By David Bates, Benjamin Bederson

ISBN-10: 0080564798

ISBN-13: 9780080564791

ISBN-10: 0120038196

ISBN-13: 9780120038190

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**Extra info for Advances in Atomic and Molecular Physics, Vol. 19**

**Example text**

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.

The linear trajectory was accurate above u = 0. ; the nonlinear trajectory was used at lower energies. B. H . Bransden and R. K. Janev 24 - 20-E = 15z i 0 0 c wl 8 10- 5- v OO 2 4 6 8 7 L ~ LABORATORY ENERGY (keV/amu) ’* 10 FIG. 2. Cross sections for electron capture by Li3+ from H(ls) at low velocities. (A) Experimental data of Seim et a/. (1980). Theoretical cross sections: (-) atomic expansion (Bransden and Noble, 1982); (---) molecular orbital expansion (Kimura and Thorson, I981 b): (----) UDWA (Ryufuku and Watanabe, 1979a,b).

A different approach, suggested by Mittleman and Quong (1968) and developed by Dewangan (1975, 1977), is based on the eikonal, or Glauber, approximation. The exact amplitude for charge exchange to a final level can be represented as (in the notation of Section II1,B) In the eikonal approximation (see, for instance, Bransden, 1983), the exact wave function for the system, y(r,l), is approximated by The phase factor represents scattering between the projectile of charge Z2 and the bound electron in the initial state, treating the bound electron as a fixed charge, which seems physically reasonable when the velocity of the projectile is large.

### Advances in Atomic and Molecular Physics, Vol. 19 by David Bates, Benjamin Bederson

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