Two-Body Atomic Systems Confined by an External Harmonic Oscillator Potential

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Beykent Üniversitesi

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When space of a free particle having P momentum is restricted continuously, its energy evolves from continuum to discrete levels. Restriction, sometimes called confinement or compression, is created either by any physical boundary, like wall or shell, or by any confining field like a potential well or an external harmonic oscillator potential. Hydrogen atom itself is a confined two-body system whose electron moves under the influence of their attractive Coulomb and repulsive angular momentum potential. These two potentials together give a potential well. Unlike free particle, the system has negative discrete energies. While interparticles distance becomes larger, its energy goes to zero and the system is disintegrated. This means that the atom is ionized. Quantum mechanical problem for two charged particles within an external harmonic oscillator has a great attention mainly because of creating an atom like system without nucleus, called artificial atom or harmonium, and of allowing to determination of the correlation of charged particles, variation of which depends on oscillator frequency w. In case of harmonium, mass of particles m and magnitude of charges are identical, i.e. two electron or one positron and one electron. From the point of atomic view, in this study we examined analytical and an approximate solution for some atomic systems beginning from positronium atom, similar to harmonium except that repulsive Coulomb is replaced with attractive one, to two-body atomic systems having arbitrary mass m1, m2 and arbitrary nuclear charge Z.


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confined hydrogenlike atoms, two-body atomic systems within an external oscillator potential, weak confinement, muonic atoms


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Journal of Science and Technology 1 (2), 2007, 275-292