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Manuscript Title: The reduced rotation matrix.
Authors: W.J. Braithwaite, J.G. Cramer
Program title: DS
Catalogue identifier: ABOR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 3(1972)318
Programming language: Fortran.
Computer: IBM 360/91.
Operating system: OS 360.
RAM: 1K words
Word size: 64
Keywords: Atomic physics, General purpose, Nuclear physics, Rotation matrix, Rotation group, Correlation, Euler angle, Symmetry, Helicity, Representation.
Classification: 4.1.

Nature of problem:
Subprogram DS is a Fortran IV double precision function which calculates the reduced matrix elements of finite rotations in the angular momentum representation, using a standard phase convention. The four arguments of the FUNCTION are J2, twice the total angular momentum; MI2 and MF2, twice the z-projection of the total angular momentum in the inital and final coordinate systems, respectively and BETA, the Euler angle-of-rotation around y..

Solution method:
A Wigner-closed-sum expression for djmm'(beta) is evaluated. Each term contains products of factorials. Using a method similar to that of Wills (Comp. Phys. Commun. 2(1971)381), a common coefficient (containing factorials) is evaluated by combining the logarithms of the factorials, followed by one expotentiation. The remaining expression is written, without factorials, as a nested product. This method contracts well, in speed and accuracy, with methods that evaluate factorial products in the closed-sum coefficients term-by-term, before adding.