Abstract
Two-state coupled equations within the continuum distorted-wave representation (CDW) are derived using the time-dependent second-order Euler-Lagrange variational principle of Sil (1980). Matrix elements are simplified using generalised non-orthogonal coordinates. It is shown that the original CDW theory of Cheshire (1964) is a variation-perturbation approximation, analogous to the Oppenheimer-Brinkman-Kramers approximation (OBK) in the travelling atomic eigenstate representation. It is also shown that unlike OBK the CDW wavefunctions are in general not normalised and the CDW wavefunction normalisation integrals are therefore calculated numerically using a complex Laplace transform. The implications of a variational CDW theory of ionisation are briefly considered.
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