THEORY OF SPLITTING OF THE TRIPLY DEGENERATE VIBRATIONAL LEVEL BY THE INFLUENCE OF ANHARMONICITY
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Publisher:Ohio State University
This study is concerned with the effect of anharmonicity on the triply degenerate vibrational level in a molecule or in a crystal lattice. When a triply degenerate harmonic vibration is excited by several quanta, a splitting occurs into sublevels of slightly different energy under the influence of anharmonicity of the vibration. These anharmonic levels can be calculated by the use of perturbation theory. The three normal coordinates of the triply degenerate vibration are transformed into fictitious spherical polar coordinates, by which the harmonic (zero order) wave functions are represented. For simplicity the anharmonic potential is assumed to be spherically symmetrical around the origin of the coordinates. The cubic and the quartic terms are treated as the first order perturbations. By the use of a recursion formula of a polynomial in the radial wave function, a general expression for anharmonic levels can be obtained to the first order, together with their symmetry properties. The results show that the degeneracy of each harmonic level is not completely removed to this approximation. The first excited level does not split, the second and the third split into doublets respectively, and the fourth into triplets, while the corresponding harmonic levels are three-fold, six-fold, ten-fold and fifteen-fold degenerate. These results will permit explnation of fine structures in overtone bands of the triply degenerate vibration.
Author Institution: Institute for Science and Engineering, Waseda University 3-153 Kugayama
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