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The Lehmann-Symanzik-Zimmermann formalism is used to solve the V-0 sector of the Lee model. The solution to one singular integral equation solves the entire sector, giving the two elastic-scattering amplitudes and the production amplitude. The behavior of the various amplitudes and phase shifts is discussed as a function of energy and coupling constant. Also, the bound-state problem is discussed. This approach is compared with the eigenvalue and dispersion treatments of this sector found in the literature. * Work performed under the auspices of the U. S. Atomic Energy Commission. 1 M. S. Maxon and R. B. Curtis, Phys. Rev. 137, B996 (1965). 2 The r functions are the vacuum expectation values of timeordered products of the Heisenberg fields. 3 T. D. Lee, Phys. Rev. 95, 1329 (1954); G.

Recent progress in the design and analysis of soft X-ray laser experiments at the Lawrence Livermore National Laboratory is reviewed. The modelling of optical laser irradiated targets used to produce X-ray lasers is discussed. Two types of atomic inversion schemes have been explored-collisional excitation in neon-like and nickel-like ions, and recombination in lithium-like and hydrogen-like ions. Results for each scheme are discussed and compared with experimental data. The authors describe work on X-ray optics, including refraction by electron density gradients in the lasing plasma, techniques for increasing spatial coherence and the use of multilayer mirrors to improve laser efficiency and coherence.

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