Relativistic Three-Body Harmonic Oscillator

Improvement of the Envelope Theory for Systems with Different Particles

“…Accurate numerical solutions for this Hamiltonian do not seem to be available in the literature. Fortunately, it is shown in [29] that such solutions can be obtained from a rescaling of solutions for a nonrelativistic 3-body systems with a linear potential. This latter property can also be seen on the ET and IET solutions ( 14) and (15) where it is clear that the energy is invariant under the exchanges α ↔ β and F ↔ G when β > 0 and N = 3.…”

“…where N = N e + 1 is the number of the nucleus with a mass m. Energies in eV are obtained by multiplying the eigenvalues of H by the usual factor α 2 m e = 27.21 eV. Hamiltonian (29) contains the main contributions to the binding energy in an atom. So, the approximate results are compared with the experimental data about ionisation energies [32] which are very close to the eigenvalues of (29).…”

“…Hamiltonian (29) contains the main contributions to the binding energy in an atom. So, the approximate results are compared with the experimental data about ionisation energies [32] which are very close to the eigenvalues of (29). Due to the mixing of attractive and repulsive parts, the approximate eigenvalues have no variational character.…”

“…Ground state binding energies (in eV) of Hamiltonian(29) for some atoms with two or more electrons. Results from the ET and the IET with (φa, φ b ) are compared with the experimental values (see text).Exp.…”