A method for the treatment of pairing correlations at finite temperature is proposed within the path integral formalism,based on the square root extraction of the pairing term in the Hamiltonian of the system.Gap equa...A method for the treatment of pairing correlations at finite temperature is proposed within the path integral formalism,based on the square root extraction of the pairing term in the Hamiltonian of the system.Gap equations and expressions for the pairing gap parameterΔ,energy E,and heat capacity C are established.The formalism is first tested using the Richardson model,which enables comparison with an exact solution.The results obtained using this formalism are also compared with the finite temperature BCS(FTBCS)results.An improvement over the FTBCS model is noted,especially at low temperatures.Indeed,the agreement between theΔvalues of this study and the exact values is good at low temperatures.This leads to better agreement between the values of E and C of this model and the exact values than with the FTBCS values.However,a critical value of temperature remains.Subsequently,realistic cases are considered using single-particle energies of a deformed Woods-Saxon mean-field for the nuclei ^(162)Dy and ^(172)Yb.In the framework of the current approach,pairing effects persist beyond the FTBCS critical temperature.Moreover,at low temperatures,a good agreement between the model and semiexperimental values of the heat capacity is observed,and a clear improvement compared to the FTBCS method is noted.This is no more the case at higher temperatures.展开更多
文摘A method for the treatment of pairing correlations at finite temperature is proposed within the path integral formalism,based on the square root extraction of the pairing term in the Hamiltonian of the system.Gap equations and expressions for the pairing gap parameterΔ,energy E,and heat capacity C are established.The formalism is first tested using the Richardson model,which enables comparison with an exact solution.The results obtained using this formalism are also compared with the finite temperature BCS(FTBCS)results.An improvement over the FTBCS model is noted,especially at low temperatures.Indeed,the agreement between theΔvalues of this study and the exact values is good at low temperatures.This leads to better agreement between the values of E and C of this model and the exact values than with the FTBCS values.However,a critical value of temperature remains.Subsequently,realistic cases are considered using single-particle energies of a deformed Woods-Saxon mean-field for the nuclei ^(162)Dy and ^(172)Yb.In the framework of the current approach,pairing effects persist beyond the FTBCS critical temperature.Moreover,at low temperatures,a good agreement between the model and semiexperimental values of the heat capacity is observed,and a clear improvement compared to the FTBCS method is noted.This is no more the case at higher temperatures.
