In most textbooks on nuclear physics1–3 the set of radioactive decay chain equations is solved analytically for a maximum of three nuclides. The general Bateman solution4 is given as a final result or only with a brief mention of the elaborate recursive procedure needed to obtain it.3 Here, a short method for obtaining the general solution is demonstrated.
REFERENCES
1.
Robley D. Evans, The Atomic Nucleus (Krieger, Malabar, FL, 1982), reprint of 14th ed., pp. 470–490.
2.
Kenneth S. Krane, Introductory Nuclear Physics (Wiley, New York, 1987), pp. 170–173.
3.
K. Heyde, Basic Ideas and Concepts in Nuclear Physics (IOP, Bristol, 2000), 2nd ed., pp. 59–65.
4.
H.
Bateman
, “Solution of a system of differential equations occurring in the theory of radioactive transformation
,” Proc. Cambridge Philos. Soc.
15
, 423
–427
(1910
).5.
Mary L. Boas, Mathematical Methods in the Physical Sciences (Wiley, New York, 1983), 2nd ed., pp. 662–663.
6.
C. L.
Bohn
and R. W.
Flynn
, “Real variable inversion of Laplace transforms: An application in plasma physics
,” Am. J. Phys.
46
, 1250
–1254
(1978
).
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© 2002 American Association of Physics Teachers.
2002
American Association of Physics Teachers
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