Using a generalized Bohr model and the hyper-spherical formalism for a three-body system, we derive the universal energy functions. We apply our model to 4 He atom where only the Coulomb potential is dominant and find that its binding energy is well reproduced (less than 5.5% difference). Later, we focus on the equal mass three-body systems and derive the Thomas theorem assuming a simple interaction depending on the range of the potential. We discuss the conditions for which an unbound two-body system produces a bound three-body system and apply our model to 4 He and triton atoms as well as to the triton nucleus. Using their scattering lengths and effective ranges, we are able to reproduce the two-body or the three-body binding energies (less than 5% difference) with only one parameter fitted. Prediction for excited (Efimov) levels are also given and in particular we demonstrate that for some hyper-angles two equal minima appear which indicate a phase (shape)...

中文翻译：

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广义玻尔模型中的托马斯定理和Efimov态

使用广义玻尔模型和三体系统的超球形形式，我们得出了通用能量函数。我们将模型应用于只有库仑势占优势的4 He原子，发现其结合能得到了很好的复制（相差小于5.5％）。稍后，我们将重点放在等质量的三体系统上，并根据势能范围假设简单相互作用来推导托马斯定理。我们讨论了一个无约束的两体系统产生一个约束的三体系统的条件，并将我们的模型应用于4 He和Triton原子以及Triton核。利用它们的散射长度和有效范围，我们仅用一个参数就能重现两体或三体结合能（相差小于5％）。