Nuclear Physics A439 (1985) 86-116 0 North-Holland Publishing Company MICROSCOPIC DESCRIPTION OF COLLECTIVE STATES NEAR THE YRAST LINE OF NUCLEI WITH STABLE OCTUPOLE DEFORMATION J. KVASIL* and R.G. NAZMITDINOV** Joint Institute for Nuclear Research, Laboratory of Theoretical Physics, Dubna, 141980, USSR Received 24 September 1984 Abstract: Collective states near the yrast tine in nuclei with stable octupole deformation are discussed in the framework of the random phase approximation (RPA) based on the cranking model. These vibrational states are characterized by the quantum number of generalized signature (eigenvalue of the operator S, = PR;‘( T)). In the zero-octupole deformation limit the RPA equations of motion are reduced to the well-known ones characterized by both values of parity and signature, respectively. The connection of the translational and rotational symmetry of the model hamiltonian with the spurious solutions of the RPA equation of motion is discussed. Expressions for the reduced probabilities B(El), B(E2) and B(E3) are obtained. These expressions confirm the conclusions of phenomenologica1 models for the strong El and E3 intraband transitions in nuclei with stable octupole deformation. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 1. Introduction In the last few years experimental I-*) as well as theoretical 9-‘6) investigations have indicated the possible existence of a stable octupole deformation in some nuclei in the actinide region. The octupole deformation of a nuclear field is demon- strated spectrally by spin states with alternating parity in the frame of a one-rotational band and by collective El and E3 transitions along the rotational bands. Such a situation has indeed been observed in nuclear spectroscopy at high spins (I - 4- 17) for the 222Th [see refs. ‘*‘)I and ‘l*Ra [see refs. “*“)I nuclei. The theoretical papers on this topic can be divided into various groups according to their approach. The first group [see e.g. refs. 9-12,‘4*1s)]starts with the Nilsson, folded Yukawa or Woods-Saxon deformed nuclear field,with stable quadrupole and octupole deformation. Using the adiabaticity approach with inclusion of pairing and Coriolis effects these authors have tried to explain the experimental data on low-lying states of nuclei in the Ra-Th region. The second group of papers [see e.g. ref. “)I uses a version of the Bohr-Mottelson model “) containing quadrupole and octupole degrees of freedom coupled to each other. This approach allows one to study phenomenologically the influence of octupole deformation on collective * Permanent address: Department of Nuclear Physics, Math.-Phys. Faculty, Charles University, es-180 00 Prague 8, Povltavska 1, Czechoslovakia. ** Permanent address: Institute of Applied Physics of Tashkent State University, Tashkent, USSR. 86