Abstract
The relative importance of diffusion and recombination of the products of ionizing radiations is examined in several typical cases and methods for the solution of the differential equation of columnar ionization are discussed. It is shown that Jaffé's method is not applicable to radiobiological or purely radiochemical processes in which no external electric fields are acting. A method based on a recent suggestion of Kramers (see Gerritsen, 1948) appears to be particularly good when recombination is strong.
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Literature
Barrer, M. 1941. Diffusion in and through solids. Cambridge: University Press.
Cobine, J. D. 1941. Gaseous Conductors. New York: McGraw-Hill.
Compton, K. T. and I. Langmuir. 1930. “Electrical Discharges in Gases.”Rev. Mod. Physics,2, 123–242.
Creighton, H. J. 1943. Electrochemistry. Vol. I. New York: John Wiley and Sons.
Failla, G. 1949. “Biological Effects of Radiation and Health Protection.”Nucleonics,4, 42–4.
Fletcher, A. 1944. “Note on tables of an integral.”Philos. Mag.,35, 16–17.
—, Miller, J. C. P. and L. Rosenhead, 1946.An index of mathematical tables. New York: McGraw Hill.
Gerritsen, A. N. 1948. “Ionization by Alpha-Particles in liquids at low temperatures.”Physica,14, 381–424.
Glasstone, S., K. Laidler, and H. Eyring. 1941. Theory of rate processes. New York: McGraw-Hill.
Gray, L. H. 1947. “The distribution of the ions resulting from the irradiation of living cells.”Brit. Jour. Radiol. Suppl., No. 1, 7–15.
Jaffé, G. 1913. “Zur Theorie der Ionisation in Kolonnen.”Ann. d. Physik,42, 303–41.
— 1929. “Kolonnenionisation in Gasen bei erhöhtem Druck.”Physik. Z.,30, 849–56.
Landau, H. G. 1950. “A problem in radiobiology: diffusion and recombination of ions.”Bull. Math. Biophysics,12, 27–34.
Lea, D. E. 1946. Actions of Radiations on Living Cells. Cambridge: University Press.
— 1947. “The action of radiations on dilute aqueous solutions: the spatial distribution of H and OH.”Brit. Jour. Radiol. Suppl., No. 1, 59–64.
Mathematical Tables Project. 1940. Tables of Sine, Cosine and Exponential Integrals. Vol. I. New York: Works Progress Administration.
Moelwyn-Hughes, E. A. 1940. Physical Chemistry. Cambridge: University Press.
Opatowski, I. 1951. “Determination of the Sensitive Volume by Irradiation and the Ionization, Density.”Bull. Math. Biophysics,13, 263–71.
Placzek, G. 1946. The functions\(E_n (x) = \int_1^\infty {e^{ - xu} u^{ - n} du} \).Nat. Res. Counc. of Canada. Div. Atomic Energy. Chalk River, Ontario.
Pollard, E. C. and F. Forro, Jr. 1949. “Examination of the target theory by deuteron bombardment ofT−1 phage.”Science,109, 374–75.
Powell, E. O. 1943. “An integral related to the radiation integrals.”Philos. Mag.,34, 600–07.
Timoféeff-Ressovsky, N. W. and K. G. Zimmer. 1947. Biophysik. Leipzig: Hirzel.
Toulis, W. J. 1950. “The decomposition of water by radiation.”U. S. Atomic Energy Commission. UCRL-583.
Zirkle, R. E. 1935. “Biological effectiveness of α-particles as a function of ion concentration produced in their paths.”Amer. Jour. Cancer,23, 558–67.
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Opatowski, I., Tangherlini, F.R. Diffusion and recombination of products of ionizing radiations. Bulletin of Mathematical Biophysics 13, 273–288 (1951). https://doi.org/10.1007/BF02477922
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DOI: https://doi.org/10.1007/BF02477922