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We propose a new variational principle for scattering theory which extends the Schwinger variational principle beyond the static-exchange approximation and to inelastic scattering. Application of this formulation to the scattering of electrons by hydrogen atoms at energies below k' = 0.64 demonstrates the rapid convergence of the phase shift with respect to the number of basis functions for both the open-and closed-channel orbitals. Furthermore, we show that the convergence of the phase shift with respect to the number of expansion functions (exact states or pseudostatesj is also fast. In our theory, the resulting phase shifts can be more accurate than those of the close-coupling method even if the same expansion basis is used. The phase shifts in our ls-2s-2p calculation are comparable to those of 1s-2s-2p-3p-3d calculation of Matese and Oberoi [Phys. Rev. A 4 569 (1971j],which are very close to the exact values. Several aspects of the convergence characteristics are also discussed.

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