Optical-Potential Models

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... 

G. Jolicard, J. Humbert, Study of the one-channel resonance states. Method without a stabilization procedure in the framework of the optical potential model, Chem. Physics, 118 (3) (1987) 397. 

Gersh and Bernstein [145] explain the high energy decrease in the cross-section as due to the increasing contribution of inelastic scattering which is ignored in the low-energy optical potential model (see Section 3.3.1(c)). 

During the past few years we have observed an intensive development of many-channel approaches to the collision problem. In particular, the coupled-channels method is based on an expansion of the total wave fmiction in internal states of reactants and products and a numerical solution of the coupled-channels equations.This method was applied in the usual way to the atom-diatom reaction A + BC by MOR-TENSBN and GUCWA /86/, MILLER /102/, WOLKEN and KARPLUS /103/, and EL-KOWITZ and WYATT /101b/. Operator techniques based on the Lippmann-Schwinger equation (46.II) or on the transition operator (38 II) has also been used, for instance, by BAER and KIJORI /104/ The effective Hamiltonian approach( opacity and optical-potential models) and the statistical approach (phase space models, transition state models, information theory) provide other relatively simple ways for a solution of the collision problem in the framework of the many-channel method /89/<. 

While an experiment designed to vary b systematically is inconceivable at this time, it may not always be so and such experiments are highly desirable. (It is worth noting that some information can be obtained both directly from rotational state analysis of the products and indirectly from data analysis using the optical potential model. )... 

The conditions required by (ii) are not allowed quantum mechanically the sharp discontinuity would be smoothed. Indeed, what few examinations there have been of the nature of P(fe, ), either by analysis of reactive scattering using the optical potential model or by trajectory calculation, show a different dependence than that required by (ii). This is merely support for the familiar idea that, even in the absence of energy barriers, reactivity is dependent upon the total angular momentum. 

Summary of nonrelativistic proton-nucleus optical potential models... 

No calculation has been made which includes all of the quantities listed in eqs. (3.100) and (3.102). Table 3 provides a summary of several current nonrelativistic optical potential models for proton-nucleus scattering and indicates which terms in eqs. (3.98)-(3.103) are included and notes the key approximations made. Further progress toward a calculation along the lines of eqs. (3.100) and (3.102) is expected in the near future. 

The RIA optical potential model specified by eqs. (4.23)-(4.32) requires six separate target densities corresponding to scalar, vector and tensor distributions for both protons and neutrons. With the exception of the proton vector density, these must be obtained from theoretical models. The dependence of the RIA proton-nucleus scattering predictions on these theoretical nuclear structure models can be minimized, however, by the method discussed in the next two paragraphs. 

Off-shell and nuclear medium effects occur in the relativistic optical potential models, just as in the NR theory. Fewer calculations of these effects have been done in the relativistic approach, however. 

We close this sedion on relativistic optical potentials by summarizing the principal assumptions and key ingredients in the three, relativistic optical potential models discussed here [Ra 85, Ho 85, Tj 87b]. This summary is provided in table 4. 

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