State-of-the-art of beyond mean field theories with nuclear density functionals
J. Luis Egido
备注：
To be published in Physica Scripta as an invited comment in a focus issue to celebrate the 40-year anniversary of the 1975 Nobel Prize to Aage Niels Bohr, Ben Roy Mottelson and Leo James Rainwater
We present an overview of beyond mean field theories (BMFT) based on the generator coordinate method (GCM) and the recovery of symmetries used in nuclear physics with effective forces. After a reminder of the Hartree-Fock-Bogoliubov (HFB) theory a discussion of the shortcomings of any mean field approximation (MFA) is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. The lack of fluctuations around the average values of the MFA is a shortcoming of this approach. To build in correlations in BMFT one selects the relevant degrees of freedom: quadrupole, octupole and the pairing vibrations as well as the single particle ones. In the GCM the operators representing these degrees of freedom are used as coordinates to generate a collective subspace. The highly correlated GCM wave function is finally written as a linear combination of a projected basis of this space. The variation of the coefficients of the linear combination leads to the Hill-Wheeler equation. We discuss the classical beta and gamma vibrations by considering the quadrupole operators as coordinates. We present pairing fluctuations by considering the pairing gaps as generator coordinates. Lastly the explicit consideration of the time reversal symmetry breaking in the HFB wave function by the cranking procedure allows the alignment of nucleon pairs opening a new dimension in the BMFT calculations. Abundant calculations with the Gogny force illustrate the state-of-the-art of BMFTs with density functionals. We conclude with a thorough discussion on the potential poles of the theory.
Non-local orbital-free density functional theory incorporating nuclear shell effects
Fuzhou University（福州大学）；Università degli Studi di Milano（米兰大学）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）；Kyoto University（京都大学）；RIKEN Nishina Center for Accelerator-based Science, RIKEN（理化学研究所西村加速器科学中心）；Peking University（北京大学）
Calculations for nuclear matter and finite nuclei within and beyond energy--density--functional theories through interactions guided by effective field theory
Simulation of heavy ion collision using a time-dependent density functional theory including nuclear superfluidity
利用含时密度泛函理论对重离子碰撞进行了模拟。我们称之为正则基含时Hartree-Fock-Bogoliubov理论（Cb-TDHFB），它可以在三维坐标空间中描述核动力学，处理核对关联。我们用具有接触型配对泛函的Cb-TDHFB方法模拟了20 O +20 O碰撞，并给出了碰撞过程中带隙能量的衰减和振动行为.
本文评述了最近在轻核（A=2-6）的{ \it ab initio}计算中取得的成功，并将其与手征对称性的动力学结果联系起来。这些结果所显示的核物理学的易处理性是这种对称性的证据。我们将在有效场论和维度功率计数的背景下讨论三核子力、四核子力、多π介子交换和相对论修正的相对重要性。本文还将讨论核力中的Isospin破坏。
Density functional approaches to collective phenomena in nuclei: Time-dependent density-functional theory for perturbative and non-perturbative nuclear dynamics
Model nuclear energy density functionals derived from ab initio calculations
我们提出了[Journal of Physics G：Nuclear and Particle Physics，43，04LT 01（2016）]中提出的一种新方法的首次应用，以从从头算哈密顿量推导Skyrme能量密度泛函（EDF）的耦合常数。通过用定义Skyrme EDF的几个函数生成器扰动从头算哈密顿算子，我们创建了一组元数据，然后用于约束泛函的耦合常数。我们使用统计分析来获得这样一个从头算等效的Skyrme EDF。我们发现所得泛函对原子核和无限核物质的性质描述得很差。这可能会指出建立从头等效泛函从更复杂的生成元的必要性。然而，我们也指出，目前的从头计算的精度可能是不够的推导有意义的核EDF。
