# Atom-Atom Scattering in the Field of a Laser

Chapter

## Abstract

Atom-atom scattering is a much richer phenomenon than electron-atom scattering in that there are a greater number of degrees of freedom and consequently a greater number of physical effects which can be observed in it. The introduction of the laser into either problem further enriches them but the degree of enrichment of the atom-atom problem is greatest when the scattering occurs at low relative energy. We therefore restrict our discussion to this problem, which can also be considered an introduction to the theory of laser-controlled chemistry.

## Keywords

Atomic State Laser Field Pauli Principle Nuclear Motion Coupling Operator
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## Notes and References

- 1.See N. F. Mott and H. S. W. Massey,
*The Theory of Atomic Collisions*, Oxford University Press, London (1965), for an early discussion of this approximation.Google Scholar - 2.
- 3.
- 4.
- 5.
- 6.
- 6a.
- 7.J. von Neumann and E. Wigner,
*Phys. Z*.**30**, 467 (1929); however, see O. J. Heilman,*J. Math. Phys.***11**, 3317 (1970).Google Scholar - 8.
- 8a.
- 8b.
- 9.See J. B. Delos and W. Thorson,
*Phys. Rev. A***6**, 728 (1972), for a comprehensive review and compilation of results.CrossRefGoogle Scholar - 10.K. M. Watson, in
*Properties of Matter under Unusual Conditions*(H. Mark and S. Fembach, eds.), Wiley, New York (1968).Google Scholar - 11.Such laser-induced reactions have been observed by D. B. Lidow, R. W. Falcone, J. F. Young, and S. Harris,
*Phys. Rev. Lett.***37**, 1590 (1976).CrossRefGoogle Scholar - 12.P. Lett, R. Watts, C. Westbrook, and W. Phillips,
*Phys. Rev. Lett*.**61**, 169 (1988), and S. Chu, L. Hollberg, J. Bjorkholm, A. Cable, and A. Ashkin,*Phys. Rev. Lett.***55**, 48 (1985).CrossRefGoogle Scholar - 13.This was first suggested by A. Gallagher and D. E. Pritchard,
*Phys. Rev. Lett*.**63**, 957 (1989). Refinements were made in P. S. Julienne and J. Vigué,*Phys. Rev. A***44**, 4464 (1991), and Y. B. Band and P. S. Julienne,*Phys. Rev. A***46**, 330 (1992).CrossRefGoogle Scholar - 14.M. H. Mittleman,
*Phys. Rev. A*14, 586 (1976).CrossRefGoogle Scholar - 15.The translation factors exp(±
*im***R**x*/2ħ)*have been omitted, which limits the validity of the treatment to center-of-mass energies below a kilovolt or so. The translation factors could be included at the expense of a little algebraic complication by the method of Ref. 2. However, the technique used there is not unique as shown in Ref. 3.Google Scholar - 16.A simple time-dependent generalization of Feshbach’s [Ann
*. Phys. (N.Y.)***19**, 287 (1962)] optical potential formalism can be used. See Section 8.2.Google Scholar - 17.The crossing point
*R*_{x}should be well separated from the classical turning point of the motion. This is a fine point which was discussed briefly in Section 9.2.Google Scholar - 18.N. M. Kroll and K. M. Watson,
*Phys. Rev. A***13**, 1018 (1976), have obtained these states with the approximation that there are only two electronic states and a single-mode laser.CrossRefGoogle Scholar - A. M. F. Lau and C. K. Rhodes,
*Phys. Rev. A***16**, 2392 (1977), have extended the treatment to a few electronic states and laser modes.CrossRefGoogle Scholar - 19.The index / that appears in (8.3.23) is not necessary here since we neglect direct coupling between the laser and the translational motion in the scattering. This neglect would not be legitimate for projectiles which are electrons (charged and not massive) but is here.Google Scholar
- 20.
- 20a.
- 20b.
- 21.J. von Neumann and E. Wigner,
*Phys. Z*.**30**, 467 (1929); however, see O. J. Heilman,*J. Math. Phys.***11**, 3317 (1970).Google Scholar - 22.
- 23.When the atoms are far enough apart, this potential goes over to an
*R~*^{7}behavior due to the retardation of the interaction. See H. B. G. Casimir and D. Polder,*Phys. Rev.***73**, 360 (1948), for the original treatment.CrossRefGoogle Scholar - 24.C. D. Wallace, T. P. Dinneen, K.-Y. Tan, T. T. Grove and P. L. Gould,
*Phys. Rev. Lett.***69**, 897 (1992).CrossRefGoogle Scholar - 25.The second term in (9.7.3) is formally nonlocal in
*R.*The low-energy approximation can be used to show that it is effectively local.Google Scholar - 26.
- 27.See Ref. 13, P. S. Julienne and J. Vigué,
*Phys. Rev. A***44**, 4464 (1991), and M. Trippenbach,CrossRefGoogle Scholar - B. Gao, J. Cooper, and K. Burnet,
*Phys. Rev. A***45**, 6555 (1992). See also the last of Ref. 13 for a density matrix approach which treats part of the problem.CrossRefGoogle Scholar

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© Springer Science+Business Media New York 1993