Factorisation of zero-width resonance wave functions

ABSTRACT

A zero-width resonance (ZWR) is also called a bound state in a continuum. Such resonances occur when the Floquet method is applied to a diatomic molecule submitted to a continuous wave field. This circumstance requires particular choices of wavelength and electric field amplitude. The corresponding wave function can be factorised with a method devised for bound states. The result is a product of an electronic factor depending parametrically on the nuclear coordinate by a nuclear factor. The factorisation of the wave function is done through the introduction of a fictitious time-independent Hamiltonian yielding the same coupled equations as the Floquet algorithm applied to the time-dependent Hamiltonian. The potential which determines the nuclear factor is calculated and used to recover the real ZWR quasi-energy. Application is made to the molecule Na₂ prepared by photoassociation in the metastable ³Σ⁺ _u state. Photodissociation of this state by laser-coupling to the (1)³Π _g state requires an intensity low enough to require the consideration of only two channels (one photon interaction) in the application of the Floquet method.

KEYWORDS:

• Floquet theory
• zero-width resonances
• factorisation of molecular wave functions

Acknowledgments

Stimulating discussions with Osman Atabek are acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author.