By David Bates, Benjamin Bederson

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85)l. , 1979). , 198l), and the probability P, = Ib,(+ m)I2is given by P, = n-3 1 JI dt V(t)exp [-r(t) + i Jr0,(7) d 1 ~ ] (88) where r(t)= $ J‘ V ( t’) dt ’ -m and for the H( 1s) + 2 system , 1 2 2 o,(R)=---+2 2n2 2-1 R (90) 27 ELECTRON CAPTURE The partial cross section anis now a, = 2n s,“ Pnbdb b being the impact parameter. It is interesting to note that this analytical model for the charge-transfer problem predicts strong Z-oscillations of the total cross section in the region Z < 30. Such 2-oscillators are found also in some other descriptions of the charge-exchange process and will be discussed in more detail in the subsequent sections.

For this reason it is not surprising that the results of calculations using atomic and molecular basis sets containing the same asymptotic states agree over a wide velocity range (at least 5 = 0. O), even if the molecular orbitals are not constructed from the atomic orbitals. The two-center basis can be improved by the addition of further functions, centered on nuclei I and 2, which are not solutions of the unperturbed atomic Schrodinger equations, but are of a more general nature. To be able to determine the required cross sections easily, it is convenient to choose these “pseudostate” functions to be orthogonal to the atomic orbitals which are necessary to describe the important entrance, excitation, and charge-exchange channels.

The same result is obtained also if Vo,(R,Z) exp(-aRZ-1/2). One of the main merits of the M- VPS theory for charge exchange is that it is able to include both the Landau- Zener and the tunneling transitions. 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.