Programs in Physics & Physical Chemistry
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|Manuscript Title: Analytic formulation of SU(3) vector coupling coefficients for n particles.|
|Authors: J.M. Casilio, M.E. Noz|
|Program title: SU(3)VCC|
|Catalogue identifier: AAWA_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 5(1973)365|
|Programming language: Fortran.|
|Computer: IBM 360/40.|
|Operating system: DISK OPERATING SYSTEM.|
|RAM: 8K words|
|Word size: 32|
|Keywords: Nuclear physics, Su(3), Projection operator, Algebras, High energy Interaction, Vector coupling, General purpose, Wigner coefficient, Racah coefficient, Recoupling coefficient, Isoscaler factor, Symmetry principles, Elliott model, Fractional parentage.|
|Classification: 4.2, 17.18.|
Nature of problem:
A standard quantum mechanical problem is to combine commuting angular momenta to get simultaneous eigenvectors and eigenvalues of J**2 and JZ. This program calculates analytically SU(3) vector coupling coefficients for a product of n particles.
The calculation is done by evaluating the matrix elements of the SU(3) projection operator. This is done by using polynomial techniques. The raising and lowering operators of DeSwart are used to formulate the projection operator.
The intermediate matrix used in the problem solution may become quite large. Therefore, no problem may be done where the intermediate matrix exceeds the storage capacity of the computer used. In the test run, an intermediate matrix of dimension 10 X 10 was used.
The technique employed uses a theorem which says that the projection onto any final state of n particles, is exactly equal to the projection onto the one dimensional state of n+1 particles. This greatly simplifies the algebra involved. The resulting formula is in closed form and contains fewer sums than any other to be found in the literature. Also SU(3) isoscalar factors for n particles are obtainable by using only part of the program.
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