The oscillator representation and the stability of three-body Coulomb systems |
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Authors: | M Dineykhan G V Efimov |
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Institution: | (1) Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia;(2) Present address: Institute of Nuclear Physics, Kazakh Academy of Sciences, 480082 Alma-Ata, Kazakhstan |
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Abstract: | Within nonrelativistic quantum mechanics the Wick-ordering method, called the oscillator representation, is suggested for calculating the energy spectrum for a wide class of potentials allowing the existence of a bound state. As test cases, anharmonic (V(r)=r
2 ) and screened Coulomb potentials are considered. In particular, the method is applied to three-body Coulomb systems to obtain the dependence of the bound-state energy on the masses and charges of the particles. The calculations of the bound-state energies for the moleculesH
–=(pee),H
2
+
=(ppe), (e
–e–e+) and (pp ), (dd ), (dt ) prove the accuracy of the zeroth approximation to be better than one per cent. For the three-body Coulomb system with charges +, –, – and arbitrary masses the region of stability is determined. For the systems (pe
–C+), (A
+e–e+), and (pB
–e–) the critical masses are calculated to beM
c=1.945me,M
A=4.350me andM
B=1.575me. It turns out that the system (pe
–e+) is unstable. |
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Keywords: | |
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