Single particle calculations for a Woods–Saxon potential with triaxial deformations, and large Cartesian oscillator basis (TRIAXIAL 2014, Third version of the code Triaxial)

Abstract

Theory and FORTRAN program of the first version of this code (TRIAXIAL) have already been described in detail in Computer Physics Comm. 156 (2004) 241–282. A second version of this code (TRIAXIAL 2007) has been given in CPC 176 (2007) 634–635. The present FORTRAN program is the third version (TRIAXIAL 2014) of the same code. Now, It is written in free format. As the former versions, this FORTRAN program solves the same Schrodinger equation of the independent particle model of the atomic nucleus with the same method. However, the present version is much more convenient. In effect, it is characterized by the fact that the eigenvalues and the eigenfunctions can be given by specific subroutines. The latters did not exist in the old versions (2004 and 2007). In addition, it is to be noted that in the previous versions, the eigenfunctions were only given by their coefficients of their expansion onto the harmonic oscillator basis. This method is needed in some cases. But in other cases, it is preferable to treat the eigenfunctions directly in configuration space. For this reason, we have implemented an additional subroutine for this task. Some other practical subroutines have also been implemented. Moreover, eigenvalues and eigenfunctions are recorded onto several files. All these new features of the code and some important aspects of its structure are explained in the document ‘Triaxial2014 use.pdf’. New version program summaryProgram title: Triaxial2014Catalogue identifier: ADSK_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSK_v3_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.: 13672No. of bytes in distributed program, including test data, etc.: 217598Distribution format: tar.gzProgramming language: FORTRAN 77/90 (double precision).Computer: PC. Pentium 4, 2600MHz and beyond.Operating system: WINDOWS XP, WINDOWS 7, LINUX.RAM: 256 Mb (depending on nmax). Swap file: 4Gb (depending on nmax)Classification: 17.7.Does the new version supersede the previous version?: YesCatalogue identifier of previous version: ADSK_v2_0Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 634Nature of 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).Solution method: 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. Two quantum numbers are conserved: the parity and the signature. Due to the Kramers degeneracy, only positive signature is considered. Therefore, calculations are made for positive and negative parity separately (with positive signature only).Reasons for new version: Now, there are several ways to obtain the eigenvalues and the eigenfunctions. The eigenvalues can be obtained from the subroutine ‘eigvals’ or from the array ‘energies’ or also from the formatted files ‘valuu.dat’, ‘eigenvalo.dat’, ‘eigenva.dat’ or better from the unformatted file ‘eigenvaunf.dat’. The eigenfunctions can be obtained straightforwardly in configuration space from the subroutine ‘eigfunc’ or by their components on the oscillator basis from the subroutine ‘compnts’. The latter are also recorded on a formatted file ‘componento.dat’ or on an unformatted file ‘componentounf.dat’.Summary of revisions: This version is characterized by the fact that the eigenvalues and the eigenfunctions can be given by specific subroutines which did not exist in the old versions (2004 and 2007) of the program. Moreover, the eigenvalues and the eigenfunctions can also be deduced directly from files. It is to be noted that this version is now written in free format. All these reasons contribute to make the use of this code easier.Restrictions: There are two restrictions for the code: The number of the major shells of the basis should not exceed Nmax=26 (which is very sufficient in usual cases). For the largest values of Nmax (∼23–26), the diagonalization takes the major part of the running time, but the global run-time remains reasonable.Additional comments: Software used: (1) COMPAC VISUAL FORTRAN (with full optimizations in the settings project options on WINDOWS XP); (2) SILVERFROST PLATO VERSION 4.63 (with debug.net option on WINDOWS 7); (3) APPROXIMATRIX SIMPLY FORTRAN VERSION 2.13 BUILD (on WINDOWS XP and WINDOWS 7).Running time: (With full optimization in the project settings of the Compaq Visual Fortran on Windows XP) With NMAX=23, for the neutrons case, the running time is about 50 s on the intel core i5 processor.