Long-wavelength approximation in on- and off-resonance transitions

Komninos, Y; Mercouris, T; Nicolaides, CA

dc.contributor.author	Komninos, Y	en
dc.contributor.author	Mercouris, T	en
dc.contributor.author	Nicolaides, CA	en
dc.date.accessioned	2014-03-01T01:22:37Z
dc.date.available	2014-03-01T01:22:37Z
dc.date.issued	2005	en
dc.identifier.issn	1050-2947	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16623
dc.subject.classification	Optics	en
dc.subject.classification	Physics, Atomic, Molecular & Chemical	en
dc.subject.other	Atomic spectroscopy	en
dc.subject.other	Electron resonance	en
dc.subject.other	Hamiltonians	en
dc.subject.other	Laser applications	en
dc.subject.other	Laser pulses	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Electric dipole approximation (EDA)	en
dc.subject.other	Laser spectroscopy	en
dc.subject.other	Long-wavelength approximation (LWA)	en
dc.subject.other	Wave functions	en
dc.subject.other	Electron transitions	en
dc.title	Long-wavelength approximation in on- and off-resonance transitions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1103/PhysRevA.71.023410	en
heal.identifier.secondary	http://dx.doi.org/10.1103/PhysRevA.71.023410	en
heal.identifier.secondary	023410	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	In view of the possibilities of laser spectroscopy with very short pulses and relatively high frequencies, we examine aspects of the theory of atom-field interactions that are related to violation of the condition of the long-wavelength approximation (LWA) according to which kr 1, where r is ""of the order of atomic dimensions"" and k is the magnitude of the wave vector. On- and off-resonance transitions are considered, with kr being larger than unity due to the large extent of the two wave functions involved in the coupling matrix element. The implementation of the analysis uses bound-free transition matrix elements with the n=50 and 80 hydrogenic functions as initial states and values of k up to 27 eV, which is sufficient to produce kr >1, thereby rendering the LWA inoperative. In spite of this, it is shown that, for on-resonance transitions, the results from the use of the well-known multipole operators resulting from the LWA [e.g., the electric dipole approximation (EDA)] agree with those from the exact expressions derived here from the application of the multipolar Hamiltonian. This numerical agreement is proven analytically. As a test of the kind of convergence of the multipole series expansion for small values of k and large r, it is shown that the lowest-order ratio of electric dipole to quadrupole matrix elements decreases rapidly within 1.0 atomic unit above threshold. Finally, it is shown that off-resonance couplings lead to differences between the full-interaction operator and the EDA which cannot be neglected. In the extreme case of intrashell couplings for the n=50 shell, calculation shows that the 50p state is coupled to angular momentum states up to =21, compared to the electric dipole coupling of Δ =±1. © 2005 The American Physical Society.	en
heal.publisher	AMERICAN PHYSICAL SOC	en
heal.journalName	Physical Review A - Atomic, Molecular, and Optical Physics	en
dc.identifier.doi	10.1103/PhysRevA.71.023410	en
dc.identifier.isi	ISI:000227483900085	en
dc.identifier.volume	71	en
dc.identifier.issue	2	en