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Manuscript Title: The Sp(3,R) representations of an A-particle nucleus. | ||

Authors: C.N.M. Ng, M.J. Carvalho | ||

Program title: SPPLETH | ||

Catalogue identifier: ADDG_v1_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 96(1996)288 | ||

Programming language: C. | ||

Computer: Sun Sparc 1000. | ||

Operating system: UNIX. | ||

RAM: 16M words | ||

Word size: 32 | ||

Keywords: Symplectic shell model, Configuration space, Collective spaces, Irreps, Sp(3, r), U(3), Orthogonal group, Plethysm, S-functions, S-function series, Generating functions, Symmetric group, Character table, Nuclear physics, Shell model, General purpose, Algebras. | ||

Classification: 4.2, 17.19. | ||

Nature of problem:Evaluation of the plethysm of the fundamental representation of the non- compact sp(3,R) algebra. | ||

Solution method:Problem is solved by evaluating the S-function expansion [1] M otimes {f} * C where M and C are particular S-functions series [2, 3], {f} is a single S-function (in Littlewood's notation [2]) corresponding to a partition f of A and the symbold otimes and * denote, respectively, plethysm (symmetrized product) and outer product of S-functions. Appropriately to sp(3,R), only S-functions with up to 3 parts are retained. | ||

Restrictions:The main restriction is cpu time. Also, for large values of A, memory storage may become a problem. Since the S-function expansion is an infinite expansion, a weight cut-off has to be specified. Execution time increases with increasing value of A as well as with increasing value of weight cut-off. For large values of A, execution time can be reduced by giving the expected minimum weight (dictated by Pauli principle) of the S-functions in the expansion. See long write-up for details. | ||

Unusual features:In order to handle very large integers with infinite precision a new data type, called "astro", was introduced. This is a linked list of integers with each node of the list representing a digit of the integer. The linked-list itself is a doubly linked list, i.e. each node has a 'previous pointer' and a 'next pointer'. The linked list has also a 'header node' which contains the start pointer, the end pointer, the length of the integer (i.e. the number of digits) and its sign. | ||

References: | ||

[1] | M.J. Carvalho, J. Phys. A: Math. Gen. 23(1990)1909. | |

[2] | D.E. Littlewood The Theory of Group Characters (Oxford: Clarendon) (2nd edition 1950). | |

[3] | R.C. King, J. Phys. A: Math. Gen. 8(1975)429; M. Yang and B.G. Wybourne, J. Phys. A: Math. Gen. 19(1983)3513. |

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