Waves distorted

A number of improvements to the Bom approximation are possible, including higher order Born approximations (obtained by inserting lower order approximations to i jJ into equation (A3.11.40). then the result into (A3.11.41) and (A3.11.42)), and the distorted wave Bom approximation (obtained by replacing the free particle approximation for the solution to a Sclirodinger equation that includes part of the interaction potential). For chemical physics... 

The vibrational relaxation of simple molecular ions M+ in the M+-M collision (where M = 02, N2, and CO) is studied using the method of distorted waves with the interaction potential constructed from the inverse power and the polarization energy. For M-M collisions the calculated values of the collision number required to de-excite a quantum of vibrational energy are consistently smaller than the observed data by a factor of 5 over a wide temperature range. For M+-M collisions, the vibrational relaxation times of M+ (r+) are estimated from 300° to 3000°K. In both N2 and CO, t + s are smaller than ts by 1-2 orders of magnitude whereas in O r + is smaller than t less than 1 order of magnitude except at low temperatures. 

For the present 12-6-4 potential we then have C 2 = 4Da12, C6 = —4Da, and C4 = — ae2/2. The WKB evaluation of the perturbation integral of the method of distorted waves results in the (temperature) average transition probability in the form (29) ... 

This study has made no substantial improvement in the original theory of distorted waves. By evaluating the vibrational transition probability explicitly for the inverse (12-6-4) power potential, however, we were able to study some interesting aspects of the ion-molecule collisions. We summarize them here. 

Blaha, M. Davis, J. Electron Ionization Cross Sections in the Distorted Wave Approximation. N.R.L. Memorandum Report 4245, Naval Research Laboratory, Washington, DC, 1980. 

Giant dipole resonance. Isovector giant resonances contain information about the SE through the restoring force. In particular the excitation of the isovector giant dipole resonance (GDR) with isoscalar probes has been used to extract A R/R [32], In the distorted wave Bom approximation optical model analysis of the cross section the neutron and proton transition densities are needed as an input. For example, in the Goldhaber-Teller picture these are... 

Continuum Distorted Wave Eikonal Initial State Method... 

In the present section we present a theoretical description for the continuum-distorted-wave eikonal-initial-state (CDW-EIS) model. This model is one of the most advanced and complete perturbative theories of heavy particle collisions which has been formulated to date. The reasons for the success of this model particularly in describing ionization at high energies in the MeV/amu range are that ... 

To conclude we have examined the applicability of the continuum-distorted-wave theory to experiments carried out using the reaction microscopy technique for both doubly differential cross sections for longitudinal electron velocities and fully differential cross sections applied to the single ionization of 3.6 MeV amu on neutral target atoms. For the case of the... 

Distorted Wave Bom Approximation. Quantum scattering calculations are sometimes made using the distorted wave Bom approximation (15). Such calculations have the advantage of almost always being feasible numerically. For simple cases, one can also obtain some results analytically (16). However, the accuracy of the results is generally poor, for most molecular collisions. A... 

Distorted-wave Born Qualitative agreement with quasiclassical ... 

The cross sections have been obtained through a quantum mechanical calculation of the transition matrix elements in the distorted-wave approximation, for low and ultra-low collisional energies. 

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