Frozen-planet resonances in doubly excited helium atom; adiabatic approach
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
Frozen-planet resonances in doubly excited helium atom; adiabatic approach Tasko P. Grozdanov1,a , Alexander A. Gusev2 , Evgeni A. Solov’ev2 , and Sergue I. Vinitsky2,3 1 2 3
Institute of Physics, University of Belgrade, Pregrevica 118, Belgrade 11080, Serbia Joint Institute for Nuclear Research, Dubna, Moscow Region 141980, Russia Peoples’ Friendship University of Russia (RUDN University), Moscow 117198, Russia Received 7 April 2020 / Received in final form 1 June 2020 Published online 23 July 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. An improved adiabatic method is applied to study the highly excited asymmetric two-electron configurations of helium atom known as frozen-planet resonances. It is shown that our approach provides much better agreement with numerically calculated resonance positions than the previously used Born– Oppenheimer type approximation. Wide range of states were studied, related to N = 7−15 first-ionization thresholds. We show that estimates of tunneling widths of these states however are not reliable, because of the breakdown of adiabatic approximation in the underbarrier region of configuration space. We also provide computational evidence that a single-potential approximation in hyperspherical coordinates would be inferior to our approach.
1 Introduction Frozen-planet (FP) resonances of helium atom correspond to highly correlated, asymmetrically excited two-electron configurations localized on the same side of the nucleus. The origin of these states has been explained by Richter and Wintgen [1] who discovered a classical stable periodic orbit describing the collinear system Zee in which the inner electron oscillates between the nucleus and an external turning point while the outer electron stays fixed at some distant point. The nearby regular trajectories describe the motion around the nucleus of the inner electron along the Stark-like polarized trajectories while a distant electron is dynamically localized and performs slow oscillations. It is possible to formulate the semiclassical quantization of these trajectories [1]. The large-scale numerical calculations have been performed [2] in order to obtain the energy positions, widths and wave functions characterizing FP resonances. The classical stability has manifestation in long lifetimes. In accord with semiclassical picture, the strong correlation between the electrons leads to formation of a Stark-type inner electronic wave function and a vibrational, highly nonhydrogenic wave function for the outer electron. In recent years, the reduced-dimensionality, that is 1D [3] and 2D [4,5], models of He atom have been used to study the non-dispersive wave packets formed as a result of periodically driven FP configurations. The existence of FP resonances is inherently tied to the repulsive electron-electron interaction and standard a
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perturbation theory starting from the independentparticle
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