Simple method for calculating time dependence of individual radionuclide activities in decay series
A rapid method for calculating the time dependence of activities of individual radionuclides in genetically coupled decay series has been proposed. The method is based on the mathematical procedure, in which the matrix method is used for calculating a set of decay equations given in the vector form. The developed method is computerized and uses the modern Scilab software. This simple method eliminates certain drawbacks of older methods used previously for this purpose and is applicable to even solve calculations which are not easily treatable with the older methods. Some practical examples of such calculations are presented. Moreover, the new method is universal and it also enables a more general approach to the problem of the calculation of decay series in nuclear chemistry. [...]
-  H. Bateman: “The solution of a system of differential equations occurring in the theory of radioactive transformations”, Proc. Cambridge Phil. Soc., Vol. 16, (1910), pp. 423–427.
-  J.F. Duncan and G.B. Cook: Isotopes in Chemistry, Clarendon Press, Oxford, 1968.
-  M. Wiernik: “Time-dependent relative activities in the radioactive families”, J. Radioanal. Chem., Vol. 31, (1976), pp. 529–568. http://dx.doi.org/10.1007/BF02518517[Crossref]
-  G. Faure: Principles of Isotope Geology, 2nd ed., J. Wiley and Sons, New York, 1986.
-  J. Tölgyessy and E. Bujdosó: CRC Handbook of Radioanalytical Chemistry, Vol I, CRC Press, Boca Raton, 1991.
-  S. Mirzadeh and P. Walsh: “Numerical Evaluation of the Production of Radionuclides in a Nuclear Reactor - Part I”, Appl. Radiat. Isot., Vol. 49, (1998), pp. 379–382. http://dx.doi.org/10.1016/S0969-8043(97)00287-X[Crossref]
-  M. Ivanovich and R.S. Harmon: Uranium-series Disequilibrium, Applications to Earth, Marine, and Environmental Sciences, 2nd ed., Clarendon Press, Oxford 1992.
-  K. Rasilainen and J. Suksi: “A multisystem modelling approach for uranium-series dating”, Nucl. Technol., Vol. 120, (1997), pp. 254–260.
-  S. Azzam and J. Suksi: “DECSERVIS: A tool for radioactive decay series visualization”, Centr. Europ. J. Chem., published online: July 4, 2006, DOI 10. 10.2478/s11532-006-0026-0.
-  L. Motl and M. Zahradník: Let us pursuing linear algebra (in Czech), Karolinum Press, Prague, 2002.
-  Ch. Hacker: Radiation Decay, Version 4, FreeWare, Griffith University, Brisbane, 2005.
-  Scilab Reference Manual, On-line Documentation, Scilab Group, http://www:scilab.org/, http://www:scilab.org/download/index download.php, http://www:gu.edu.au/school/eng/mmt/RadDec.html.