Programs in Physics & Physical Chemistry
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|Manuscript Title: Representations of U(3) in U(N).|
|Authors: J.P. Draayer, Y. Leschber, S.C. Park, R. Lopez|
|Program title: UNTOU3|
|Catalogue identifier: ABLJ_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 56(1989)279|
|Programming language: Fortran.|
|Computer: IBM 3090/600E.|
|Operating system: MVS/XA-311, VMS 4.5.|
|RAM: 231K words|
|Word size: 32|
|Keywords: General purpose, Algebras, Harmonic oscillator, Three-dimensional Oscillator, Elliott su(3) scheme, Symplectic shell model, Microscopic collective Model, U(3) symmetry, Algebraic theory, Dynamical symmetry, U(n) -> u(3), Unitary group plethysm, Nuclear physics, Fractional parentage.|
|Classification: 4.2, 17.18.|
Nature of problem:
U(N) -> U(3) plethysm, that is, finding the complete set of irreducible representations (irreps) of U(3) in specific irreps of U(N) where N=(n+1) (n+2)/2 for nonnegative integer n values.
Solutions are obtained by applying a simple difference algorithm to the U(3) weight distribution function. The latter is generated in three steps: 1) by indentifying the N levels of U(N) as the distinguishable arrangements of n oscillator quanta in three cartesian directions, 2) by distributing the total number of qaunta (n * m if m is the number of valence particles) among these levels subject to restrictions (betweeness conditions) of the Gelfand scheme for labeling basis states of U(N), and 3) by summing over all the N levels to determine the final distribution of quanta in the three cartesian directions.
The main limitation is CPU time, see below. Storage can be a problem but the time constraint usually sets in long before program size becomes a problem. A PC with 640K of memory is sufficient to run most cases of interest in nuclear physics.
Return codes set in the subprograms are used to fix branch points in the calling program. This modus operandi is implemented as a way of mocking-up recursive subprogram calls which is forbidden in FORTRAN but not, for example, in PASCAL.
Execution times increase approximately linearly with d, the dimension of the irrep, and expotentially with n, the number of oscillator quanta. That is, t(cpu) ^ ( Alpha d) * exp(Beta n) where the constants Alpha and Beta are arround 13 * 10**-7 sec and 2.4 on the VAX 11/750 and 0.7 * 10**-7 sec and 2.6 on the IBM 3090/E, respectively.
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