Temperature and angular momentum dependence of the quadrupole deformation in sd-shell

Abstract

Abstract. Temperature and angular momentum dependence of the quadrupole deformation is studied in the middle of the sd-shell for 28 Si and 27 Si isotopes using the spherical shell model approach. The shell model calculations have been performed using the standard USD interaction and the canonical partition function constructed from the calculated eigen-solutions. It is shown that the extracted average quadrupole moments show a transitional behavior as a function of temperature and the infered transitional temperature is shown to vary with angular-momentum. The quadrupole deformation of the individual eigen-states is also analyzed.The study of phase transition in quantum many-body systems is one of frontier research topics in physics. Phase transitions are observed both in macroscopic as well as in small quantum many-body systems. In macroscopic systems, for instance a metallic superconductor, the linear dimension of the system is quite large and the transition from one phase to the other occurs at one point [1]. For small systems, the fluctuations play a very central role and the existence of the discontinuity in the heat capacity critically depends on the number of constituent particles in the system. This has been demonstrated in small metallic grains that discontinuity is observed with large number of electrons in the grain. However, as the number of electrons in the grain approaches around 100, the discontinuity or the peak structure in the heat capacity disappears [2][3][4][5].Phase transitions have also been studied extensively in atomic nuclei using the HartreeFock-Bogoliubov (HFB) method. The HFB theory predicts phase transition as a function of rotational frequency (angular momentum) and temperature (excitation energy). The shape transition as a function of rotational frequency has been well studied in most of the regions of the nuclear chart. In particular, in the rare-earth region the examples of the shape transition are documented in the text books [6,7]. Most of the nuclei in this region are prolate deformed with the rotational axis perpendicular to the symmetry axis at low spins and it is known that this shape changes to oblate non-collective at higher angular momenta in many nuclei in this region. For instance, in the case 160 Yb, the shape is prolate for spins up to 40h and above this spin value the shape becomes oblate noncollective. The phase transition has also been investigated using the finite temperature HFB approach [8,9] and Landau theory [10]. The main conclusion from these studies is that nuclei which are deformed at low temperatures exhibit a shape transition to spherical shape as the temperature of the system is raised. The critical temperature at which this shape transition occurs has a maximum value for isotopes between magic numbers and in 1