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ANP QUARlERlY PROGRESS REPORT character of the data is evident from the straight- line fit to the points on semilogarithm paper. ENERGY ABSORPTION RESULTING FROM INCIDENT GAMMA RADIATION AS A FUNCTION OF THICKNESS OF MATERIALS WITH SLAB GEOMETRY C. D. Zerby The interaction of radiation with the atomic particles of matter results in an energy transfer to the particles or in the creation of secondary radiation. The secondary radiation, in turn, is usually absorbed close to the primary interaction. With high radiation intensity, the absorption of radiation energy in biological shields or in structural members can be important. Since essentially all the energy absorbed becomes heat, problems of induced thermal stresses in already stressed structural members may well determine design limitations. The heating effect may also be a limiting design factor in some cases in which material strength is seriously dependent on temperature. In all cases some knowledge of the energy absorption distribution within a material is necessary. Only a preliminary study of heating in beryllium has been completed thus far, and results are reported here. Most radiation absorption problems can be at least approximated by known analytical methods. For the gamma radiation absorption distribution, however, solution of the Boltzmann transport equation is necessary for accuracy. At NDA, extensive 3 calculations have been carried out to solve the transport equation for the penetration of gamma rays. The NDA calculations included the energy absorption as a function of position for a point isotropic sourcef4 but it was not possible to include the absorption distribution for plane slabs. At ORNL, the total energy absorption of incident gamma radiation in the different materials of finitely thick composite slabs was also calculated,2 but, again, the calculation did not include the absorption distribution, In this study the Monte Carlo method is being used for the calculation of the energy absorption distribution in finitely thick slabs, and the calculations are programmed for solution on the ORACLE 3H. Goldstein and J. E. Wilkins, Jr., CaZcuZations o the Penetration of Gamma Rays, NYO-3075 (also ND 1 15C-41) (June 30, 1954). ‘lbid, Tables 7.113, 7.116, 7.119, 7.122, and 7.127. 144 at ORNL. For a monodirectional beam of monoenergetic photons on a slab of material of finite thickness, the energy absorption was calculated in every interval of 0.10 in, through the slab. The absorption included the energy transmitted to the material in a scattering collision as well as that transmitted in an absorption collision; in every case the photon was followed until it was reflected from the slab, was absorbed, or had penetrated the slab, The scattering cross sections were calculated with the use of the Klein-Nishina scatteringcross-section formul~,~ while the absorption cross sections were obtained by empirical fits to published data, A 9-in.-thick slab of beryllium was used, and the incident photons were considered to have energies of 0.5, 1.5, and 5.0 mOc2 and to be normally incident. For the 1.5-moc2 case, angles of incidence of 30, 60, and 85 deg were also investigated (1 mOc2 = 0.51 Mev), The results obtained for the normally incident 0.5-rn0c2 photons on the slab of beryllium are shown in Fig. 12.3, The histogram indicates the statistical nature of the Monte Carlo solution, while the smooth curve is a fit, by eye, to the data. The values given on the histogram are the averages of the values for the 0.10-in. intervals. In the future it is intended that a rigorous method of fitting the data will be employed. The area under the curve is the total energy absorption. 5W. Heitler, The Quantum Theory of Radiation, 3d ed., Eq. 39, p 219, Oxford University Press, New York, 1954. 6G. R. White, X-Ray Attenuation Coefficients from 10 Keu to IO0 MeV, Table I, NBS-1003 (May 13, 1952). 0 20 018 016 014 012 010 008 006 0 04 NETRATING 0 087 UNCLASSIFIED 2-0!-059-!3 002 01 0 1 2 I 3 I 4 I 5 I 6 I 7 8 9 I 10 THICKNESS (in) Fig. 12.3. Radiation Heating of a 9=in.-Thick Beryllium Slab by Normally Incident 0.5-mOc 2 Photons. Smooth fit to statistical data shown. (1 I -i ’-*’ a ,rqr . c- L 1 J - 5 . I
$ 030 028 !?? 026 024 m 022 a $ 020 018 0 016 5 014 5 012 W g 010 Z 008 8 006 5 004 5 002 a E O UNCLASSIFIED 2-01-059-!5 0 1 2 3 4 5 6 7 8 9 THICKNESS (in ) Fig. 12.4. Radiation Heating of a 9din.-Thick Beryllium Slab by Normally Incident Photons. In Fig. 12.4 the smooth fits to the statistical data are presented for normally incident photons of energy 0.5, 1.5, and 5.0 mOc2, The effect of the reflected photons on the energy absorption curve is readily seen at the entrance face of the slab. The value of the fraction of energy absorbed per inch at the entrance face for the incident photons can be calculated by multiplying ps, the scattering cross section, by f, the average fraction of energy absorbed by the ~naterial.~ These values for 0.5, 1.5, and 5.0 mOc2 are, respectively, 0.118, 0.123, and 0.089. The large contribution of the reflected component is especially evident for the 0.5-m0c2 Dhotons at the entrance face as the difference be- tween 0.1 18 12.4. The e 1.5-mnc2 ph 5 060 Z 056 052 8 048 044 8 040 036 032 5 028 5 024 g 020 PERIOD ENDING DECEMBER 10,7954 UNC-ASSI~IEO 2-01-059-14 Z 016 8 012 6 008 k 004 $ 0 0 1 2 3 4 5 6 7 8 9 THICKNESS (in ) Fig. 12.5. Radiation Heating of a 9-ireThick Beryl lium Slab by Slant-inci dent 1.5.m oc2 F'hoton s. induced injury with time. Just recently the ANP Medical Advisory Group (ANP-MAG) issued recommendations' which made some concessions in this direction in that increased total doses were allowed for schedules which distributed the radiatilon over longer times. It has been demonstrated9 that the ANP-MAG recommendations can be expressed to within 4% by a mathematical formulation with three parameters based on a model of partly irreparable injury and partly injury which recovers exponen- tially with time, The model was previou:jly sug- gested by Blair.10'12 The mathematical formulation is much more flexible than the Biological Planning Chart which expresses the ANP-MAG recommendations, since it gives a unique value of '"Yjnutes of the 3rd ANP-MAG Meetin - 11-12 May 1954, School of Aviation Medicine, 5-18,862. Several Weeks, UR-312 (Feb. 10, 1954). 145
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