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Manuscript Title: Computation of total, differential, and double-differential cross sections for compound nuclear reactions of the type (a,b), (a,bgamma) and (a,bgamma-gamma) (II) Generalized programs MANDY and BARBARA for arbitrary angular momenta in Hauser-Feshbach-Moldauer formalism. See erratum Comp. Phys. Commun. 1(1970)224.
Authors: E. Sheldon, R.M. Strang
Program title: BARBARA
Catalogue identifier: ABOB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 1(1969)37
Programming language: Algol.
Computer: BURROUGHS B5500.
Operating system: MARK VIII.
RAM: 8K words
Word size: 48
Keywords: Nuclear physics, Cross section, Spin-parity, Transmission coefficient, Penetrability, Hauser-feshbach, Biedenharn-rose, Statistical, Mechanism, Double differential cross section, Differential cross section, Total cross section, Multipolarity, Clebsch-Gordan Coefficients, Racah coefficients, Fano x-coefficients, Legendre hyperpolynomial, Optical potential, Spin-orbit coupling, Satchler, Compound nucleus, Angular correlation, Mixing ratio, Racah functions, Associated legendre Functions, Moldauer.
Classification: 17.10.

Revision history:
Type Tit le Reference
correction 000A CORRECTION 23/04/71 See below

Nature of problem:
Evaluation of total and double-differential cross sections in absolute and normalized form for angular correlations in low-energy nuclear reactions of the type (a,bgamma) or (a,bgamma-gamma) according to statistical compound-nucleus theory in j-j coupling formalism. The program constitutes a generalization of an earlier version to make provision for arbitrary spin, mass and relative orbital momentum of the interaction partners; the emergent gamma-radiations may be of pure or mixed multipolarity. It can take extra exit channels and Moldauer level- width fluctuation effects into account, with provision for in-plane and/or azimuthal variation of angle.

Solution method:
Following automatic statistical tabulation of the relevant angular momenta, partities and summation variables permitted by conservation rules, the program evaluates Hauser-Feshbach penetrability terms (with or without the Moldauer modification) and Racah-function products in accordance with the compound-nucleus theory of angular correlation. Summing the products, the code evaluates the weighting coefficients of successive orders of Legendre hyperpolynomials (bipolar spherical harmonics, expressed in terms of products of associated Legendre functions) and thence calculates the double-differential cross section in absolute and normalized form as a function of angles characterizing the emission direction of the emergent radiations.

Restrictions:
The program is designed to cater for particles of arbitrary mass, spin and orbital momentum (rather than gamma-radiation) in the CN formation and decay channels, but although there is no restriction up to l<= 12 upon the orbital momenta the computation time lengthens progressively with increase in lmax and in practice it is usual to restrict the partial waves to lmax<= 6. When it becomes necessary to distinguish 0- form 0+ nuclear levels, machine-specific provisions have to be incorporated.

Running time:
About 3-40 min per case, depending on the complexity, but may exceed this for high partial waves or fine angular gradiation steps.

CORRECTION SUMMARY
Manuscript Title: (See footnote CPC vol 2 page 278.) Computation of total, differential and double-differential cross sections for compound nuclear reactions of the type (a,b), (a,bgamma) and (a,bgamma-gamma) (II) Generalized programs mandy and barbara for arbitrary angular momenta in hauser-feshbach-moldauer foramlism. (C.P.C. 1(1969)35).
Authors: E. Sheldon, R.M. Strang
Program title: 000A CORRECTION 23/04/71
Catalogue identifier: ABOB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)278
Classification: 17.10.