6533b831fe1ef96bd1298124

RESEARCH PRODUCT

Algebraic study of pyramidal molecules in the very excited vibrational states.

subject

description

In the frame of the algebraic formalism U(p+1), we developed the method to build a vibrational Hamiltonian corresponding to a set of three identical oscillators. In order to test the model, we apply it to the molecules of stibine and arsine. We introduce a supplementary intermediate group K(3) inspired by the similar formalism used in nuclear physics. This group K(3) gives additional labels for classification of the energy levels. The eigenvalues of these invariant operators distinguish the local states of the molecule. Then we study the coupling of the vibrational modes of stretching and bending for the non plane XY3 molecules. We present the construction of an algebraic operator of coupling of these different degrees of freedom as well as the correspondance between the model and experimental data. We show how the introduction of the quantum number of polyad K=2ne + np allows modelisation of the problem, particularly for the process of Hamiltonian matrix diagonalization.