摘要
自从发现在星体表面存在较强的磁场,原来自由场的研究计算数据不再适用于天文观测。近三十年来,随着天体物理学对光谱数据的需求,强磁场中原子和分子体系理论计算一直是计算物理中前沿课题。本文首次介绍利用Hylleraas基函数计算四体系统在磁场中任意束缚态能级。通过具体计算基态和低激发态在磁场中的锂原子再次证明Hylleraas基在描述系统之间的电子关联效应时较其他试探波函数表现出优越的性能。
根据宇宙大爆炸的核聚变理论,宇宙中丰度最高的是一些最轻的元素—氢、氦、锂等等的少体系统。氢和氦作为其中结构较为简单的体系,加上在自由场对氢和氦研究方法比较成熟,精度也已经非常高。所以比较容易推广到磁场中的计算利用以前的方法。这些计算得到的数据在天文观测中提供了详细的依据。
但是随着电子的增加,原子体系的计算难度越来越大。锂原子这种三电子原子体系在自由场中变分能量也是最近5年在精度上有所提高达到了14位有效数值。相对于自由场,磁场中三电子原子体系的数据精度就差很多,同时可用的数据也很少。正是这样,本文首次将目前在处理自由场中锂原子最精确的方法推广到磁场中,对提高磁场中三电子原子体系束缚态的变分能量的精度做出尝试。在方法上我们完成了磁场中三电子原子体系算符在Hylleraas基矢下积分公式的解析推导,给出可供计算的公式依据。随后具体计算了一些低激发态的变分能量值。比起已经公布的其他方法计算的结果,我们的结果极大的改进了三电子原子体系在强磁场下非相对论变分能量上限,与此同时我们改进了相应的锂原子跃迁振子。
Since the discovery of the existence of a strong magnetic field of dense stars surface, the original research data is not suitable for astronomical observation for atomic and molecular system without a magnetic field. In the past thirty years, along with the demand of the spectroscopic data in astrophysics, the theoretical calculation in a strong magnetic field has been the subject of computational physics for the atomic and molecular system theory. This paper first introduced that the arbitrary bound states of four-body atomic system were calculated based on the Hyllerass-type trial wave function.
According to the standard theory of Big Bang Nucleosynthesis (BBN), some of the lightest elements-hydrogen, helium, lithium and other few-body systems are the highest abundance in Cosmos. Because hydrogen and helium have the relatively simple structure of the atomic system, the research method of them is already mature in free-field. The calculation accuracy is very high. Previous methods are easy extended to the calculation of these simple systems in a strong magnetic field. These calculated data provide a detailed basis in astronomy.
With the number of electrons increasing, however, calculation of the atomic systems is getting more and more difficult. The accuracy of the variational energy for low-lying states of lithium in free-field increases to14effective numerical in recent5years. Compared to the situation without magnetic fields, the accuracy of the variational energies for low-lying states of lithium is much worse in a magnetic, and the available data are rare. For that reason, the most accurate method to handle three-electron atomic systems in free-field was first extended to calculate the non-relativistic energies for three-electron atomic systems in a magnetic field. The main work of this dissertation is to improve the accuracy of the non-relativistic energies for three-electron atomic systems in a magnetic field. In the method, we solve the integeral formula for the arbitrary bound states of three-electron atomic systems in Hylleraas coordinates with magnetic, and give the basis for practice calculation, and then calculate the variational energies for low-lying states of three-electron atomic systems. Our calculation greatly improved the accuracy of the non-relativistic energies for three-electron atomic systems atom in a magnetic fields compared with the results obtained by other methods. Meanwhile some improved values for the dipole-oscillator strengths are obtained for lithium atom.
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