Elsevier

Annals of Physics

Volume 232, Issue 2, June 1994, Pages 243-291
Annals of Physics

Regular Article
New Class of Resonant States for Potentials with Coulomb Barrier: Quasimolecular States

https://doi.org/10.1006/aphy.1994.1054Get rights and content

Abstract

The global method for all S-matrix poles identification is extended to a short-range potential with Coulomb and centrifugal barrier. The pole function k = kl(g) is analyzed by constructing the Riemann surface on which it is single valued and analytic. New-class poles are identified and their properties are studied. They are located in finite regions of the k-plane in a neighborhood of the stable-points on the images of certain Riemann sheets. The new-class poles approach the stable-points for a sufficiently deep potential well. For a given potential strength g there are new-class poles on the images of some Riemann sheets and old-class poles on the others. The special points of the Riemann surface acquire a remarkable physical meaning. The branch-points are transition points of the quantum system from the old-class resonant states localized in the region of the potential well to the new-class resonant states localized in the region outside the potential well. The stable-points are points where the system is almost insensitive to the variation of the potential strength. The new-class resonant states are doorway states whose stability is a consequence of the localization of the wave function rather than of a symmetry. The states of the system are characterized by the quantum number n with precise topological meaning: the label of the Riemann sheets. Analytical formulas for the energy and width of a new-class resonant state corresponding to a pole in the neighborhood of a stable-point are given. Quasimolecular states are new-class resonant states corresponding to poles in the neighborhood of certain stable-points. The properties of the quasimolecular states (energy, widths, deviation from the linear dependence of the energy on l(l + 1), doorway character, and criteria for observability) result naturally from the general properties of the new-class resonant states. A unitary treatment of the quasimolecular states both below and above the Coulomb barrier is given.

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