Approximation methods pseudostates

The B-spline K-matrix method follows the close-coupling prescription a complete set of stationary eigenfunctions of the Hamiltonian in the continuum is approximated with a linear combination of partial wave channels (PWCs) [Pg.286]

Table (8.1) shows results of test calculations of e-He partial wave phase shifts, compared with earlier variational calculations [383], The polarization pseudostate was approximated here for He by variational scaling of the well-known hydrogen pseudostate [76]. The present method is no more difficult to implement for polarization response (SEP) than it is for static exchange (SE). 

Fig. 10.14. Total ionisation cross section for hydrogen. Experimental data, Shah et al. (1987) full curve, convergent close coupling (Bray and Stelbovics, 1992fc) plus signs, coupled channels optical (Bray et al., 1991c), crosses, pseudostate method (Callaway and Oza, 1979) long-dashed curve, intermediate-energy R-matrix (Scholz et al., 1990) short-dashed curve, distorted-wave Born approximation.

The FHBS method is unitary, i.e., probability is preserved. We can accurately identify the probability of making a transition to all bound states as the probability calculated from transitions to all negative energy pseudostates. Within this approximation we can identify ionization as the missing probability, i.e.. 

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