Jacobi Transformations in Four-cluster Systems

多体量子系统中的物质并不总是均匀分布的。它里面的粒子，无论是分子、原子还是核子，都可以聚集在一起形成团簇。在轻原子核中，已知许多状态，其中核子聚集成三个团簇中的两个。最近，来自伯明翰、萨里和约克的实验学家研究了表现为四簇系统的核状态，即由两个α粒子和两个质子组成的碳同位素10 C，以及表现为四个单独的α粒子系统的16 O中的一些激发态。本文的建议是开始一个理论模型来处理四团簇态，并将这个模型应用到~（10）Be、~（10）C和~（16）O。这将使我们能够发现16 O中的任何4-α态是否可以被认为是四个单独α粒子的玻色-爱因斯坦凝聚体。

The matter in many-body quantum systems is not always uniformly distributed. Particles inside it, whether they are molecules, atoms or nucleons, can gather together forming clusters. In light atomic nuclei, many states are known in which nucleons gather into two of three clusters. Recently, experimentalists from Birmingham, Surrey and York have studied nuclear states that behave like four-cluster systems, namely, the carbon isotope 10C which is made of two alpha-particles and two protons, and some excited states in 16O that behave like systems of four individual alpha-particles. The present proposal is to begin a theoretical model to deal with four-cluster states and to apply this model to 10Be, 10C and 16O. This will later enable us find out if any of the 4-alpha states in 16O can be considered as a Bose-Einstein condensate of four individual alpha-particles.