能量密度泛函理论和有限力程可分离对相互作用研究核的超流性质
Superfluid of Finite Nuclei in Density Functional Theory with Finite Range Separable Pairing Interaction
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摘要: 在相对论密度泛函理论框架下引入了可分离的对相互作用， 它的参数是由拟合核物质中Gogny力对关联性质来确定。在有限核的相对论HartreeBogoliubov和相对论准粒子无规位相近似的理论框架下， 建立了可分离对相互作用在球形核和变形核中粒子粒子道矩阵的计算方法。通过Talmi和Moshinsky变换， 这种新的对相互作用在坐标空间下可以展开成一系列可分离项， 并且很快收敛。它不仅保持了平移不变性， 而且作为有限力程的对力， 可以避免零程对力在高动量截断的困难。通过对Sn同位素链核基态、 E2和E3激发态性质， 以及Sm同位素链基态的性质研究， 发现可分离对相互作用能够再现用Gogny对力得到的球形核的超流性质， 并能够很好地符合已有的实验结果。这种方法还可用来描述任意微观对相互作用， 并推广于三轴形变原子核以及转动系统的研究。为考虑角动量投影和粒子数投影的生成坐标（GCM）方法和粒子振动耦合（PVC）理论提供更加真实的对关联性质描述。A separable pairing interaction is introduced in the covariant density functional theory. The parameters of the separable force are adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. It preserves translational invariance and has finite range. Applying well known techniques of Talmi and Moshinsky, this pairing interaction can be used in relativistic and in non-relativistic Hartree-Bogoliubov or Hartree-Fock-Bogoliubov calculation of finite nuclei. It avoids the complicated problem of a cutoff at large momenta or energies inherent in other zero range pairing forces. This finite range separable pairing force is applied to study the properties of the ground and excited states for spherical Snisotopes in the relativistic Hartree Bogoliubov and relativistic quasiparticle random phase approximation. The superfluid properties of the ground state for the axially deformed Smisotopes are also studied in the deformed RHB theory with the separable pairing force. It has been shown that with this force the pairing properties of ground states can be well depicted on almost the same footing as with the original Gogny pairing interaction. There are also many extensions of relativistic density functional theory beyond mean field, such as applications using projection onto subspaces with good symmetries, generator coordinate methods, or investigation of complex configurations in the framework of particle vibrational coupling(PVC). All these methods require a more realistic description of pairing correlations in the future.Abstract: A separable pairing interaction is introduced in the covariant density functional theory. The parameters of the separable force are adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. It preserves translational invariance and has finite range. Applying well known techniques of Talmi and Moshinsky, this pairing interaction can be used in relativistic and in non-relativistic Hartree-Bogoliubov or Hartree-Fock-Bogoliubov calculation of finite nuclei. It avoids the complicated problem of a cutoff at large momenta or energies inherent in other zero range pairing forces. This finite range separable pairing force is applied to study the properties of the ground and excited states for spherical Snisotopes in the relativistic Hartree Bogoliubov and relativistic quasiparticle random phase approximation. The superfluid properties of the ground state for the axially deformed Smisotopes are also studied in the deformed RHB theory with the separable pairing force. It has been shown that with this force the pairing properties of ground states can be well depicted on almost the same footing as with the original Gogny pairing interaction. There are also many extensions of relativistic density functional theory beyond mean field, such as applications using projection onto subspaces with good symmetries, generator coordinate methods, or
investigation of complex configurations in the framework of particle vibrational coupling(PVC). All these methods require a more realistic description of pairing correlations in the future.
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