Nilsson模型中自旋佯谬的解决
Resolution of the spin paradox in the Nilsson model
摘要：
在著名的尼尔逊图中，描述了核单粒子能级与四极形变的关系，出现了自旋佯谬（随着形变的开始，从球形变成具有圆柱对称性的扁长形变形状）。对应于球壳模型轨道的能级束，共享相同的轨道角动量和相同的总角动量，似乎对应于尼尔森能级，用柱坐标中的渐近量子数标记，其中一些自旋向上，而另一些自旋向下。此外，对于某些轨道，球壳模型量子数与Nilsson渐近量子数的对应关系对质子和中子并不相同。通过引入两组量子数之间的新的对应规则，我们证明了自旋佯谬的解决，并建立了质子和中子Nilsson图之间的完全一致。作为四极形变函数的尼尔森图的形式保持不变，新图与传统图之间的唯一区别是某些单粒子能级对的尼尔森标记的相互交换。
英文摘要：
In the well-known Nilsson diagrams, depicting the dependence of the nuclear single-particle energy levels on quadrupole deformation, a spin paradox appears {as the deformation sets in, leading from spherical shapes to prolate deformed shapes with cylindrical symmetry}. Bunches of levels corresponding to a spherical shell model orbital, sharing the same orbital angular momentum and the same total angular momentum, appear to correspond to Nilsson energy levels, labeled by asymptotic quantum numbers in cylindrical coordinates, some of which have spin up, while some others have spin down. Furthermore, for some orbitals the correspondence between spherical shell model quantum numbers and Nilsson asymptotic quantum numbers is not the same for protons and for neutrons. Introducing a new rule of correspondence between the two sets of quantum numbers, we show that the spin paradox is resolved and full agreement between the proton and neutron Nilsson diagrams is established. The form of the Nilsson diagrams as a function of the quadrupole deformation remains unchanged, the only difference between the new diagrams and the traditional ones being the mutual exchange of the Nilsson labels for certain pairs of single-particle energy levels.
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