Spectrum of hydrogen atom having a harmonically bound nucleus: Beyond the BornOppenheimer approximation
Abstract
Spectral features of a quantum mechanical model system are determined within the formalisms of degenerate and nondegenerate perturbation theory. These features include energy level shifts, vibronic intensities, and interactions between members of degenerate manifolds not predicted by the application of the BornOppenheimer approximation to the model system. Timedependent processes resulting in vibrationally induced preionization are also investigated. The model system consists of a proton subject to a Hooke's law potential (constrained to quantum mechanical motion in one dimension) and an electron attracted to the proton by a Coulombic potential. The equilibrium position of the proton is the origin of an imposed coordinate frame. Such a system may be compared with a diatomic molecule such as rubidium hydride. The energy of the ground state of the model system as calculated by perturbation theory deviates from the BornOppenheimer approximation prediction by 2.6% of the zeropoint energy of the proton.
 Publication:

Ph.D. Thesis
 Pub Date:
 1978
 Bibcode:
 1978PhDT........69B
 Keywords:

 Atomic Spectra;
 BornOppenheimer Approximation;
 Ground State;
 Hydrogen Atoms;
 Nuclei (Nuclear Physics);
 Coulomb Potential;
 Electron Transitions;
 Hookes Law;
 Perturbation Theory;
 Quantum Mechanics;
 Rydberg Series;
 Atomic and Molecular Physics