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Partial Dynamical Symmetry in Molecules

✍ Scribed by Jia-Lun Ping; Jin-Quan Chen

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 372 KB
Volume: 255
Category: Article
ISSN: 0003-4916
DOI: 10.1006/aphy.1996.5644

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✦ Synopsis

It is shown that any Hamiltonian involving only one-and two-bond interactions for a molecule with n bonds and having a point group P as its symmetry group may have the S n #P partial dynamical symmetry, i.e., the Hamiltonian can be solved analytically for a part of the states, called the unique states. For example, the XY 6 molecule has the S 6 #O h partial dynamical symmetry. The model of Iachello and Oss for n coupled anharmonic oscillators is revisited in terms of the partial dynamical symmetry. The energies are obtained analytically for the nine unique levels of the XY 6 molecule and the structures of the eigenstates are disclosed for the first time, while for non-unique states they are obtained by diagonalizing the Hamiltonian in the S 6 #O h symmetry adapted basis with greatly reduced dimension.

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