核中的单粒子空间色散和团簇
Single-particle spatial dispersion and clusters in nuclei
摘要：
在基于核能密度泛函的自洽平均场框架下，在核势的谐振子近似下，分析了单核子波函数的空间色散。结果表明，色散依赖于径向量子数n，但只显示出很弱的依赖于轨道角动量。导出了明确考虑了径向量子数的定域化参数的解析表达式。在相对轻的原子核中，占据$A \leq 30$和$n=1$态时，满足了单核子局域化和形成团簇结构的条件.较重的原子核呈现核子物质的量子液相，因为源自$n > 1$球形态的占据能级大部分是离域的。然而，个别的$α$类簇可以由价核子填充源自$n=1$球形平均场态的单粒子能级形成。
英文摘要：
The spatial dispersion of the single-nucleon wave functions is analyzed using the self-consistent mean-field framework based on nuclear energy density functionals, and with the harmonic oscillator approximation for the nuclear potential. It is shown that the dispersion depends on the radial quantum number n, but displays only a very weak dependence on the orbital angular momentum. An analytic expression is derived for the localization parameter that explicitly takes into account the radial quantum number of occupied single-nucleon states. The conditions for single-nucleon localization and formation of cluster structures are fulfilled in relatively light nuclei with $A \leq 30$ and $n=1$ states occupied. Heavier nuclei exhibit the quantum liquid phase of nucleonic matter because occupied levels that originate from $n > 1$ spherical states are largely delocalized. Nevertheless, individual $α$-like clusters can be formed from valence nucleons filling single-particle levels originating from $n=1$ spherical mean-field states.
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