**1. NAME AND TITLE**

BIGGI 3P,4T: Numerical Gamma-Ray Transport Code for Plane or Spherical Multilayer Geometry.

The code BIGGI 3P is the first of the BIGGI series to be published. BIGGI stands for "Boltzmann's Integralgleichung für Gamma-Intensitaeten (Boltzmann's Integral Equation for Gamma Intensities)," 3 for the third version and P means that the pair production process can be included, if wanted. The next version, BIGGI 4T, is also included in the package. The first work on the code was done in 19621963 at Reaktorstation Geesthacht (Elbe), Western Germany.

The code is also available in the OECD NEA Data Bank, abstracted as E147.

**2. CONTRIBUTOR**

EURATOM, Ispra (Varese) Italy.

**3. CODING LANGUAGE AND COMPUTER**

FORTRAN IV; IBM 360/75 and UNIVAC 1108.

**4. NATURE OF PROBLEM SOLVED**

BIGGI 3P,4T solves the Boltzmann transport equation in plane or spherical multilayer geometry without iteration (since there is only energetic downscattering). It computes gamma-ray angular fluxes, spectra, buildup factors and albedos. The buildup factors calculated in this way are compared with those of the moments method. The sources must be monoenergetic and located on one outer boundary. Their angular distribution can be isotropic or collimated.

**5. METHOD OF SOLUTION**

BIGGI 3P,4T integrates the Boltzmann equation numerically. The basis is the pair of coupled
integral equations, discussed (for the case of neutrons) in Weinberg and Wigner, [*The Physical
Theory of Neutron Chain Reactors*, Chicago 1959, p. 228 f. ("third form of the Boltzmann
equation")]. Discrete ordinate meshes are defined in all the three concerned dimensions (angle,
space, and gamma-ray wave length), and the integrals figuring in the transport equation are
approximated by sums. The program solves the integral equations without iteration, since they
belong to the Volterra type (as long as only energetic downscattering is assumed). The gamma-ray
cross section (in Thomson Units per electron) of each considered slab must be given in input. The
contribution of the low-energetic tail below the cutoff energy to the four buildup factors (energy
and particle flux, dose and energy absorption rate) and the two albedos (energy and particle
current) is estimated. An exponential transformation allows rather great spatial integration steps,
up to 2 or 3 mfp.

**6. RESTRICTIONS OR LIMITATIONS**

The program allows a maximum of 5 slabs, 8 angular, 26 spatial, and 71 wavelength mesh points.

**7. TYPICAL RUNNING TIME**

A study of typical running time has not been made by RSIC.

**8. COMPUTER HARDWARE REQUIREMENTS**

Execution requires a 32 K memory. Tape units are not needed explicitly, with the exception of the standard input, output, and systems procedures.

**9. COMPUTER SOFTWARE REQUIREMENTS**

The code was originally designed for the FORTRAN II Monitor System of the IBM 7090 and now runs in FORTRAN IV systems.

**10. REFERENCES**

H. Penkuhn, "BIGGI* A Generalized Gamma Transport Program," Informal Notes.

H. Penkuhn, "User's Manual for the Gamma Transport Codes BIGGI 3P and BIGGI 4T," EUR 3555.e (September 1967).

H. Penkuhn, "A Numerical Solution of the Boltzmann Equation Applied to Concrete Slabs," EUR 2488.e, (1965).

H. Penkuhn, "Provisory Description of the gamma Transport Program BIGGI 3 P," informal notes.

U. Canali, B. Chinaglia, C. Manduchi, et al., "Research on Radiation Shielding," Reprint from EUR 11643.e, pages 87-108.

**11. CONTENTS OF CODE PACKAGE**

Included are the referenced documents and one (1.2MB) DOS diskette which contains the source code and input and output for a sample problem.

**12. DATE OF ABSTRACT**

January 1968; updated July 1981, February 1985.

**KEYWORDS: ** NUMERICAL INTEGRATION; SLAB; SPHERICAL GEOMETRY; ONE-DIMENSION; GAMMA-RAY; DISCRETE ORDINATES; INTEGRAL
BOLTZMANN EQUATION