Potentials optical

Neuhauser D and Baer M 1990 A new accurate (time independent) method for treating three-dimensional reactive collisions the application of optical potentials and projection operators J. Chem. Phys. 92 3419... 

Neuhauser D, Baer M and Kouri D J 1990 The application of optical potentials for reactive scattering a case study J. Chem. Phys. 93 2499... 

Jolicard G, Leforestier C and Austin E J 1988 Resonance states using the optical potential model. Study of Feshbach resonances and broad shape resonances J. Chem. Phys. 88 1026... 

Leforestier C and Wyatt R E 1983 Optical potential for laser induced dissociation J. Chem. Phys. 78 2334... 

Kinetic equation, optical potential, tensor theory and structure factor refinement in high-energy electron diffraction... 

Dederichs, P.H. (1972) Dynamical diffraction theory by optical potential methods, Solid State Phys., 27, 125. 

In the projection operator formalism, which leads to a rigorous basis for the optical potential, the absorptive imaginary part is associated with transitions out of the elastic channel from which no return occurs. Whereas Pgl transitions are in this category, excitation transfer (ET) transitions are not, since return ( virtual excitation ) can occur during the ET collision. In the event that a localized avoided curve crossing with one other state dominates the inelastic process (expected for many endoergic transfers), the total absorption probability (opacity) can still be defined ... 

Figure 30. Laboratory angular distributions for He (2 5) + Ar at six collision energies from Freiburg laboratory. Solid curves are calculated from optical potential due to Haberland and Schmidt.102 (see Figs. 32 and 35).

Figure 34. Optical potential for He (23S) + Ar, due to Brutschy et al.100 (see Note 115 in References Section).

Figure 46. Velocity dependence of total ionization cross section for He (23S) + Ar. Solid curve is calculated from optical potential due to Brutschy et al.100 Symbols represent measurements by other authors.,39-140,142 (see text). Spikes result from orbiting resonances labeled by vibrational (v) and rotational (J) quantum number.

Figure 48. Temperature dependence of total quenching rate constant for He + Ar. Solid curves represent measurements by Lin-dinger et al. MI dashed curves are calculated from optical potentials due to other authors.100 102...

B. Zygelman, P. Froelich, A. Saenz, S. Jonsell, and A. Dalgarno. Optical Potential for Hydrogen - Antihydrogen Collisions at Cold Temperatures - preprint. 

As the positron approaches the target system it interacts with and distorts it, so that the total wave function no longer has the separable form of equation (3.3). Nevertheless, an equivalent Schrodinger equation can be derived for the positron, the solution to which is a function of the positron coordinate rq only, with the correct asymptotic form but at the cost of introducing a non-local optical potential. 

It has been shown by Gailitis (1965) that the optical potential defined by equation (3.22) is less attractive than the exact optical potential for energies below the lowest eigenvalue of QHQ, and the resulting phase shifts are therefore lower bounds on the exact values. Furthermore, as the number of basis functions used in the matrix representation of the operator QHQ is increased, the optical potential becomes more attractive and the resulting phase shift therefore also increases, becoming closer to the exact value. 

When elastic scattering is the only open channel, k is positive but all other values of kf, and all values of nj, are negative. Consequently, all the functions F)(ri) and Gj(p), except for Fi(ri), decay exponentially for large values of r and p. The resulting equation for Fj(ri) is similar in form to equation (3.20), in which the optical potential Vopt was introduced indeed a truncated coupled-state expansion essentially defines an approximation to the optical potential which satisfies the conditions for the phase shifts to be lower bounds on the exact values. 

Probably the most accurate positron-hydrogen s-wave phase shifts are those obtained by Bhatia et al. (4974), who avoided the possibility of Schwartz singularities by using a bounded variational method based on the optical potential formalism described previously. These authors chose their basis functions spanning the closed-channel Q-space, see equation (3.44), to be of essentially the same Hylleraas form as those used in the Kohn trial function, equation (3.42), and their most accurate results were obtained with 84 such terms. By extrapolating to infinite u in a somewhat similar way to that described in equation (3.54), they obtained phase shifts which are believed to be accurate to within 0.0002 rad. They also established that there are no Feshbach resonances below the positronium formation threshold. 

Bartschat, K., McEachran, R.P and Stauffer, A.D. (1988). Optical potential approach to positron and electron scattering from noble gases I. Argon. J. Phys. B At. Mol. Opt. Phys. 21 2789-2800. 

Byron Jr., F.W. and Joachain, C.J. (1981). A third order optical potential theory for elastic scattering of electrons and positrons by atomic hydrogen. J. Phys. B At. Mol. Phys. 14 2429-2448. 

---