Shape resonances as poles of the semiclassical Green's function obtained from path-integral theory: Application to the autodissociation of the He2++1∑g+ state

Nicolaides, CA; Douvropoulos, TG

dc.contributor.author	Nicolaides, CA	en
dc.contributor.author	Douvropoulos, TG	en
dc.date.accessioned	2014-03-01T01:54:30Z
dc.date.available	2014-03-01T01:54:30Z
dc.date.issued	2005	en
dc.identifier.issn	00219606	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/27416
dc.subject.other	Autodissociation	en
dc.subject.other	Path-integral theory	en
dc.subject.other	Shape resonances	en
dc.subject.other	Approximation theory	en
dc.subject.other	Computational methods	en
dc.subject.other	Continuum mechanics	en
dc.subject.other	Green's function	en
dc.subject.other	Integral equations	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Resonance	en
dc.subject.other	Vibration measurement	en
dc.subject.other	Helium	en
dc.title	Shape resonances as poles of the semiclassical Green's function obtained from path-integral theory: Application to the autodissociation of the He2++1∑g+ state	en
heal.type	journalArticle	en
heal.identifier.primary	10.1063/1.1961487	en
heal.identifier.secondary	http://dx.doi.org/10.1063/1.1961487	en
heal.identifier.secondary	024309	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, GSC (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 GSC (E) represent the energies and the tunneling rates of the unstable states of V (R). By analyzing the structure of GSC (E), here it is shown how one can compute the energy, Eν, and the radiationless width, Γν, of each resonance state beyond the Wentzel-Kramers-Brillouin approximation. In addition, the energy shift, Δν, due to the interaction with the continuum, is given explicitly and computed numerically. The dependence of the accuracy of the semiclassical calculation of Eν and of Γν on the distance from the top of the barrier is demonstrated explicitly. As an application to a real system, we computed the vibrational energies, Eν, and the lifetimes, τν, of the He2 ++ 4, ν=0, 1, 2, 3, 4, and He4 He ++ 3 ν=0, 1, 2, 3, ∑g+1 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 He2+4 ∑g+1 state are ν=0 level, E0 =10 309 cm-1 below the barrier top, τ0 =6400 s; ν=4 level, E4 =96.6 cm-1 below the barrier top, τ4 =31× 10-11 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. © 2005 American Institute of Physics.	en
heal.journalName	Journal of Chemical Physics	en
dc.identifier.doi	10.1063/1.1961487	en
dc.identifier.volume	123	en
dc.identifier.issue	2	en