R-matrix method

The R-matrix method, which has been used extensively in studies of electron-molecule scattering, has also been applied to positron-molecule scattering, notably by Tennyson and his collaborators (Tennyson, 1986 ... 

Danby, G. and Tennyson, J. (1990). Differential cross sections for elastic positron-H2 collisions using the R-matrix method. J. Phys. B At. Mol. 

Tennyson, J. and Danby, G. (1987). The ab initio inclusion of polarisation effects in low-energy positron-molecule collisions using the R-matrix method. In Atomic Physics with Positrons, eds. J.W. Humberston and E.A.G. Armour (Plenum Press) pp. 111-121. 

L. Malegat, P. Selles, A.K. Kazansky, Absolute differential cross sections for photo double ionization of helium from the ab initio hyperspherical R-matrix method with semiclassical outgoing waves, Phys. Rev. Lett. 85 (2000) 4450. 

Burke, P.G. (1973). The R-matrix method in atomic physics, Comput. Phys. Commun. 6, 288-302. 

Sarpal, B.J., Tennyson, J. and Morgan, L.A. (1991). Vibrationally resolved electron HeH+ collisions using the nonadiabatic R-matrix method,./. Phys. B 24, 1851-1866. 

At energies below the first excitation threshold the variational principles discussed for bound states in chapter 5 can be extended to scattering (Callaway, 1978). We do not discuss this because of its restricted validity. However, there is another extension of bound-state methods into the positive-energy range that applies at least up to the ionisation threshold and somewhat beyond. This is the R-matrix method. Its possible extension to higher energies is discussed. 

The Green s function is chosen to satisfy the boundary condition demanded by the R-matrix method. This is easily accomplished by choosing Rj (r) to be regular at the origin and requiring... 

Despite having intuitive appeal and certain computational advantages, the R-matrix method has to date seen very limited application (Nestmann et al, 1994 ... 

The OCR computations for a many-electron system become very expensive due to the extremely large size of the basis sets. In special cases like Rydberg systems in external electromagnetic fields, this difficulty can be avoided by implementing the R-matrix method (34-36). The configuration space is divided into an inner and outer regions chosen so that, on one hand, the... 

Actucdly, in the opinion of the author, the R-matrix complex-rotation method, presented above, should be considered as an implementation of the idea proposed by Nicolaides and Beck (37) and then by Simon (38), and known as the exterior complex-scaling. This interpretation is natural due to the fact that the R-matrix method and the exterior complex-scaling share the idea of dividing the configuration space into internal and external parts. 

As is well-known, the two-electron system e -F H has been attracting theoretical attention for decades, with a large number of reports on the identification and nature of its resonances. Hence, it is possible to compare the CESE results of Ref. [123,124] with those published by other groups, who applied large scale R-matrix methods [130-132], or the CCR method [133-136], or specially improved close-coupling methods [137], or implementation of Feshbach s formalism. The related references are cited in Refs. [123,124] and below. 

In order to support the above, it suffices to recall here only a subset of the results that were published in Refs. [123,124]. To this purpose, 1 chose the resonances of H in the energy region below the n = 3 threshold, for the ipo, ijy ip symmetries. The CESE results [123] are listed in Tables 4.2 and 4.3, together with those obtained from large scale computations using the R-matrix method [130-132], or the CCR method [133-136]. 

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