Imaginary potentials

In the adiabatic bend approximation (ABA) for the same reaction,18 the three radial coordinates are explicitly treated while an adiabatic approximation was used for the three angles. These reduced dimensional studies are dynamically approximate in nature, but nevertheless can provide important information characterizing polyatomic reactions, and they have been reviewed extensively by Clary,19 and Bowman and Schatz.20 However, quantitative determination of reaction probabilities, cross-sections and thermal reaction rates, and their relation to the internal states of the reactants would require explicit treatment of five or the full six degrees-of-freedom in these four-atom reactions, which TI methods could not handle. Other approximate quantum approaches such as the negative imaginary potential method16,21 and mixed classical and quantum time-dependent method have also been used.22... 

Tliis is a Schrodinger-ty p o equation for the Greensfunction of a particle in the imaginary potential i(f>(r). r playing the role of the energy. Tt shows that G is given by the resolvent... 

A negative imaginary potential in the time-independent Schrodinger equation absorbs the particle flux, thus violating the law of conservation of flux, which is satisfied for real potentials [12,13]. Then, the quantum electrodynamical phenomenon of pair annihilation can be represented by particle loss due to an effective absorption potential H = —zVabs since the exact mechanism of positron loss is totally irrelevant to the study of the atomic processes in consideration [9,10,14-16]. The only important aspect of pair annihilation for the present purpose is the correct description of the loss rate. The absorption potential H is proportional to the delta function 5 (r) of the e+-e distance vector r (Section 4.2). 

Mahapatra, S. and Sathyamurthy, K. (1993) Negative imaginary potentials in time-dcpcndcnl quantum molecular scattering, Chem,. Soc Fu,radu,y Trans. 93, 773-779. 

Numerical calculations have also been performed by Eu (1970) with the variable-phase method. He investigated changes of the opacity versus angular momentum curve for various collision energies and imaginary potentials, and for elastic collisions of K + HBr at energy E= 1-49 kcal/mole. Tables of results were presented in terms of reduced variables. 

To understand this unique feature of the negative imaginary potential it is easiest to refer to the time-dependent language, discussed later in the section. Heuristically, note that the time-dependent propagator, essentially contains ae term which decays the wavefunction in regions where is positive. The... 

The negative imaginary potentials can be applied in any scattering formalism. In close coupling, they can be implemented to block any product arrangement [31] (see figure 63.4.2) and this thereby converts the reactive problem to an inelastic one the only cost is the propagation of a complex matrix, rather than a real one. 

As a brief aside let us show here that if an external distorting potential wcxl as in Eq. (10) is used, calculating the A matrices could in some cases be simplified due to the relation reminiscent to those used in Ref. 16 for wcx being the imaginary potential. Consider... 

D. Neuhauser, Molecular scattering-Very-short-range imaginary potentials, absorbing potentials, and flux-amplitude expressions./. Chem. Phys. 103 8513 (1995). 

The Hamiltonian is normalized with ( c > ) because the wave function in the product channel is adsorbed by an imaginary potential. 

S. Giona, V. Cerbelli, V. Vitacolorma, Universality and imaginary potentials in advection-diffusion equations in closed flow,/. Fluid Meek, 2004, 513, 221. 

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