Some general consideration is given to approximate methods of passing from the exact integral equation for the spectral density of ψ-quanta to a differential equation of the first order. It is shown that the coefficients of the latter may be formed by various functions of a certain class. As a particular case, the approximation considered in [1–3] is derived. Certain approximate solutions are compared with known solutions of the integral equation . Results presented include an approximate calculation of the distribution of absorbed ψ-ray energy between the elements of the mixture for one particular case; these are compared with the corresponding exact solutions taken from .
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O. I. Leipunskii, B. V. Novozhilov, and V. N. Sakharov, Propagation of Gamma-Quanta in Matter [in Russian], Moscow, Fizmatgiz (1960).
B. V. Novozhilov, Zh. eksperim. i teor. fiz.,33, 1287 (1957).
B. M. Terent'ev, and Yu. S. Ryabukhin, Zh. tekhn. fiz.,31, 837 (1961).
B. M. Terent'ev, V. A. El'tekov, and Yu. S. Ryabukhin, Atomnaya énergiya,13, 568 (1962).
P. Karr and J. Lamkin, Phys. Rev.,76, 1843 (1949).
N. P. Syrkus, A. Kh. Breger, and B. I. Vainshtein [Russian translation], Large Radiation Sources in Industry, Vienna, IAEA, (1960), p. 15.
M. Levine and M. Steinberg, Nucl. Sci. and Engng.,12, 498 (1962).
A. Kh. Breger et al. (see Idem, p. 50).
Translated from Atomnaya Énergiya, Vol. 16, No. 4, pp. 291–295, April, 1964
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Él'tekov, V.A., Terent'ev, B.M. & Panchvidze, M.V. Gamma radiation spectrum and fractional values of absorbed energy in an arbitrary homogeneous mixture. At Energy 16, 355–360 (1964). https://doi.org/10.1007/BF01116054
- Differential Equation
- Integral Equation
- Exact Solution
- Approximate Solution