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Manuscript Title: Single particle calculations for a Woods-Saxon potential with triaxial deformations, and large Cartesian oscillator basis.
Authors: B. Mohammed-Azizi, D.E. Medjadi
Program title: Triaxial
Catalogue identifier: ADSK
Journal reference: Comput. Phys. Commun. 156(2004)241
Programming language: Fortran 77/90.
Computer: PC, AMD Athlon.
Operating system: Windows XP.
RAM: 64M words
Word size: 32
Keywords: Nuclear physics, Oscillator bracket, Energy levels, Wave functions, Schrodinger equation, Woods-Saxon potential.
Classification: 17.17.

Nature 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.

There are two restrictions for the code. The number of major shells of the basis should not exceed Nmax = 26. 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.

Running time:
(With full optimization in the project settings of the Microsoft Visual Fortran 5.0A on Windows XP). With Nmax=23, for the neutrons case, and for both parities, if we need all eigenenergies and all eigenfunctions of the bound states, the running time is about 80 sec on the AMD Athlon computer at 1GHz. In this case, the calculation of the matrix elements takes only about 20 sec. If all unbound states are required, the runtime becomes larger.