Z. Phys. A - AtomicNuclei332,331 338 (1989) Zeitschrift fur PhysikA Atomic Nuclei 9 Springer-Verlag1989 Deformed Giant Quark Nuclei Th. Sch6nfeld, D. Vasak, J.A. Maruhn, and W. Greiner Institut ffir Theoretische Physik, Johann Wolfgang Goethe-Universit/it, Frankfurt a.M., Federal Republic of Germany Received August 29, 1988; revised version November 9, 1988 We examined the dependence of the mass of giant quark nuclei on quadrupole surface deformations. We find that also for large deformations the possiblity exists that the mass of very heavy giant quark nuclei is lower than that of the corresponding ordinary nuclei, leading to a dissolution of nuclei into quarks in very heavy nuclear collision systems. PACS: 12.35.H 1. Introduction As we know today, the "elementary" building blocks of atomic nuclei, proton and neutron, as well as all other known "elementary" particles (A, X, E, f2, ...) are composite. Their hadronic constituents, the quarks, interact by exchanging gluons, the quanta of the underlying gauge group, colour-SU(3) [1]. The algebraic structure of this group gives raise to gluon- gtuon-couplings due to the fact that the gluons them- selves carry colour degrees of freedom, too. This, in turn, renders the effective quark-quark coupling de- pendent on the interquark distance. It vanishes for zero quark-quark distance ("asymptotic freedom"), but diverges with R~ oe. Hence only combinations of quarks and gluons with net colour zero have finite mass C colour confinement"). However, since the fundamental theory of strong interactions, QCD (Quantum Chromo Dynamics), is too complex, exact calculations of the properties of hadronic matter are still not accessible. Not even the structure of the QCD ground state could be derived and the mechanism of colour confinement has not yet been rigorously established. Instead, lead by em- pirical data some properties of QCD solutions have been anticipated [2, 3]. A very successful class of models leading to such predictions are the "bag-mod- els", the idea of which is the following: Quarks and gluons exist only in certain regions of space from which the true vacuum has been expelled. These re- gions are called "bags". Since the energy density is increased within these bags, the outer vacuum exerts a pressure on its boundaries, which balances the pres- sure arising from the motion of its constituents. Now the question arises what will happen if bags come close together, as it is the case for instance in nuclei. Will the quarks be able to tunnel from bag to bag? Could bags overlap or even completely dis- solve, so that only a large global bag remains, in which quarks and gluons are essentially free? It turns out that indeed for very heavy nuclei of mass numbers in the region of the heaviest nuclear systems, which might be generated in heavy ion sys- tems quark nuclei (we call them giant quark nuclei) could be energetically favoured compared to ordinary nuclei [4, 5]. Quark nuclei are objects which consist of one single global bag with essentially free quarks occupying discrete energy levels. The calculations pre- sented in [4] were however restricted to the case of spherical nuclei only, i.e. to a geomery far from the situation encountered in heavy ion experiments. The main purpose of the present work is to extend the result from [4], based on the MIT bag model [2], to the case of deformed nuclei with a geometry similar to that expected in heavy ion collisions. For this purpose we examine the dependence of the mass of giant quark nuclei on their shapes. In this paper we present calculations performed for quadrupole de- formations up to the point of scission. 2. The Model and its Single Particle Levels Let us first briefly recall the essentials of the MIT-bag model [2]. Its idea is to put the influence of the true