Shape resonances as poles of the semiclassical Green's function obtained from path-integral theory: Application to the autodissociation of the He-2(++) (1)Sigma(+)(g) state

Nicolaides, CA; Douvropoulos, TG

dc.contributor.author	Nicolaides, CA	en
dc.contributor.author	Douvropoulos, TG	en
dc.date.accessioned	2014-03-01T01:54:47Z
dc.date.available	2014-03-01T01:54:47Z
dc.date.issued	2005	en
dc.identifier.issn	0021-9606	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/27463
dc.subject.classification	Physics, Atomic, Molecular & Chemical	en
dc.subject.other	VOLCANIC GROUND-STATES	en
dc.subject.other	ENERGIES	en
dc.subject.other	HE-2(2+)	en
dc.subject.other	WIDTHS	en
dc.subject.other	DISSOCIATION	en
dc.subject.other	POTENTIALS	en
dc.subject.other	QUANTUM	en
dc.subject.other	IONS	en
dc.subject.other	WKB	en
dc.title	Shape resonances as poles of the semiclassical Green's function obtained from path-integral theory: Application to the autodissociation of the He-2(++) (1)Sigma(+)(g) state	en
heal.type	journalArticle	en
heal.identifier.secondary	024309	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	It is known that one-dimensional potentials, V(R), with a local minimum and a finite barrier towards tunneling to a free particle continuum, can support a finite number of shape resonance states. Recently, we reported a formal derivation of the semiclassical Green's function, G(SC)(E), for such V(R), with one and two local minima, which was carried out in the framework of the theory of path integrals [Th. G. Douvropoulos and C. A. Nicolaides, J. Phys. B 35, 4453 (2002); J. Chem. Phys. 119, 8235 (2003)]. The complex poles of G(SC)(E) represent the energies and the tunneling rates of the unstable states of V(R). By analyzing the structure of G(SC)(E), here it is shown how one can compute the energy, E-nu, and the radiationless width, Gamma(nu), of each resonance state beyond the Wentzel-Kramers-Brillouin approximation. In addition, the energy shift, Delta(nu), due to the interaction with the continuum, is given explicitly and computed numerically. The dependence of the accuracy of the semiclassical calculation of E-nu and of Gamma(nu) on the distance from the top of the barrier is demonstrated explicitly. As an application to a real system, we computed the vibrational energies, E-nu, and the lifetimes, tau(nu), of the He-4(2)++, nu=0, 1, 2, 3, 4, and (HeHe++)-He-4-He-3 nu=0, 1, 2, 3, (1)Sigma(g)(+) states, which autodissociate to the He++He+ continuum. We employed the V(R) that was computed by Wolniewicz [J. Phys. B 32, 2257 (1999)], which was reported as being accurate, over a large range of values of R, to a fraction of cm(-1). For example, for J=0, the results for the lowest and highest vibrational levels for the He-4(2)+ (1)Sigma(g)(+) state are nu=0 level, E-0=10 309 cm(-1) below the barrier top, tau(0)=6400 s; nu=4 level, E-4=96.6 cm(-1) below the barrier top, tau(4)=31x10(-11) s. A brief presentation is also given of the quantal methods (and their results) that were applied previously for these shape resonances, such as the amplitude, the exterior complex scaling, and the lifetime matrix methods. (c) 2005 American Institute of Physics.	en
heal.publisher	AMER INST PHYSICS	en
heal.journalName	JOURNAL OF CHEMICAL PHYSICS	en
dc.identifier.isi	ISI:000230653700015	en
dc.identifier.volume	123	en
dc.identifier.issue	2	en