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Lasers generating wavelengths shorter than one angstrom unit would have many important applications. Ever since the discovery of the Mössbauer effect it has been realized that we would be able to stimulate nuclear transitions suitable for lasers in this range if we could prepare the population inversion on which lasers depend, and it has also long been known that some nuclear isomers are producible in a state of population inversion. Why then do we not yet have any operating gamma-ray lasers?