https://doi.org/10.1140/epjd/e2012-20586-6
Regular Article
Hyperspherical three-body calculation for muonic atoms
Department of Physics, Raiganj Surendranath Mahavidyalaya (A
College affiliated to “University of Gour Banga”), P.O. Raiganj, Dist. Uttar Dinajpur,
P in-733134
West Bengal,
India
a e-mail: drakhan.rsm.phys@gmail.com
Received:
10
October
2011
Received in final form:
2
December
2011
Published online:
29
March
2012
Ground state energies of exotic three-body atomic systems consisting two muons and a positively charged nucleus like: 1H+ μ- μ-, 4He2+ μ− μ−, 3He2+ μ− μ−, 7Li3+ μ− μ−, 6Li3+ μ− μ−, 9Be4+ μ− μ−, 12C6+ μ- μ-, 16O8+ μ- μ-, 20Ne10+ μ−μ−, 28Si14+ μ− μ− and 40Ar18+ μ−μ− have been calculated using hyperspherical harmonics expansion (HHE) method. Calculation of matrix elements of two body interactions involved in the HHE method for a three body system is greatly simplified by expanding the bra- and ket- vector states in the hyperspherical harmonics basis states appropriate for the partition corresponding to the interacting pair. This involves the Raynal-Revai coefficients (RRC), which are the transformation coefficients between the hyperspherical harmonics bases corresponding to the two partitions. Use of these coefficients found to be very useful for the numerical solution of three-body Schrödinger equation where the two-body potentials are other than Coulomb or harmonic oscillator type. However, in this work the interaction potentials involved are purely Coulomb. The calculated energies have been compared with (i) those obtained by straight forward manner; and (ii) with those found in the literature (wherever available). The calculated binding energies agree within the computational error.
Key words: Atomic Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2012