By David Bates, Benjamin Bederson
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Example text
As the energy increases, the results of the two models become significantly different. By 25 keV/amu, about 10 terms were required in the basis set, if plane wave translational factors are used, but the PSS model converged much more slowly, at least twice that number of terms being required. For Z > 2, PSS calculations have been reported by Hare1 and Salin ( 1977) (for Z = 4,5,8) and by Salop and Olson (1977, 1979)(for 2 = 6,8), but above 1 keV/amu only results of limited accuracy can be expected from this model.
103), has been derived (in a different way) by Duman and Smirnov (1978). 577 . . is the Euler's constant. As seen from Eq. (108), the quantity xo = xo(u, Z ) depends logarithmically on u and is almost independent of Z . 5 X Zln(314/u) (cm2) (109) The basic idea ofthe decay model, namely the existence of a large number of ionic states available for the reaction, may also be formulated in terms of a dense multi-curve-crossingsystem. In that case one can introduce an internuclear distance R,,such that for R > R, all crossings are passed diabatically (with zero transition probability) and for R G R, the capture probability is equal to unity.
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. This approach does not work well in practice since, although over a finite region of space the wave function can be represented accurately by a large, but finite, single centered basis, the representation of the rearranged system in the asymptotic region Itl- 00 requires an infinite number of terms.