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Manuscript Title: A program to generate closed basic diagrams for product operators.
Authors: B.D. Chang, S.S.M. Wong
Program title: CONTRACTION-BASIC-DIAGRAM
Catalogue identifier: ACZI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 18(1979)35
Programming language: Fortran.
Computer: IBM 360/65.
Operating system: HASP/OSMVT, MVS/JES2.
RAM: 52K words
Word size: 32
Peripherals: disc.
Keywords: General purpose, Statistical spectroscopy, Scalar trace, Configuration trace, Perturbation theory, Hugenholtz diagram, Unitary symmerty, Permutation, Rotation group, Basic diagram, Symmetry matrix element.
Classification: 4.1.

Nature of problem:
Operators, referred to here as basic operators, such as Hamiltonian, electromagnetic transition and nucleon transfer, are defined in terms of products of single particle creation and annihilation operators (and their matrix elements). In many physical problems, it is necessary to evaluate the scalar and configuration traces of a product of basic operators. The easiest way to achieve this is to find all the diagrams, i.e., complete contractions among the single particle operators. Because of symmetry relations, such as permutations, matrix element and unitary symmetries, many diagrams are related and the minimum set from which all other diagrams can be generated is called the basic diagrams. Consequently, the capability to find all the basic diagrams for an arbitrary product operator is most essential in trace evaluations.

Solution method:
A digital representation is devised so that a definite order between different diagrams can be established. A basic diagram is recognized by the fact that the application of symmetry considerations can only produce diagrams later in the order. The algorithm for programming on the computer is made efficient by making all possible attempts, while the diagram is being generated, to recognize the pattern for a diagram to be rejected as a basic one.

Restrictions:
The dimensions in the program restrict the number of basic operators in a product to be no more than 20 and the total number of single particle operators to be no more than 40. These restrictions can be easily removed by changing the dimension specifications in the program. The number of single particle operators in any one basic operator is restricted to be less than or equal to 4.