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A nuclear experiment has been designed for use in the undergraduate laboratory. Following a theoretical treatment of alpha barrier penetration and the kinematics and Q value of alpha decay, a semiclassical calculation is made for the half-life for alpha decay, followed by a more exact quantum mechanical result. The decay schemes of three commercially available sources are studied. The branching ratios to various excited states in the residual nuclei are measured along with the precise energies of the decay. The absolute activity of one source ([sub.241.Am]) is determined from its measured alpha activity, and from its gamma activity as measured by a low-energy photon detector.

Gamow vectors are generalized eigenvectors of the Hamiltonian with complex eigenvalues that describe exponentially decaying (or growing) states. The energy wavefunctions corresponding to Gamow vectors have a pole immediately below (or above) the real axis in the complex energy plane. Although complex energy values were introduced more than half a century ago for the theory of alpha decay, they have become disreputable and have been banished from quantum mechanics textbooks because of mathematical problems and incorrect physical interpretation. Developments in modern mathematics have now provided a mathematical foundation that has led to the correct physical interpretation. In this article, energy eigenvectors with complex eigenvalues are first introduced by explicitly considering a specific simple decaying system. Then, an elementary account of the properties of Gamow vectors is given. The results from the decaying system provide a motivation for the introduction of Gamow vectors and some of the background information needed to understand their properties.