本文首先介绍了V.M. Strutinsky是A. B. Migdal和合作者。然后，我们更详细地介绍了壳效应的半经典理论，也是Strutinsky根据M。古兹威勒我们特别强调了轨道分叉对壳结构的影响。我们首先给出一个简短的概述半经典的轨迹公式，它连接壳振荡的量子系统与相应的经典系统的周期轨道的总和，在通常被称为“周期轨道理论”。然后，我们提出了一个案例研究中，一个典型的双峰核裂变屏障，包括质量不对称的影响，可以得到的最短周期轨道的腔模型与现实的变形有关的核裂变的总功能。接下来，我们研究壳结构的球形空腔模型，这是可积的，并允许远的分析计算。我们显示，特别是，如何倍周期分岔密切相关的存在所谓的“超变形”的能量最小值，对应于裂变异构体的锕系元素核。最后，我们提出了一类在束缚区域内很好地逼近Woods-Saxon势形状的径向幂律势，给出了它的解析迹公式，并讨论了各种极限（包括谐振子和球箱势）.
英文摘要：
We first give an overview of the shell-correction method which was developed by V. M. Strutinsky as a practicable and efficient approximation to the general selfconsistent theory of finite fermion systems suggested by A. B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the "periodic orbit theory". We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called "superdeformed" energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).
Erratum: Exact solutions to the fermion propagator Schwinger-Dyson equation in Minkowski space with on-shell renormalization for quenched QED \newline [Phys. Rev. D 96, 036021 (2017)]
Shell-Model Monte Carlo Simulations of Pairing in Few-Fermion Systems
利用壳模型蒙特卡罗方法研究了具有吸引零程两体相互作用的费米子囚禁系统。该方法提供了平均场论不适用的低$N$限值的{ \em ab initio}结果。能量和配对属性的相互作用强度，粒子数和温度的函数。在有趣的区域，其中典型的矩阵元素的两体相互作用的陷阱的水平间距相比，我们发现大的奇偶效应和签名的壳结构。作为温度的函数，我们观察到这些效应的消失，如在相变。
Shell-Model Monte Carlo Simulations of BCS-BEC Crossover in Few-Fermion Systems
利用壳模型蒙特卡罗方法研究了零射程两体相互作用下的费米子囚禁系统，给出了平均场论不适用的低粒子数极限下的{ \em ab initio}结果.我们目前的结果为$N$体能量的相互作用强度，粒子数和温度的函数。在有限的模型空间中的重正化的微妙问题的解决和我们的方法的收敛性和跨BCS-BEC交叉的适用性进行了讨论。我们的研究结果表明，非常好的定量结果可以得到BCS侧，而在酉和BEC制度的收敛是不太清楚。比较N=2分析在零和有限的温度，并在文献中的其他计算$N>2$显示非常好的协议。
Relation to a property of the angular momentum zero space of states of four fermions in an angular momentum $j = 9/2$ shell unexpectedly found to be stationary for any rotationally invariant two-body interaction
