Abstract.
The semiclassical spectrum of quadruply highly excited four-electron atomic systems has been calculated for the plane model of equivalent electrons. The energy of the system consists of rotational and vibrational modes within the circular skeleton orbit approximation, as used in a previous calculation for the triply excited three-electron systems. The full dynamical analysis is carried out within the Hamiltonian theory, accounting for the inertial effects and the complete coupling between different degrees of freedom. Here we present numerical results for energy spectrum of the beryllium atom. The lifetimes of the semiclassical states are estimated via the corresponding Lyapunov exponents. The vibrational modes relative contribution to the energy levels rises with the degree of the Coulombic excitation.
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References
S. Hasegawa, F. Yoshida, L. Matsuoka, F. Koike, S. Fritzsche, S. Obara, Y. Azuma, T. Nagata, Phys. Rev. Lett. 97, 023001 (2006)
H. Nagaoka, Bull. Math. Phys. Soc. Tokyo 2, 140 (1904)
J.W. Nicholson, Month. Not. Roy. Astr. Soc. 72, 49 (1912)
Bao Cheng-guang, Phys. Rev. A 47, 1752 (1993)
Bao Chengguang, Duan Yiwu, Phys. Rev. A 49, 818 (1994)
C.G. Bao, J. Phys. B 25, 3725 (1992)
C.G. Bao, Phys. Lett. A 250, 123 (1998)
C. Nicolaides, N. Pianos, Y. Komninos, Phys. Rev. A 48, 3578 (1993)
Y. Komninos, C. Nicolaides, Phys. Rev. A 50, 3782 (1994).
L. B. Madsen, J. Phys. B. 36, R223 (2003)
P. Grujić, Eur. Phys. J. D 6, 441 (1999)
M. Poulsen, P. Madsen, Phys. Rev. A 72, 042501 (2005)
M. Poulsen, P. Madsen, Phys. Rev. A 71, 062502 (2005)
T. Morishita, C.D. Lin, Phys. Rev. A 71, 012504 (2005)
M. Walter, J.S. Briggs, J.M. Feagin, J. Phys. B. 33, 2907 (2000)
L.B. Madsen, K. Molmer, Phys. Rev. A 64, 060501(R) (2001)
L.B. Madsen, K. Molmer, Phys. Rev. A 65, 022506 (2002)
P. Grujić, J. Phys. B 21, 63 (1988)
N. Simonović, Phys. Rev. A 50, 4390 (1994)
N. Simonović, M. Predojević, V. Panković, P. Grujić (unpublished)
S. Cvejanović, Z.D. Dohčević, P. Grujić, J. Phys. B 23, L167 (1990)
P. Grujić, X Eur. Symp. Dyn. Few-Body Sys., Balatonfuüred, 1986, edited by Gy. Bencze, P. Doleshall, J. Reval (Budapest, 1986), pp. 253–281
N. Simonović, P. Grujić, in Adv. Math. Study of Atomic Doubly-Excited States, Medellin, Colombia, 1995, edited by J. Mahecha, J. Botero (Universidad de Antioquia, 1996), pp. 107–153
Y. Kuchiev, V. Ostrovsky, Phys. Rev. A 58, 321 (1998)
G.H. Wannier, Phys. Rev. 90, 817 (1953)
N. Norcliffe, in Case Studies in Atomic Physics, Vol. 4, edited by W. McDaniel, M.R.C. McDowell (North-Holland, Amsterdam, 1975), pp. 45-55
A.F. Ozorio de Almeida, Hamiltonian Systems: Chaos and Quantization (Cambridge University Press, New York, 1992)
L. Landau, E. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, 1965)
P. Grujić, J. Phys. B 16, 2567 (1983)
H. Goldstein, Classical Mechanics (Addison-Wesley, London, 1981)
I.M. Gel'fand, Lectures in Linear Algebra (Nauka, Moscow, 1966) (in Russian)
N.S. Simonović, J. Chem. Phys. 124, 014108 (2006)
N.S. Simonović, J.M. Rost, Classical Lifetimes for Quantum Resonances, Twenty Second International Conference on Photonic, Electronic, and Atomic Collisions (XXII ICPEAC), Abstracts of Contributed Papers, edited by S. Datz, M.E. Bannister, H.F. Krause, L.H. Saddiq, D.R. Schultz, C.R. Vane (Rinton Press, 2001), p. 212
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Simonović, N., Grujić, P. Quadruply excited beryllium-like atoms – a semiclassical model. Eur. Phys. J. D 42, 1–10 (2007). https://doi.org/10.1140/epjd/e2006-00269-9
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DOI: https://doi.org/10.1140/epjd/e2006-00269-9