By Benjamin Bederson, Alexander Dalgarno

**Advances in Atomic, Molecular, and Optical Physics , verified in 1965, keeps its culture of excellence with quantity 32, released in honor of Founding Editor Sir David Bates upon his retirement as editorof the sequence. This quantity provides experiences of subject matters with regards to the purposes of atomic and molecular physics to atmospheric physics and astrophysics.
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1989). J. Phys. B 22, 2195. , and Ghosh, A. S. (1990). J. Phys. B 23,2641. Bransden, B. H. (1969). Case Stud. At. Collision Phys. 1, 171. Bransden, B. H. (1983). , Benjamin/Cummings, Reading, Mass. Bransden, B. , Joachain, C. , and McCann, J. F. (1992). J. Phys B 25,4965. Bransden, B. , and McDowell, M. R. C. Charge Exchange and the Theory of lon-Atom Collisions, Oxford University Press, Oxford. Brown, C. , and Humberston, J. W. (1984). J. Phys. B 17, L423. Brown, C. , and Humberston, J. W. J.

1992). A different approach has been followed by Deb et al. , 1986), who used a method (DMS) of approximating the full Green’s function that includes all second-order and some higher order terms, but the evaluation involves a number of approximations that are difficult to assess. Some cross sections for ground-state capture from hydrogen calculated from these second-order calculations are shown in Table I, compared with those arising from the two-state coupled channel approximations. , 1989). 266-3 FW2 EIK FB = first Born approximation; CC = two-state close coupling; SB = second Born model; CCSB = two-state close coupling with second Born terms (all from Basu and Ghosh, 1988).

3) with N + 1 replaced by N. We will assume in what follows that sufficiently accurate target states can be calculated. The solution for Eq. (2) corresponding to the process defined by Eq. (1) then has the asymptotic form where x~/~,,,, and xlllmj are the spin eigenfunctions of the incident and scattered electrons, where the direction of spin quantization is usually taken 4) is the scattering amplitude to be the incident beam direction, and hi(& corresponding to scattering angles 0, 4. The wave numbers ki and k j are related to the total energy of the system by the equation E = wi +fkjZ = wj + $ k j (6) The outgoing wave term in Eq.