Although H and He-like resonantly photopumped laser schemes were among the earliest methods proposed for producing x-ray lasers, demonstrating these schemes in the laboratory has proved to be elusive. Nevertheless the resonantly photopumped schemes remain interesting both because of their potential to improve the efficiency of lasers that otherwise operate through other process such as recombination and because of their potential for yielding entirely new and relatively efficient lasers. We present an expanded list of candidate lasers that operate by utilizing Ly-α or He-α radiation from a pump ion to photopump an electron from the ground state of a H or He-like lasant ion to the n = 3 or 4 state, with subsequent lasing between the n = 4 → n = 3 or n = 3 → n = 2 states of the H or He-like ion. The example of the potassium-pumped chlorine scheme, which exhibits both 4 → 3 and 3 → 2 laser lines, has been modeled extensively, and the results of the calculation are presented.
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