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Manuscript Title: Nilsson orbits for a particle in a Woods-Saxon potential with Y20 and Y40 deformations, and coupled to core rotational states.
Authors: B. Hird
Program title: NILSSON ORBITS
Catalogue identifier: ABOV_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 6(1973)30
Programming language: Fortran.
Computer: IBM 360/65.
Operating system: HASP.
RAM: 22K words
Word size: 32
Keywords: Nuclear physics, Schroedinger equation, Woods-saxon, Deformation, Hexadecapole, Energies, Expansion coefficient, Nilsson, Shell model, Collective model.
Classification: 17.19, 17.20.

Subprograms used:
Cat Id Title Reference

Nature of problem:
The eigenvalues and expansion coefficients of a single nucleon in an axially symmetric potential are obtained for any quadrupole and hexadecapole deformations. The central part of the potential is assumed to have a Woods-Saxon shape, with the derivative of this shape for the spin-orbit and the deformed parts. The rotational excitations of the core are added to the particle states together with all the rotation- particle Coriolis terms to generate the band mixed collective excited state spectrum of a deformed odd A nucleus.

Solution method:
The hamiltonian is diagonalised in three successive steps. The spherically symmetric part is first diagonalized in a harmonic oscillator basis, using numerically integrated radial matrix elements. The second diagonalization generates the deformed single particle states in a basis of the spherically symmetric eigenstates of the first diagonalization, and, finally, the core and RCP terms are diagonalized in a basis of the deformed states. A reduction in the size of each of the matrices to be diagonalized and the total number of diagonalizations results from separating the problem in this way.

The maximum radial quantum number of the harmonic oscillator basis and hence of any of the other basis states is restricted to 13 for odd parity, and to 12 for even parity systems. Deformations are restricted to Y02 and Y04 shapes. The Woods-Saxon basis which is used in the deformed state diagonalization is truncated to include only eigenstates with energies below +10 MeV. The above restrictions are fairly easy to relax by small changes in the programme. There is no provision for triaxial deformations, or for vibrational degrees of freedom.

Running time:
The radial integrals, which only need to be calculated once for a given Woods-Saxon potential take 160 s of CPU time with NMAX = 12 or 13. The three diagonalizations, using, for example, all the states of the 1s, 2s -1d and 1g-2d-3s shells takes a further 45 s.