Fifty Years of the Shell Model — The Quest for the Effective Interaction
Fifty Years of the Shell Model — The Quest for the Effective Interaction
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DOI：
10.1007/0-306-47916-8_1
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发表时间：
2003
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影响因子：
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通讯作者：
I. Talmi
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作者：
I. Talmi
1999 年，我们庆祝了现代版本的原子核壳模型问世 50 周年。在该模型中，假设核成分（质子和中子）在中心势阱中独立移动。这个井应该是由于这些成分（核子）之间的平均相互作用造成的。为了获得观察到的单个核子轨道之间的间距，势阱应该包括每个核子的自旋和轨道角动量之间相当强的相互作用。事实证明，强自旋轨道相互作用是一个重要因素。它由 Maria G. Mayer (1949) 提出，并由 Haxel、Jensen 和 Suess (1949) 独立提出，并导致观测到的单核子轨道和主壳层完全填充的正确幻数。壳模型彻底改变了核物理理论。受影响最大的领域是核结构理论，该理论涉及原子核的能级、它们的波函数以及它们之间的电磁和β跃迁。另一个广泛的领域，即原子核之间以及核子与原子核之间的各种反应，也受到了强烈影响。壳模型是由 MG Mayer (1948) 总结的大量实验数据强加给核理论家的。理论的发展启发了实验学家，更常见的是，新颖的实验给理论家带来了挑战。要回顾壳模型在前 50 年对核物理的影响，需要一本真正的百科全书。这篇评论的目的相当温和。它涉及壳模型内某些能量和波函数计算的相当有限的目标。核能的计算是一个非常困难的问题。具有神奇质子和中子数的原子核的特殊稳定性直接取决于它们在势阱中的能级。尽管如此，平均势能是由两个核子相互作用引起的，因此，通过使用壳模型波函数计算它们可以获得势能的更好近似值。然而，由于几个重要原因，这是非常困难的。首先，自由质子和中子之间的相互作用还没有被充分了解。散射实验的结果和氘核的性质已经通过几种相当现象学的“现实”相互作用来拟合。尽管如此，由于这些相互作用缺乏既定理论，因此没有明确的处方。质子和中子的夸克和胶子的内部结构大大增加了复杂性。然而，这个问题只是“根据第一原理”计算核能的困难的一部分。许多身体问题的解决通常是极其复杂的。自由核子之间强烈而奇异的相互作用使得普通的微扰方法变得毫无用处。受到壳模型明显成功的推动，核多体理论家试图推导出一个重整化（有效）的因
In 1999 we celebrated 50 years of the modern version of the shell model for nuclei. In this model it is assumed that the nuclear constituents-protons and neutrons-move independently in a central potential well. This well should be due to the average interaction between these constituents, the nucleons. To obtain the observed spacings between single nucleon orbits, the potential well should include a rather strong interaction between the spin and orbital angular momentum of each nucleon. The strong spin-orbit interaction turned out to be an essential ingredient. It was introduced by Maria G. Mayer (1949) and independently by Haxel, Jensen and Suess (1949) and led to the observed single nucleon orbits and the correct magic numbers for which major shells are completely filled. The shell model revolutionized the theory of nuclear physics. The field mostly affected was nuclear structure theory which deals with energy levels of nuclei, their wave functions and electromagnetic and beta transitions between them. Another wide field, of various reactions between nuclei and between nucleons and nuclei, was also strongly affected. The shell model was imposed on nuclear theorists by a large variety of experimental data summarized by MG Mayer (1948). Theoretical developments inspired experimentalists and, more frequently, novel experiments presented challenges to theorists. To review the impact of the shell model on nuclear physics in the first 50 years, a real encyclopaedia would be necessary. This review has a rather modest aim. It deals with the rather limited goal of calculation of certain energies and wave functions within the shell model.The calculation of nuclear energies is a very difficult problem. The special stability of nuclei with magic proton and neutron numbers follows directly from their energy levels in the potential well. Still, the average potential is due to two-nucleon interactions and, hence, a better approximation to the potential energy could be obtained by calculating them using shell model wave functions. This, however, is very difficult for several important reasons. First, the interaction between free protons and neutrons is not sufficiently well known. Results of scattering experiments and properties of the deuteron have been fitted by several, rather phenomenological,“realistic” interactions. Still, in the absence of an established theory for these interactions, no definite prescription is available. The internal structure of protons and neutrons in terms of quarks and gluons adds much to the complications. This problem, however, is only part of the difficulty of calculating nuclear energies “from first principles”. The solution of the many body problem is usually extremely complicated. The strong and singular interaction between free nucleons makes ordinary perturbation methods useless. Motivated by the apparent success of the shell model, nuclear many body theorists have tried to derive a renormalized (effective) in-