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.
Graphical abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. Richter, D. Wintgen, Phys. Rev. Lett. 65, 1965 (1990)
K. Richter, J.C. Briggs, D. Wintgen, E.A. Solov’ev, J. Phys. B: At. Mol. Opt. Phys. 25, 3929 (1992)
P. Schlagheck, A. Buchleitner, Eur. Phys. J. D 22, 401 (2003)
J. Madroñero, A. Buchleitner, Phys. Rev. A 77, 053402 (2008)
A. González-Melan, J. Madroñero, Phys. Rev. A 101, 013414 (2020)
T.P. Grozdanov, E.A. Solov’ev, Eur. Phys. J. D. 74, 50 (2020)
I.V. Komarov, L.I. Ponomarev, S.Y. Slavyanov, Spheroidal and Coulomb Spheroidal Functions (Nauka, Moscow, 1976)[in Russian]
D. Baye, M. Hesse, M. Vincke, Phys. Rev. E 65, 026701 (2002)
N. Froman, P.O. Froman, Physical Problems Solved by Phase-Integral Method (Cambridge University Press, Cambridge, 2004)
J.R. Hiskes, C.B. Tarter, D.A. Moody, Phys. Rev. 133, A424 (1964)
J. Macek, J. Phys. B 1, 831 (1968)
A.G. Abrashkevich, D.G. Abrashkevich, I.V. Puzynin, S.I. Vinitsky, J. Phys. B 24, 1615 (1991)
C.D. Lin, Phys. Rep. 257, 1 (1995)
A.A. Gusev, O. Chuluunbaatar, S.I. Vinitsky, A.G. Abrashkevich, Comput. Phys. Commun. 185, 2636 (2014)
M. Domke, K. Schulz, G. Remmers, G. Kindl, D. Wintgen, Phys. Rev. A 53, 1424 (1996)
P. Camus, T.F. Gallagher, J.M. Lecomte, P. Pillet, L. Pruvost, J. Boulmer, Phys. Rev. Lett. 62, 2365 (1989)
U. Eichmann, V. Lange, W. Sandner, Phys. Rev. Lett. 64, 274 (1990)
K.D. Heber, M. Seng, M. Halka, U. Eichmann, W. Sandner, Phys. Rev. A 56, 1255 (1997)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Grozdanov, T.P., Gusev, A.A., Solov’ev, E.A. et al. Frozen-planet resonances in doubly excited helium atom; adiabatic approach. Eur. Phys. J. D 74, 161 (2020). https://doi.org/10.1140/epjd/e2020-10202-9
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2020-10202-9