The superdeformed bands in the A 150 region are studied with the cranking Bohr-Mottelson Hamiltonian proposed by us. The transition energies can be represented satisfactorily and the level spins are extracted. The validity of our formulas and the reliability of the spin determinations are discussed.PACS number(s): 21.10. Re, 21.60.Ev, 27.60. +j, 27.70.+q The superdeformed (SD) bands in the A 190 region have been well studied and several models have been proposed for their spin determinations with similar results [1 -5]. In contrast to the A 190 region, the SD bands in the A 150 region have higher spins and their spin determinations are more difficult. The empirical formula I(I + 1) expansion [1] and the a[pl + b(I + 1) -1] approximation [3] have been used successfully to determine the spins of the SD bands in the A 190 region. However, when they are applied to A150 region, the quality of the Gt to the observed energies is good but insensitive to spin assignment. In the Harris cu expansion method, another difficulty is encountered in the A 150 region, as will be discussed in this paper. Cheng-Li Wu et al. [6] have pointed out that any theoretical spin determination must be model dependent and the present status of the models is not accurate enough to make a reliable spin determination. Hence, it is worthwhile to develop more reliable models which may contribute towards the spin determination and the nuclear structure studies of the SD states, especially for I the A 150 region. Recently, we have developed a nuclear rotationvibration model based on the cranking Bohr-Mottelson (BM) Hamiltonian [7]. The model has been successfully applied to the normally deformed bands [7] and the SD bands in the A 190 region [5]. As commented in our former papers [5,7], it is a well-founded model with physically significant parameters. In [7,5], we have given the cranking BM Hamiltonian for the normally deformed states and the SD states in the A 190 region. The SD bands in the A 150 region have higher rotational frequencies, hence next order (fourth-order) perturbation should be considered in the derivation of the BM Hamiltonian &om the cranked shell model [8]. The fourth-order perturbation term can be approximately written as Daz~, where ao is the quadrupole deformation parameter,~is the rotational frequency, and D is the coefficient of the fourth-order perturbation term. Then the cranking BM Hamiltonian is written as H' = --, --Bt(3ap + 2a2)u) + Dao~+ E(ap, a2), 2Bo Oao 4B2 &a2 E(ao, a2) = U(ao) + 2 C2a2 (2) Hence, the ao-dependent part of the effective potential can be written as where E(ap, a2) is the static collective potential; ap and a2 are the quadrupole deformation parameters; and Bo, Bt, and B2 are the mass parameters [7,5]. The superdeformed states of the nuclei in the A 150 region are mainly axisymmetrical deformations [ll]. In this case, E(ap, a2) is assumed separable [5,7]: V(ap,~) = U(ap) -2Bicu ao+ D~a o .For the SD band to exist, we shall assume V(ap, ur) has a clear minimum at a certain ao value which depends slight...