A dressing of zero-range potentials and electron-molecule scattering problem at Ramsauer-Townsend minimum
A dressing technique is used to improve zero range potential (ZRP) model. We consider a Darboux transformation starting with a ZRP, the result of the "dressing" gives a potential with non-zero range that depends on a seed solution parameters. Concepts of the partial waves and partial phases for non-spherical potential are used in order to perform Darboux transformation. The problem of scattering on the regular X$_{\hbox{n}}$ and YX$_{\hbox{n}}$ structures is studied. The results of the low-energy electron-molecule scattering on the dressed ZRPs are illustrated by model calculation for the configuration and parameters of the silane ($\hbox{SiH}_4$) molecule. \center{Key words: low-energy scattering, multiple scattering, Ramsauer-Townsend minimum, silane, zero range potential.