Shape resonance

A shape resonance is a metastable state in which an electron is trapped due the shape of a potential barrier. Altunata describes a state as being a shape resonance if, "the internal state of the system remains unchanged upon disintegration of the quasi-bound level." A more general discussion of resonances and their taxonomies in molecular system can be found in the review article by Schulz,; for the discovery of the Fano resonance line-shape and for the Majorana pioneering work in this field by Antonio Bianconi; and for a mathematical review by Combes et al.

In quantum mechanics, a shape resonance, in contrast to a Feshbach resonance, is a resonance which is not turned into a bound state if the coupling between some degrees of freedom and the degrees of freedom associated to the fragmentation (reaction coordinates) are set to zero. More simply, the shape resonance total energy is more than the separated fragment energy. Practical implications of this difference for lifetimes and spectral widths are mentioned in works such as Zobel.

Related terms include a special kind of shape resonance, the core-excited shape resonance, and trap-induced shape resonance.

Of course in one-dimensional systems, resonances are shape resonances. In a system with more than one degree of freedom, this definition makes sense only if the separable model, which supposes the two groups of degrees of freedom uncoupled, is a meaningful approximation. When the coupling becomes large, the situation is much less clear.

In the case of atomic and molecular electronic structure problems, it is well known that the self-consistent field (SCF) approximation is relevant at least as a starting point of more elaborate methods. The Slater determinants built from SCF orbitals (atomic or molecular orbitals) are shape resonances if only one electronic transition is required to emit one electron.

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