Influence of Quantal and Statistical Fluctuations on Phase Transitions in Finite Nuclei

Abstract

Investigations on thermal evolution of pairing-phase transition and shape-phase transition in light nuclei are made as a function of pair gap, deformation, temperature and angular momentum using a finite temperature statistical approach with main emphasis to fluctuations. The occurrence of a peak structure in the specific heat predicted as signals of the pairing-phase and shape-phase transitions are reviewed and it is found that they are not actually true phase transitions and it is only an artifact of the mean field models. Since quantal number and spin fluctuations and statistical fluctuations in pair gap, deformation degrees of freedom and energy when incorporated, it wash out the pairing-phase transition and smooth out the shape-phase transition. Phase transitions due to collapse of pair gap and deformation is discussed and a clear picture of pairing-phase transition in light nuclei is presented in which pairing transition is reconciled.

Nuclear Specific Heat and Phase Transition in Finite Nuclear Systems

“…It shows the presence of a bump at T of the order of 2.0 to 3.5 MeV for all the light nuclei. The results obtained from our calculations are similar to reported in [17,20,38].…”

“…Similar effects are seen for 24 12 Mg, at I = 0 with the change in the slope at T ≈ 3.7 MeV and for 28 14 Si shows transformations at T ≈ 1.5 MeV and T ≈ 3.0 MeV. Usually, a change in the slope at T ≈ 1.5 MeV implies a change in the system from a triaxial to an axially symmetric shape and a change at T ≈ 3.0 MeV signifies a deformed to spherical phase transition [16,38]. Therefore, for all the four nuclei considered, one can see a sudden transformation at T ≈ 3.5 MeV (Fig.…”

“…Liu and Alhassid [37] have developed a new method for calculating the heat capacity using the shell model Monte Carlo (SMMC) approach, for iron isotopes 52−62 Fe, and identified a signature of phase transition in the heat capacities despite the large fluctuations. Strictly speaking, quantal and statistical fluctuations are of essential importance since they smooth out the singularities allied with phase transitions [38]. In the statistical theory, the equilibrium shape of the nucleus at given angular momentum and temperature has been obtained by minimizing the free energy as a function of deformation.…”