# Algebraic manipulation of the states associated with the U(5) ⊃ O(5) ⊃ O(3) chain of groups: orthonormalization and matrix elements

## Description

Abstract A collection of procedures able to perform algebraic manipulations for the orthonormalization and for the calculation of matrix elements between the states associated with the U(5) ⊃ O(5) ⊃ O(3) chain of groups is presented. These procedures combine both the exact- and the bigfloat-arithmetic modes and thus return arbitrarily accurate results; this is particularly relevant to the Gram-Schmidt orthonormalization, where strong cancellations usually pose serious problems in all floating-point im... Title of program: PHIMANIP Catalogue Id: ABJA_v1_0 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 ... Versions of this program held in the CPC repository in Mendeley Data ABJA_v1_0; PHIMANIP; 10.1016/0010-4655(89)90094-5 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)