Single particle calculations for a Woods–Saxon potential with triaxial deformations, and large Cartesian oscillator basis (new version code)

Abstract

We present a new version of the computer program which solves the Schrödinger equation of the stationary states for an average nuclear potential of Woods–Saxon type. In this work, we take specifically into account triaxial (i.e. ellipsoidal) nuclear surfaces. The deformation is specified by the usual Bohr parameters. The calculations are carried out in two stages. In the first, one calculates the representative matrix of the Hamiltonian in the Cartesian oscillator basis. In the second stage one diagonalizes this matrix with the help of subroutines of the EISPACK library. This new version calculates all the eigenvalues up to a given cutoff energy, and gives the components of the corresponding eigenfunctions. For a more convenient handling, these results are stored simultaneously in the computer memory, and on a files. Program summary Title of program:Triaxial2007 Catalogue identifier:ADSK_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADSK_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Summary of revision:One input file instead two. Reduced number of input parameters. Storage of eigenvalues and eigenvectors in memory in a very simple way which makes the code very convenient to the user. Reasons for the new version: More convenient handling of the eigenvectors Catalogue number old version: ADSK Catalogue number new version:ADSK_v2_0 Journal: Computer Physics Commun. 156 (2004) 241–282 Licensing provisions: none Computer: PC Pentium 4, 2600 MHz Hard disk: 40 Gb RAM: 256 Mb Swap file: 4 Gb Operating system: WINDOWS XP Software used: Compaq Visual FORTRAN (with full optimizations in the settings project options) Programming language used:Fortran 77/90 (double precision) Number of bits in a word: 32 No. of lines in distributed program, including test data, etc.:4058 No. of bytes in distributed program, including test data, etc.:75 590 Distribution format:tar.gz Nature of the problem: The single particle energies and the single particle wave functions are calculated from one-body Hamiltonian including a central field of Woods–Saxon type, a spin–orbit interaction, and the Coulomb potential for the protons. We consider only ellipsoidal (triaxial) shapes. The deformation of the nuclear shape is fixed by the usual Bohr parameters ( β , γ ) . Method of solution: The representative matrix of the Hamiltonian is built by means of the Cartesian basis of the anisotropic harmonic oscillator, and then diagonalized by a set of subroutines of the EISPACK library. Two quadrature methods of Gauss are employed to calculate, respectively, the integrals of the matrix elements of the Hamiltonian, and the integral defining the Coulomb potential. Restrictions: There are two restrictions for the code: The number of the major shells of the basis does not have to exceed N max = 26 . For the largest values of N max (∼23–26), the diagonalization takes the major part of the running time, but the global run-time remains reasonable. Typical running time: (With full optimization in the project settings of the Compaq Visual Fortran on Windows XP) With N max = 23 , for the neutrons case, and for both parities, the running time is about 40 sec on the P4 computer at 2.6 GHz. In this case, the calculation of the matrix elements takes only about 17 sec. If all unbound states are required, the runtime becomes larger.