DOI 10.1140/epja/i2002-10336-9 Eur. Phys. J. A 20, 119–122 (2004) T HE EUROPEAN P HYSICAL JOURNAL A Spherical shell model description of deformation and superdeformation A. Poves 1, a , E. Caurier 2 , F. Nowacki 2 , and A. Zuker 2 1 Departamento de F´ ısica Te´orica, Universidad Aut´onoma de Madrid, Cantoblanco, 28049 Madrid, Spain 2 Institut de Recherches Subatomiques, IN2P3-CNRS-Universit´ e Louis Pasteur, F-67037 Strasbourg Cedex 2, France Received: 29 October 2002 / Published online: 16 March 2004 – c  Societ` a Italiana di Fisica / Springer-Verlag 2004 Abstract. Large-scale shell model calculations give at present a very accurate and comprehensive descrip- tion of light and medium-light nuclei, specially when 0ω spaces are adequate. The full pf -shell calculations have made it possible to describe many collective features in an spherical shell model context. Calculations including two major oscillator shells have proven able to describe also superdeformed bands. PACS. 21.60.Cs Shell model – 21.60.-n Nuclear structure models and methods – 21.10.Hw Spin, parity, and isobaric spin – 21.10.Ky Electromagnetic moments 1 Introduction The spherical shell model approach to the nuclear dynam- ics has three main ingredients: the effective interaction, the valence space and the computational tools that make it possible to solve the huge secular problems involved. Our understanding of the effective interaction used in shell model calculations changed radically through the realiza- tion of the key spectroscopic role played by the monopole terms of the Hamiltonian that determine the evolution of the spherical single-particle orbits and the relative loca- tion of the different configurations [1], setting the initial conditions for the action of the correlation terms of the nu- clear force (pairing, quadrupole, etc.). A new generation of shell model codes, that can treat problems involving basis dimensions as large as a few billions, has opened the possibility to access new regions of the chart of nu- clides [2]. Full 0ω calculations in the pf -shell have demon- strated the ability of the spherical shell model to treat in an unified framework all the variety of nuclear excita- tions: single-particle modes, neutron-neutron and proton- neutron pairing correlations, rotational bands based upon well-deformed intrinsic states, etc. [3]. Other collective manifestations such as backbending, alignment, superfluid moments of inertia, etc., until now confined to the realm of heavy nuclei and treated by deformed mean-field models, have been experimentally found in medium-light nuclei us- ing the large γ -detectors GASP, EUROBALL and GAM- MASPHERE [4,5]. The shell model calculations have pre- dicted or explained this full panoply of effects. More re- cently, excited superdeformed bands have been experimen- a e-mail: alfredo.poves@uam.es tally found in 36 Ar and 40 Ca [6,7]. As we shall discuss in this paper, shell model configurations involving 4p-4h and 8p-8h excitations from the sd- to the pf -shell account nicely for its more salient features [8]. 2 Superdeformed bands in 36 Ar and 40 Ca The existence of excited deformed bands in spherical nu- clei is a well documented fact, dating back to the ’60s. A classical example is provided by the four-particle– four-holes (4p-4h) and eight-particles–eight-holes (8p-8h) states in 16 O, starting at 6.05 MeV and 16.75 MeV of exci- tation energy [9,10]. However, it is only recently that simi- lar bands, of deformed and even superdeformed character, have been discovered in other medium-light nuclei such as 56 Ni [5], 36 Ar [6] and 40 Ca [7] and explored up to high spin. One characteristic feature of these bands is that they belong to rather well-defined spherical shell model config- urations. For example, the deformed excited band in 56 Ni can be associated with the configuration (1f 7/2 ) 12 (2p 3/2 , 1f 5/2 ,2p 1/2 ) 4 while the (super)deformed band in 36 Ar has the structure (sd) 16 (pf ) 4 . The states we aim to are dom- inantly core excitations from the sd-shell to the pf -shell. The natural valence space would thus comprise both ma- jor oscillator shells. However, the inclusion of the 1d 5/2 orbit in the valence space produces a huge increase in the size of the basis and massive center-of-mass effects, thus we are forced to exclude it from the valence space; this is equivalent to take a closed core of 28 Si. We are aware that this truncation will reduce slightly the quadrupole coher- ence of the solutions. Our valence space will consist of the