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
Expressions of the spectroscopic factors（SFs） corresponding to one-particle transfer reactions have been established using a schematic definition.These expressions have been derived by taking into account the isovec...Expressions of the spectroscopic factors（SFs） corresponding to one-particle transfer reactions have been established using a schematic definition.These expressions have been derived by taking into account the isovector neutron-proton（np） pairing correlations and a particle-number projection in the framework of the generalized SharpBCS（SBCS） method.Recently proposed expressions of the projected wave-functions of odd-mass nuclei have been used for this purpose.The formalism has first been tested using the single-particle energies of the schematic picketfence model.It is shown that the np pairing and particle-number fluctuation effects are far from negligible and they depend on the pairing gap parameter values.Their behavior is not the same when the parent nuclei are even-even or odd.Predictions dealing with the SFs corresponding to one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei have then been established within the framework of the realistic Woods-Saxon model.It is shown that the np pairing effect as well as the particle-number projection effect are important and thus have to be included in future calculations of the SF corresponding to these kinds of reactions.展开更多
Isovector neutron-proton（np） pairing and particle-number fluctuation effects on the spectroscopic factors（SF） corresponding to one-pair like-particle transfer reactions in proton-rich even-even nuclei are studied....Isovector neutron-proton（np） pairing and particle-number fluctuation effects on the spectroscopic factors（SF） corresponding to one-pair like-particle transfer reactions in proton-rich even-even nuclei are studied. With this aim, expressions of the SF corresponding to two-neutron stripping and two-proton pick-up reactions, which take into account the isovector np pairing effect, are established within the generalized BCS approach, using a schematic definition proposed by Chasman. Expressions of the same SF which strictly conserve the particle number are also established within the Sharp-BCS（SBCS） discrete projection method. In both cases, it is shown that these expressions generalize those obtained when only the pairing between like particles is considered. First, the formalism is tested within the Richardson schematic model. Second, it is applied to study even-even proton-rich nuclei using the single-particle energies of a Woods-Saxon mean-field. In both cases, it is shown that the np pairing effect and the particle-number projection effect on the SF values are important, particularly in N =Z nuclei, and must then be taken into account.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.
文摘Expressions of the spectroscopic factors（SFs） corresponding to one-particle transfer reactions have been established using a schematic definition.These expressions have been derived by taking into account the isovector neutron-proton（np） pairing correlations and a particle-number projection in the framework of the generalized SharpBCS（SBCS） method.Recently proposed expressions of the projected wave-functions of odd-mass nuclei have been used for this purpose.The formalism has first been tested using the single-particle energies of the schematic picketfence model.It is shown that the np pairing and particle-number fluctuation effects are far from negligible and they depend on the pairing gap parameter values.Their behavior is not the same when the parent nuclei are even-even or odd.Predictions dealing with the SFs corresponding to one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei have then been established within the framework of the realistic Woods-Saxon model.It is shown that the np pairing effect as well as the particle-number projection effect are important and thus have to be included in future calculations of the SF corresponding to these kinds of reactions.
文摘Isovector neutron-proton（np） pairing and particle-number fluctuation effects on the spectroscopic factors（SF） corresponding to one-pair like-particle transfer reactions in proton-rich even-even nuclei are studied. With this aim, expressions of the SF corresponding to two-neutron stripping and two-proton pick-up reactions, which take into account the isovector np pairing effect, are established within the generalized BCS approach, using a schematic definition proposed by Chasman. Expressions of the same SF which strictly conserve the particle number are also established within the Sharp-BCS（SBCS） discrete projection method. In both cases, it is shown that these expressions generalize those obtained when only the pairing between like particles is considered. First, the formalism is tested within the Richardson schematic model. Second, it is applied to study even-even proton-rich nuclei using the single-particle energies of a Woods-Saxon mean-field. In both cases, it is shown that the np pairing effect and the particle-number projection effect on the SF values are important, particularly in N =Z nuclei, and must then be taken into account.
