Pushing the pseudo-SU(3) model towards its limits: Excited bands in even-even Dy isotopes Carlos E. Vargas * Facultad de Física e Inteligencia Artificial, Universidad Veracruzana, Sebastián Camacho 5; Xalapa, Ver., 91000, México Jorge G. Hirsch ² Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, México 04510 DF, México (Received 24 March 2004; published 23 December 2004) The energetics of states belonging to normal parity bands in even-even dysprosium isotopes, and their BE2 transition strengths, are studied using an extended pseudo-SU(3) shell model. States with pseudospin 1 are added to the standard pseudospin 0 space, allowing for a proper description of known excited normal parity bands. A realistic Hamiltonian is employed. Both the success of model and its limitations are discussed. DOI: 10.1103/PhysRevC.70.064320 PACS number(s): 21.60.Fw, 23.20.Js, 27.70.+q I. INTRODUCTION The nuclear shell model [1] provides a detailed micro- scopic description of a number of properties of atomic nu- clei. Although powerful computers and special algorithms for diagonalizing large matrices have allowed systematic studies of the nuclei up to A =56 [2], a shell model descrip- tion of heavy nuclei requires further assumptions, being of particular relevance the systematic and proper truncation of the Hilbert space. The SU(3) shell model [3] has been successfully applied in light nuclei, where an harmonic oscillator mean field and a residual quadrupole-quadrupole interaction can be used to describe dominant features of the nuclear spectra [4]. How- ever, the strong spin-orbit interaction renders the SU(3) model useless in heavier nuclei, while at the same time pseu- dospin emerges as a good symmetry [5,6]. It refers to the well known quasidegeneracy observed in heavy nuclei be- tween single-nucleon orbitals with j = l -1/2 and j = l -2 +1/2 in the shell . These orbitals can therefore be labeled as pseudospin doublets with quantum numbers j ˜ = j ,  ˜ =  -1, and l ˜ = l -1. The success of the pseudo-SU(3) model [7] lies on the goodness of this symmetry. The first applications of the pseudo-SU(3) model consid- ered it as a dynamical symmetry, using a single irreducible representation (irrep) to describe the yrast band [8,9]. The development of a computer code to evaluate SU(3) triple reduced matrix elements [10] enabled mixed-representation calculations. A realistic Hamiltonian including SU(3) symmetry-breaking terms such as Nilsson single-particle en- ergies and pairing correlations could be diagonalized [11].A fully microscopic description of many rotational bands and electromagnetic transition strengths in both even-even [12] and odd-A [13,14] heavy deformed nuclei emerged. The in- clusion of states with pseudospin 1 and 3 / 2 (in addition to those with S ˜ =0 and 1/2) for protons and neutrons allowed the description of up to eight rotational bands in odd-mass nuclei [15]. Scissors M1 excitations in odd-mass heavy nu- clei [16] were also described. In this work we present new results for excited bands in even-even dysprosium isotopes. It is shown that their proper description requires the inclusion of states with pseudospin 1, in addition to the fully symmetric pseudospin 0 configu- rations. The systematic parametrization of the principal part of the Hamiltonian, namely the single-particle energies and quadrupole-quadrupole and pairing interactions, is also a fundamental tool to describe the dominant features of the energy spectrum. Four rotorlike terms in the Hamiltonian are employed to “fine-tune” the energy levels, although they are kept small to avoid noticeable changes in the whole band structure. Both the extension of the Hilbert space and the restrictions imposed over the Hamiltonian parameters repre- sent an important improvement with respect to previous studies [17]. In Sec. II the pseudo-SU(3) classification scheme is pre- sented, underlining the relevance of including the states with pseudospin 1. The Hamiltonian and its parametrization are presented in Sec. III. Results for the low-lying energy spectra in dysprosium isotopes are discussed in Sec. IV, while Sec. V is devoted to the analysis of their wave functions and BE2 transitions. Finally, a brief summary and conclusions are drawn in Sec. VI. II. THE PSEUDO-SU(3) BASIS The first step in any application of the pseudo-SU(3) model is to build the many-body basis. As a starting point the proton and neutron valence Nilsson single-particle levels are filled from below for a fixed deformation, allowing the de- termination of the most probable normal and unique parity orbital occupancies [13]. In Table I the occupation numbers assigned to each nucleus are presented. As it has been the case for almost all pseudo-SU(3) stud- ies to date, the intruder level with opposite parity in each major shell is removed from active consideration and pseudo-orbital and pseudospin quantum numbers are as- signed to the remaining single-particle states. Nucleons in abnormal parity orbital are considered to renormalize the dy- namics that is described using only nucleons in normal parity *Email address: cavargas@uv.mx ² Email address: hirsch@nuclecu.unam.mx PHYSICAL REVIEW C 70, 064320 (2004) 0556-2813/2004/70(6)/064320(9)/$22.50 ©2004 The American Physical Society 064320-1