**1. NAME AND TITLE**

GAKER-KIRA: Energy Transfer of Protons in H2O or Polyethylene and Deuterons in D2O.

**2. CONTRIBUTOR**

Institutt
for Atomenergi, Kjeller, Norway through the OECD Nuclear Energy Agency Data
Bank, Issy-les-Moulineaux, France.

**3. CODING LANGUAGE
AND COMPUTER**

Fortran IV; CDC 3600 (C00813C360000).

**4. NATURE OF
PROBLEM SOLVED**

Evaluation of the energy transfer matrix and its first, second and third Legendre components for protons bound in water or polyethylene, and for deuterons bound in heavy water. Further output, the isotropic scattering matrix with diagonal elements corrected for first order anisotropy, scattering and transport cross sections, nth moment of energy transfer mn(e) (n=1,2,3), and Maxwellian averages of these moments, of the transport mean free path and of the scattering cross sections.

**5. METHOD OF
SOLUTION**

For down-scattering the elements of the matrix are calculated directly from the analytical formula. For scattering in the same speed (energy) group, a linear average is taken of four terms, scattering from the typical speed point of that group to four equidistant points in that same interval. Up-scattering elements are computed from detailed balance. The Bessel functions that appear are calculated following an algorithm due to Stegun and Abramowitz (see references). The anisotropic version of GAKER, which is due to Koppel and Young (see references) is also included in GAKER-KIRA, and the integration over the orientation angles is done by a 5-points Gauss quadrature.

**6. RESTRICTIONS OR
LIMITATIONS**

A maximum number of 55 speed groups is permitted.

**7. TYPICAL RUNNING
TIME**

Approximately 8 to 9 elements are calculated per second in the isotropic version, the anisotropic version is five times slower.

**8. COMPUTER
HARDWARE REQUIREMENTS**

Standard CDC 3600.

**9. COMPUTER
SOFTWARE REQUIREMENTS**

FORTRAN 3600 under SCOPE 5.1.

**10. REFERENCES**

**a) Included Documentation**

Stamm’ler, R. J. J. “User’s Manual for GakerK-Kira”.

**b) Background Documentation**

H.C. Honeck, BNL 5826, p 69 FF (1961).

H.C. Honeck, “Trans.Am.Nucl.Soc.”5,47 (1962).

D.T. Goldman and F.D. Federighi, BNL 719, 1,100 (1962).

Irene A. Stegun and M. Abramowitz, “Math. Tables Aids Comput”. 11, 255 (1957).

J.U. Koppel and
J.A. Young, “Nucl. Sci. Eng” 19, 412 (1964).

**11. CONTENTS OF CODE
PACKAGE**

The package is distributed on a CD with a compressed zip file including a source file with data, output and documentation.

**12. DATE OF ABSTRACT**

November 2013.

**KEYWORDS:** BESSEL FUNCTIONS, CROSS SECTIONS, DEUTRONS,
ENERGY TRANSFER, HEAVY WATER, LEGENDRE POLYNOMIALS, PROTONS, SCATTERING,
TRANSPORT THEORY