The relation between a reduced Hamiltonian suitable for fitting the observed spectra and the levelhyphen;shift transformation is discussed. A reduced Hamiltonian of an approximately symmetric rotor molecule in the absence of Coriolis interaction is obtained. Three types of terms are discussed: (i) those diagonal with respect to the zerohyphen;order Hamiltonian, (ii) those which have both diagonal and offhyphen;diagonal constituents and (iii) those which are purely offhyphen;diagonal. It is shown that in thejth order,j ge; 2,thinsp;j plus; 1of first type, 2jmdash;1 of the second type and none of the third type remain in a reduced Hamiltonian.
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