Research On Pairing Correlation For ^171,172Yb In Shell-model-like Approach Based On Covariant Density Functional Theory

Pairing correlations play a crucial role in the thermodynamic properties of atomic nuclei.In the finite temperature mean field model,one can use Bardeen-Cooper-Schrieffer（BCS）theory or Bogoliubov transformations to deal with pairing correlations.However,BCS theory and Bogoliubov transformations can violate the conservation of particle number.This symmetry breaking leads to the existence of unphysical abrupt changes in thermodynamic quantities near the critical temperature.In addition,BCS theory and Bogoliubov transformations cannot deal with blocking effects precisely,and therefore studies of odd-A nuclear pairing correlations as well as thermodynamic properties are rare.However,the shell-like model approach,by diagonalizing Hamiltonian containing the pairing forces in the multi-particle configuration space,not only deals with the blocking effect precisely and keeps the particle number strictly conserved,but has successfully described various phenomena related to open-shell atomic nuclei.On the other hand,covariant density functional theory has successfully described many nuclear phenomena and has become one of the most important microscopic models of nuclear structure studies.Therefore,in this paper,the pairing correlation of the even-even nucleus ¹⁷²Yb and the odd-A nucleus ¹⁷¹Yb are investigated in the framework of a shell-like model approach based on covariance density functional theory,using PC-PK1 point coupling effective interactions,as follows:（1）The pairing correlation of the hot nucleus ¹⁷²Yb is studied based on the covariant density functional theory.In this work,we adopt a shell-like model approach with strict conservation of particle number to deal with the pairing correlations,and calculate the thermodynamic quantities of the nucleus based on the canonical system ensemble theory.The temperature-dependent S-shaped heat capacity curve was obtained,which predicts the occurrence of the pairing correlation phase transition near the critical temperature.Since this work maintains the conservation of particle number,our calculations yield a smooth temperature-dependent pairing gap,which represents the gradual transition of the nucleus from the superfluid to the normal state.In the present work,we also calculate the temperature dependence of the different seniority components,investigate the contribution of the different seniority states to the thermodynamic quantities such as entropy and energy density,and analyze the microscopic mechanism of the onset of the pairing correlation phase transition,and find that one pair of particle-broken states and two pairs of particle-broken states play a crucial role in the appearance of the S-shaped heat capacity curve.（2）The thermodynamic properties of the pairing correlation transition of the odd A-nuclear ¹⁷¹Yb were investigated based on the covariant density functional theory with the PC-PK1 point coupling effective interaction.The correlations are treated by a shell-like model approach that can accurately handle the blocking effect as well as maintain the particle number conservation.The thermodynamic quantities are calculated using the canonical system ensemble theory.In this work,it is found that the odd-A nucleus ¹⁷¹Yb also shows an S-shaped heat capacity curve with temperature.The pairing gap of ¹⁷¹Yb is smaller than that of the even-even nucleus ¹⁷²Yb.However,by investigating the seniority component,we find that one pair of particle-broken states still causes the odd-A nucleus to exhibit an S-shaped heat capacity curve.By studying the structure of the single-particle energy level of the odd-A nucleus and the precise blocking of the single-particle energy level near the Fermi surface,the analysis of this work concludes that the S-shaped heat capacity of the odd-A nucleus may be suppressed by its blocking effect.However,due to the influence of the single-particle level structure,the S-shaped heat capacity curve of ¹⁷¹Yb appears,which should have been smoothed out by the blocking effect.