By David Bates, Benjamin Bederson

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6 ) (Olson and Salop, 1977): pi, p, = ' 1 ( 1 + m , I + m , qi + i = 1,2,3 ( I60a) i = 4, 5, 6 ( 160b) 1 ~ qi+3) Z I -++;R: R$ ( 160c) 52 B. H. Bransden and R. K. = '1 1 ( 1 + m , qi-3 ~ + 9;) Z I (160d) where R , is the internuclear (p- Z ) separation, R2 is the e-p separation, and R, is the e-Z distance. The Ri(i = I , 2, 3) are given by (161a) (161b) (161c) In order to solve Eqs. ( 1 60), the initial conditions on qp and pp must be specified. - b2)'/2 = b, q t = 0, ( 1 63) where h is the impact parameter and R.

It is therefore applicable in a very broad energy range. + - - - 2. Unitarized Distorted Wave Approximation (UD WA) Ryufuku and Watanabe (1978, 1979a) have shown that unitarization of the approximate solutions for the transition amplitudes in the H Z collision system can be easily achieved by using the interaction representation for the S-matrix. If {c,) is a complete basis, consisting of atomic orbitals centered on the proton ({(p))) and on the ion ({rib))) (and hence, (c,) = ((p)) U{

1979). Both main objectives can be achieved by taking as the expansion functions members of some complete set of discrete functions and attempting to increase the size of the basis set to convergence. Among such functions are Gaussian (Dose and Semini, 1974) and Sturmians (Gallaher and Wilets, 1968; Shakeshaft, 1976; Winter, 1982). In order to allow for all the important discrete and continuum channels, the size of the basis set can become unmanageably large as u increases, and since a single center expansion is formally complete and numerically easy to use, it might be questioned whether results could be obtained by representing the wave function by a very large single center basis, obtaining charge-exchange cross sections from an integral expression.