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Manuscript Title: Algebraic manipulation of the states associated with the U(5) include O(5) include O(3) chain of groups: orthonormalization and matrix elements.
Authors: C. Yannouleas, J.M. Pacheco
Program title: PHIMANIP
Catalogue identifier: ABJA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 54(1989)315
Programming language: Reduce.
Computer: VAX 8650.
Operating system: VMS VERSION 4.7.
RAM: 500K words
Word size: 32
Keywords: Computer algebra, Nuclear physics, Theoretical methods, U(5) include o(5) Include o(3) chain of Groups, Interacting boson Approximation, Geometrical collective Model, Five-dimensional Harmonic oscillator, Quadrupole vibrations Of the nucleus, Wave functions for Gamma-degree of freedom, Gram-schmidt Orthonormalization, Matrix elements in the Beta, gamma plane, Exact arithmetric, Bigfloat arithmetic, Computer-assisted Algebra, Reduce.
Classification: 5, 17.16.

Subprograms used:
Cat Id Title Reference
ABFN_v1_0 PHISYM CPC 52(1988)85

Nature of problem:
Group theoretical ideas and, in particular, states associated with the U(5) include O(5) include O(3) chain of groups are widely used to describe properties of nuclei, both within the framework of the Interacting Boson Approximation and of the geometric collective models of the Frankfurt group. Among the many processes and properties this chain has been applied to, prominent are the low-energy nuclear spectra, Coulomb excitation and medium-energy proton scattering, and the photoabsorption of the Giant Dipole Resonance in deformed nuclei.

Solution method:
Implementation of Gram-Schmidt orthonormalization in exact arithmetic upon the wave functions generated by the program PHISYM. Direct calculation of matrix elements by implementation of relevant integrations over the Beta- and Gamma-degrees of freedom through the use of algebraic recurrence relations and with the help of LET rules.

Restrictions:
The available computer memory in combination with the automatic space allocations of REDUCE is the most severe restriction. This situation may be alleviated by splitting the calculation into several smaller steps.

Running time:
This depends strongly on the complexity of the problem and cannot be estimated in advance.