Applying modified Ginzburg-Landau theory to nuclei

The Ginzburg-Landau theory of phase transitions is modified and used to investigate the heat capacity, energy, entropy, and order parameter of the paired phases of ${}^{208}\mathrm{Pb},{}^{88}\mathrm{Sr},{}^{48}\mathrm{Ca}$, and ${}^{20}\mathrm{Ne}$. We use the Fermi gas model to calculate the thermodynamic properties of the normal phase of the nucleons. Our results show that the total heat capacities of the studied nuclei have an $\mathsf{S}$-shape behavior, which is in accordance with the semi-empirical data, and the order parameter does not approach zero at a specific critical temperature.

Figure 1

Total heat capacities of ${}^{208}\mathrm{Pb}{,}^{88}\mathrm{Sr}{,}^{48}\mathrm{Ca},$ and ${}^{20}\mathrm{Ne}$ versus temperature. Semi-empirical [24], calculated (modified (exact) Ginzburg-Landau + Fermi gas), and Fermi gas heat capacities are plotted.

Figure 2

Total heat capacity of ${}^{88}\mathrm{Sr}$ versus temperature. Total heat capacities using the approximate formula [$C_{\mathrm{AGL}}$, Eq. (7)] and exact formula [$C_{\mathrm{EGL}}$, Eq. (15)] are plotted.

Figure 3

Effect of system size on the paired-phase heat capacity. Paired-phase heat capacity versus temperature for different values of $\delta .$

Figure 4

Total energy and paired-phase energy versus temperature.

Figure 5

Total entropy versus total excitation energy.

Figure 6

Normalized expectation value of the absolute value of the order parameter $\frac{\langle \left|\psi \right|\rangle }{\langle \left|{\psi }_0\right|\rangle }$ versus temperature.