Yoshiko Harima

Validity of the geometric-progression formula in approximating gamma-ray buildup factors

A geometric-progression (G-P) method formula, B/sub r/ = 1 + (B-1) . (K/sup x/-1)/(K-1), accurately represents the buildup factor data as a function of distance for the following reasons: 1. The value of parameter B corresponds to that of the buildup factor at 1 mfp, which is the integration of a basic spectrum for a specified material and for a specified source energy. 2. The variation of parameter K with penetration represents the photon dose multiplication and the change in the shape of the spectrum. Exposure buildup factors for point isotropic sources in an infinite medium approximated by the G-P fitting parameters are in good agreement with the basic data calculated by the PALLAS code, including that of boron for low energies, and of lead, including the effects of bremsstrahlung and fluorescence. The validity of using the G-P parameters to interpolate the buildup factor in ..mu..r and in E is ascertained. Furthermore, the extrapolation to the buildup data for depths above 40 mfp is examined.

An historical review and current status of buildup factor calculations and applications

Abstract The γ-ray buildup factor is a multiplicative factor which corrects the response to uncollided photons so as to include the contribution of the scattered photons. Buildup factors are important data implemented in point kernel codes for use in shield design, together with attenuation coefficients. The Goldstein-Wilkins buildup factors calculated with the moments in 1954 were used as standard data until recently, but new and improved data filling present needs are available based on the latest cross sections and include the secondary radiation contributions. A new fitting formula, called Geometric Progression, was developed to reproduce the data in codes used for shield design . This formula can reproduce the data over the full range of distance, energy and atomic number within a few percent.

Fuzzy measure analysis of public attitude towards the use of nuclear energy

Abstract This paper is concerned with applying fuzzy measures and fuzzy integrals to analyze public attitude towards the use of nuclear energy. To this end, a questionnaire on the use of nuclear energy is set up and data are collected in Japan, the Philippines and the FRG. Factor analysis is performed to get the primary structure of public attitude. It is shown that the attitude of the responders to the questionnaire in each country is well explained with its hierarchical structure obtained by fuzzy measure analysis.

Interpolation of gamma-ray buildup factors for point isotropic source with respect to atomic number

The values of buildup factors for a specific energy above KAPPA edges and penetration distance vary smoothly with respect to atomic number. An interpolation of buildup factors for an arbitrary elemental material is examined using geometric-progression (G-P) parameters for an equivalent atomic number. The G-P parameters are data fitted to the proposed American National Standard Buildup factor data compilation of 17 elements from beryllium to molybdenum and are calculated by the moments method.

Detailed Behavior of Exposure Buildup Factor in Stratified Shields for Plane-Normal and Point Isotropic Sources, Including the Effects of Bremsstrahlung and Fluorescent Radiation

Exposure buildup factors, energy spectra, and angular flux distribution for plane-normal incident and point isotropic source gamma rays of 0.1, 0.5, 1, 3, 6, and 10MeV penetrating two-layer water-lead and lead-water shields are calculated with the point Monte Carlo code EGS4. The effects of bremsstrahlung and fluorescent radiation are included. The value of the buildup factor in the second layer lies between those for infinite media of both materials in two source geometries in the 0.5- to 3-MeV energy range. However, this behavior varies remarkably and is enhanced with a bremsstrahlung contribution, when the source energy is higher than that corresponding to the minimum in the attenuation coefficient of lead. This varies equally with the fluorescent contribution when the source energy is close to the K edge of lead.

Annotated bibliography and discussion of gamma-ray buildup factors

Abstract The literature from 1950 to April 1987 on gamma-ray buildup factors for simple monoenergetic sources and for homogeneous media are surveyed and classified according to the source condition of point isotropic, plane normal, and plane isotropic. Based on those data, discussions have taken place to find out the status and the future issues on gamma-ray buildup factors.

A Comparison of Gamma-Ray Buildup Factors for Low- Z Material and for Low Energies Using Discrete Ordinates and Point Monte Carlo Methods

This paper discusses the calculation of exposure and absorbed dose buildup factors for a photon point source in infinite beryllium in the low-energy range of 0.03 to 0.3 MeV, for penetration depth up to 40 mfp, using two discrete ordinates codes, PALLAS-PL, SP-Br, and ANISN. Comparisons of both result to values obtained by point Monte Carlo calculations using the electron gamma shower version 4 code show reasonable agreement for two types of sources: normally incident and point isotropic sources. The fitting parameters of a geometric-progression method formula are determined for the resulting buildup factor data. These fitting parameters are in good agreement with the basic data within 5% over a great variation in magnitude.

An approximation of γ-ray buildup factors by geometrical progression

Geometrical progression formulas were derived for the approximation of the γ-ray dose, energy, and energy absorption buildup factors. The approximation formulas have the form 1 + (B−1)(KX−1)(K−1), where B and K are the two parameters and X is the source-detector distance in the medium in mean free paths. The results of the approximations were in good agreement with the basic data for all the materials used in the basic data, for the energy range of 0.5 to 10 MeV, and for thicknesses up to 20 mean free paths. An approximation using the method for the transmission probability for γ-rays obliquely incident on finite slabs was also attempted. Two parameters, B and K, of the geometrical progression form could be represented by monotonic functions of log E, in which the values of the two parameters changed monotonically with the atomic number of the media. Further, the four parameters which were used to represent B and K as linear functions of log E, and the six parameters used to represent B and K as quadratic functions of log E were also observed to change monotonically with the atomic number of the media. Therefore, the values of these parameters can be estimated for any media of different atomic number by interpolation.

Gamma-Ray Attenuation in the Vicinity of the K Edge in Molybdenum, Tin, Lanthanum, Gadolinium, Tungsten, Lead, and Uranium

This paper reports on the values of gamma-ray buildup factors and attenuation coefficients that rise steeply as the source energy decreases near the K edge in heavy materials and discontinuously fall at the K edge. However, the exposure rate attenuation factor, A(E,r) = D(E)B(E,{mu}r), given as a function of the penetration depth in centimeters, is relatively constant in the vicinity of the K edge. The development of a model that employs 4 K-shell X rays for the source shows that such behavior results from the large contribution of fluorescence radiation to the buildup factor for source photons of energies just above the K edge. In addition, an uncertainty in the extrapolation formula of the K parameter of the geometric progression buildup factor fitting function was removed for the energy range near the K edge.

An Improved Approximation Formula of Gamma-Ray Buildup Factors for a Point Isotropic Source in Two-Layer Shields

An approximation formula of buildup factor for two-layer shields proposed previously was improved to fitting to the newly calculated buildup factors for point isotropic source gamma-rays of 0.1, 0.3, 0.6, 1,3,6 and 10 MeV penetrating two-layer shields combinations of water, iron or lead materials with the Monte Carlo code EGS4 included the effects of Bremsstrahlung and fluorescent radiations. A f-function in the formula was modified to reproduce precisely the reference data up to the total thickness 40 mfp and the value of buildup factor at the interface of two-layer shields. The functions α and β used in improved f-function f(x1,x2) = α(x1)/{α(x1)+B2(x1)*β(x1,x2)x2} were represented by simple formula fitted to reference data in excellent agreement. Consequently, the two-layer shields buildup factor for any arbitrary thickness of the first-layer x1, and the second-layer x2, and for arbitrary source energy can easily be estimated by interpolation of functions α and β with respect to energy.