Complex energies and the polyelectronic Stark problem

Themelis, SI; Nicolaides, CA

dc.contributor.author	Themelis, SI	en
dc.contributor.author	Nicolaides, CA	en
dc.date.accessioned	2014-03-01T01:49:47Z
dc.date.available	2014-03-01T01:49:47Z
dc.date.issued	2000	en
dc.identifier.issn	0953-4075	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/25925
dc.subject.classification	Optics	en
dc.subject.classification	Physics, Atomic, Molecular & Chemical	en
dc.subject.other	INDUCED TUNNELING RATES	en
dc.subject.other	ABSORBING POTENTIAL METHOD	en
dc.subject.other	H-RESONANCE-SPECTRUM	en
dc.subject.other	ELECTRIC-FIELD	en
dc.subject.other	DC-FIELD	en
dc.subject.other	SEMICLASSICAL CALCULATIONS	en
dc.subject.other	THEORETICAL RESOLUTION	en
dc.subject.other	N=4 THRESHOLD	en
dc.subject.other	STATES	en
dc.subject.other	COMPUTATION	en
dc.title	Complex energies and the polyelectronic Stark problem	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2000	en
heal.abstract	The problem of computing the energy shifts and widths of ground or excited N-electron atomic states perturbed by weak or strong static electric fields is dealt with by formulating a state-specific complex eigenvalue Schrodinger equation (CESE), where the complex energy contains the field-induced shift and width. The CESE is solved to all orders nonperturbatively, by using separately optimized N-electron function spaces, composed of real and complex one-electron functions, the latter being functions of a complex coordinate. The use of such spaces is a salient characteristic of the theory, leading to economy and manageability of calculation in terms of a two-step computational procedure. The first step involves only Hermitian matrices. The second adds complex functions and the overall computation becomes non-Hermitian. Aspects of the formalism and of computational strategy are compared with those of the complex absorption potential (CAP) method, which was recently applied for the calculation of field-induced complex energies in H and Li. Also compared are the numerical results of the two methods, and the questions of accuracy and convergence that were posed by Sahoo and Ho (Sahoo S and Ho Y K 2000 J. Phys. B: Ar. Mel. Opt. Phys. 33 2195) are explored further. We draw attention to the fact that, because in the region where the field strength is weak the tunnelling rate (imaginary part of the complex eigenvalue) diminishes exponentially, it is possible for even large-scale nonperturbative complex eigenvalue calculations either to fail completely or to produce seemingly stable results which, however, are wrong. It is in this context that the discrepancy in the width of Li 1s(2)2s S-2 between results obtained by the CAP method and those obtained by the CESE method is interpreted. We suggest that the very-weak-held regime must be computed by the golden rule, provided the continuum is represented accurately. In this respect, existing one-particle semiclassical formulae seem to be sufficient. in addition to the aforementioned comparisons and conclusions, we present a number of new results from the application of the state-specific CESE theory to the calculation of field-induced shifts and widths of the H n = 3 levels and of the prototypical Be 1s(2)2s(2) S-1 state, for a range of field strengths. Using the H n = 3 manifold as the example, it is shown how errors may occur for small values of the field, unless the function spaces are optimized carefully for each level.	en
heal.publisher	IOP PUBLISHING LTD	en
heal.journalName	JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS	en
dc.identifier.isi	ISI:000166210900010	en
dc.identifier.volume	33	en
dc.identifier.issue	24	en
dc.identifier.spage	5561	en
dc.identifier.epage	5580	en