physics studies. We present here a complete version implemented with Skyrme-type interactions, with the spherical symmetry assumption, that can be used in cases where the effects of pairing correlations and of deformation can be ignored. The full self-consistency between the Hartree–Fock mean field and the RPA excitations is enforced, and it is numerically controlled by comparison with energy-weighted sum rules. The main limitations are that charge-exchange excitations and transitions involving spin operators are not included in this version. Program summaryProgram title: skyrme_rpa (v 1.00)Catalogue identifier: AENF_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AENF_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5531No. of bytes in distributed program, including test data, etc.: 39435Distribution format: tar.gzProgramming language: FORTRAN-90/95; easily downgradable to FORTRAN-77.Computer: PC with Intel Celeron, Intel Pentium, AMD Athlon and Intel Core Duo processors.Operating system: Linux, Windows.RAM: From 4 MBytes to 150 MBytes, depending on the size of the nucleus and of the model space for RPA.Word size: The code is written with a prevalent use of double precision orREAL(8) variables; this assures 15 significant digits.Classification: 17.24.Nature of problem: Systematic observations of excitation properties in finite nuclear systems can lead to improved knowledge of the nuclear matter equation of state as well as a better understanding of the effective interaction in the medium. This is the case of the nuclear giant resonances and low-lying collective excitations, which can be described as small amplitude collective motions in the framework of the Random Phase Approximation (RPA). This work provides a tool where one starts from an assumed form of nuclear effective interaction (the Skyrme forces) and builds the self-consistent Hartree–Fock mean field of a given nucleus, and then the RPA multipole excitations of that nucleus.Solution method: The Hartree–Fock (HF) equations are solved in a radial mesh, using a Numerov algorithm. The solutions are iterated until self-consistency is achieved (in practice, when the energy eigenvalues are stable within a desired accuracy). In the obtained mean field, unoccupied states necessary for the RPA calculations are found. For all single-particle states, box boundary conditions are assumed. To solve the RPA problem for a given value of total angular momentum and parity Jπ a coupled basis is constructed and the RPA matrix is diagonalized (protons and neutrons are treated explicitly, and no approximation related to the use of isospin formalism is introduced). The transition amplitudes and transition strengths associated to given external operators are calculated. The HF densities and RPA transition densities are also evaluated.Restrictions: The main restrictions are related to the assumed spherical symmetry and absence of pairing correlations.Running time: The typical running time depends strongly on the nucleus, on the multipolarity, on the choice of the model space and of course on the computer. It can vary from a few minutes to several hours.