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Description
Thermal motion and thermodynamic properties of nuclei influence nucleosynthesis in stellar environments. Precise knowledge of level density, a characteristic property of many-body quantum mechanical systems, is an important prerequisite for thermodynamic studies of atomic nuclei and consequently for the calculation of thermonuclear rates in astrophysical processes. In macroscopic conductors, pairing phase transitions show a sharp heat capacity discontinuity at the transition temperature. However, in nuclei, the smaller radius compared to pair coherence length, leads to fluctuations, suppressing the discontinuity and resulting in a shallow "kink" (S-shape) in heat capacity at the transition temperature. Till now, pairing phase transitions are observed mostly in even-even nuclei due to nucleonic Cooper pair breaking. Recently, S-shaped heat capacity was seen in odd-odd deformed $^{184}$Re, suggesting deformation induced pairing [1]. Similar discontinuities appear in even-odd $^{183,185}$W. These findings prompt further study of odd-odd and even-odd systems, especially nuclei crucial for s-process and r-process nucleosynthesis, to explore pairing correlations and nuclear structure in diverse mass regions. We investigated pairing phase transition in hot rotating $^{69}$Zn (odd-even) using nuclear level density (NLD) data experimentally extracted from $\gamma$-gated particle spectra. Experimental NLDs are compared with microscopic exact pairing plus independent-particle mode (EP+IPM), Hartree-Fock BCS (HFBCS), and Hartree-Fock-Bogoliubov combinational (HFBC) calculations at finite temperature. EP+IPM with recommended quadrupole deformation parameter β2 accurately reproduces experimental NLDs, outperforming HFBCS and HFBC methods [2]. The heat capacity calculated using the EP+IPM NLD clearly exhibits a sharp S-shape , unexpected for even-odd systems, insensitive to $\beta$2 adjustments, indicating robustness. However, increasing/decreasing pairing gaps enhances/destroys the S-shape, implying pairing correlations play a crucial role. Deformation-induced pairing correlation explains the S-shaped heat capacity in $^{69}$Zn, suggesting pairing correlations persist in hot rotating odd-even nuclei, providing insights into nuclear structure and pairing mechanisms [2].
[1] Balaram Dey et al., Phys. Lett. B 789, 634 (2019).
[2] Enakshi Senapati et al., J. Phys. G: Nucl. Part. Phys. 50 (2023) 075104.