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Manuscript Title: Single particle energies, wave functions, quadrupole moments, and g- factors in axially deformed Woods-Saxon potential with applications in the two-centre-type nuclear problems.
Authors: S. Cwiok, J. Dudek, W. Nazarewicz, J. Skalski, T.R. Werner
Program title: WSBETA
Catalogue identifier: AAXX_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 46(1987)379
Programming language: Fortran.
Computer: CDC 6400.
Operating system: SCOPE 3.4, MVS/XA, EXEC8, VAXVMS 4.4, SINTRAN II.
RAM: 147K words
Word size: 32
Peripherals: disc.
Keywords: Nuclear energy levels, Wave functions, Nuclear physics, Schrodinger equation, Woods-saxon potential, Nuclear deformation, Spin-orbit coupling, Coulomb potential, Quadrupole moments, Diagonalization method, Liquid-drop model, Deformed harmonic Oscillator, Unbound states, Independent-particle Model, Collective model.
Classification: 17.20.

Nature of problem:
Single particles energies and wave functions of an axially deformed Woods-Saxon potential are computed. The Hamiltonian used includes the spin-or-bit interaction and the Coulomb potential for protons. The nuclear shape is defined in terms of an expansion into spherical- harmonics. The standard liquid-drop model constants, effective barriers for the unbound states, single particle quadrupole moments and g-factors are also calculated. The applied shape parametrisation of the potential well allows to generate the single-particle orbitals also for the extreme deformations e.g. those approaching separation of a nucleus into fragments, with or without the so-called mass asymmetry.

Solution method:
The Hamiltonian is diagonialized in the axially deformed harmonic oscillator basis. The deformed Woods-Saxon potential is generated numerically at a deformation specified in terms of the multipole expansion by the set of the deformation parameters
               Beta = (Beta2,Beta3,Beta4,Beta5,Beta6).
All possible couplings between the basis states are included when setting up the Hamiltonian matrix. The matrix elements are computed by numerical integration using the Gauss quadrature formulae.

Restrictions:
The maximum number of harmonic oscillator shells included is NMAX =19, but this limit can be increased easily by the user. The present version of the program accepts only axially symmetric shapes. However, another code solving the Schrodinger equation for triaxial shapes, including both quadrupole and hexadecapole degrees of freedom will soon be available.

Running time:
Depends on the size of the harmonic oscillator basis used. In the example presented below where all the basis states within 15 harmonic oscillator shells have been used, the running time is 1 min 18 sec on IBM 3081K.