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Manuscript Title: Self-consistent RPA calculations with Skyrme-type interactions: the skyrme_rpa program
Authors: Gianluca Colò, Ligang Cao, Nguyen Van Giai, Luigi Capelli
Program title: skyrme_rpa (v 1.00)
Catalogue identifier: AENF_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 184(2013)142
Programming 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, Window.
RAM: From 4 MBytes to 150MBytes, 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 or REAL(8) variables; this assures 15 significant digits.
Keywords: Random Phase Approximation (RPA), Hartree-Fock (HF), Skyrme interaction.
PACS: 21.60.Jz, 21.30.Fe.
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 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.

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 approximately from few minutes to several hours.