【作者】 李洪云；

【导师】 林圣路；

【作者基本信息】 山东师范大学 ， 原子与分子物理， 2004， 硕士

【摘要】 近年来，高里德堡原子在强外场中的光吸收现象引起人们广泛的关注，它是研究和发展量子混沌概念的一个典型实例。半经典闭合轨道理论由于具有物理图像清晰、应用范围广泛等特点被普遍用来解释此类现象，并成为实现联结经典理论和量子理论的重要桥梁。该理论很好地解释了氢负离子在各种外场下的光吸收问题以及氢原子、锂原子及其他类氢原子和分子在电磁场中的光激发、电子波包动力学等问题。 与氢原子相比，对多电子原子，理论处理要困难得多，氦原子就是一个典型的量子体系，由于离子实的作用，其相应的经典行为是混沌的。通过对多电子原子强场行为的实验与理论研究，人们发现必须考虑离子实的作用，实散射产生了在单电子中没有的组合轨道，使轨道数目迅速增加。氦原子自身两个电子关联密切，使得考虑交换势成为必要。而且，在标度能量的某些点上，由于轨道发散形成的聚焦作用，导致波函数在发散点附近变为无穷大，闭合轨道理论不再适用，因而必须对理论本身做适当的改进和推广。 本文采用了包括离子实散射的分区自洽迭代方法，结合B.Hüpper的模型势和量子亏损理论，在模型势中我们特别引进电子交换势，计算了谱的大标度结构(△E大，相应时间△T小)，即作用量较小的闭合轨道的贡献，因为它们对谱性质起决定性作用。我们得到了B=3.5T，F=18.84V／cm情况下，标度能量ε=-0.03，主量子数n≈40，m=0的三重态He原子在平行电磁场和垂直电磁场中的回归谱。为与已有实验结果比较，我们还计算了同一模型势下标度能量ε=2.7，20＜n＜30，m=0的三重态He原子在电场中的回归谱，结果和M．L．Keeler的实验结果基本上是一致的，这个结果明显优于原有的未考虑交换势的理论结果，说明在对多电子原子的回归谱的分析中，核散射和电子交换都具有重要效应。由于没做统一近似，峰值大小明显比实验结果高，我们又用统一近似方法对电场中的氦原子回归谱进行了修正，结果与实验符合很好。 对于He原子在垂直电磁场中回归谱的计算，由于存在外加电场、磁场和核的库仑作用之间的相互竞争，导致规则运动区域的进一步缩小，闭合轨道变成三维。我们计算了B=3.5T，F=18.84V／cm情况下，标度能量ε=-0.03，主量子数n≈40，标度电场山东师范大学硕士学位论文中文摘要了二0.01，m二0的三重态He原子的回归谱，并与氢原子结果做了比较，同样证实了实散射的重要贡献。 对于氦里德堡原子这一研究领域，我们的工作既是对半经典理论的推广，又是对该理论的验证和完善。由于目前还没有氦原子在平行电磁场和垂直电磁场中的实验结果，希望理论计算能对实验有一定的参考作用。 论文共分为五章。第一章为综述，从总体上介绍了半经典闭合轨道理论的要点及其发展。第二章介绍了模型势和标度变换回归谱学，给出了包括电子交换势的氦原子的模型势，还给出了在电磁场同时存在时的标度变换和只有电场时的标度变换。第三章给出了平行电磁场中氦里德堡原子的回归谱的计算结果，并与M.L.Keeler的实验结果做了比较。第四章给出了垂直电磁场中氦里德堡原子的回归谱的计算结果，并与相同情况下的氢原子做了比较。第五章采用统一近似方法对氦原子回归谱进行了修正，证实了理论的正确性。关键词:半经典闭合轨道理论;交换势;回归谱;实散射;分区自洽迭代法论文分类号:0562.3更多还原

【Abstract】 The photo-absorption phenomenon of highly excited Rydberg atoms in strong external fields has attracted much attention in recent years, which is a typical example for understanding the conception of quantum chaos. The semiclassical closed-orbit theory has been extensively used to explain this phenomenon due to its clear physical picture and wide availability, and has become a link between quantum and classical theory. This theory has successfully calculated and interpreted the photo-absorption spectra of H- in various external fields and has been applied to describe the photo-excitation, wave packet dynamics of some atoms and molecules such as H, Li and so on.To multielectron atoms, the theoretical treatment is more difficult than hydrogen atoms. The helium atoms are the prototypical quantum atomic system whose underlying classical dynamics is chaotic, induced by core scattering. Previously theoretical and experimental studies about the multielectron atoms have found that the effects of the non-hydrogenic ionic core should be considered. It is core scattering that leads to new recurrence peaks called combination recurrence. Because two electrons of the He atom have significant correlation, the exchange potential must be considered. At some value of scaled energy, the returning waves would become infinite as a focus or caustic passed through the origin. So it is necessary to correct and extend the primitive closed-orbit theory.In this paper, we put forward a new model potential based on the quantum defect theory, which includes not only the core attractive potential, but also the exchange potential between the excited electron and another electron. We calculate the closed orbits and the recurrence spectra with finite resolution using special region-splitting consistent and iterative method, i.e., the spectral structure is measured in larger energy scale. In other words, there are only the contributions of closed orbits with smaller actions, which are the most decisive for the spectral behavior, have been involved. In numerical implementation of the calculating theprocess of the orbit returning and core scattering should be repeated and iterative, so as to get a convergent results. It is done we obtained the recurrence spectra of triplet helium atoms in parallel electric and magnetic fields at scaled energy ε =0.03, n≈40, m=0. In order to compare with resent of the experimental observation, we have also displayed the recurrence spectra of helium atoms with the same exchange potential but in single electric field at scaled energy ε =-2.7 case, and shown that our approach is in better agreement with the experimental data than that previous theoretical calculations. The results also imply that the core-scattering effects are important and our model potential is correct. Therefore, it is necessary to consider the electrons exchange effect for studying the absorption spectra of multielectronic atoms in strong external fields. The amplitudes of some peaks are overevaluated due to not inserting the uniform approximations, when we used the uniform approximates method to correct the recurrence spectra of helium atoms, the high of the peaks should be reduced, and our result would be in good agreement with the experimental data.For the recurrence spectra of helium atoms in perpendicular electric and magnetic fields, because of the simultaneous action and competitions of the electric field, the magnetic field and the nuclear coulomb potential, the region of regular motion reduces farther more, the closed orbits extend to three degrees of freedom, we calculate the recurrence spectra of Heatom in perpendicular magnetic and electric field at ε= -0.03, n≈40, F = 0.01,m = 0. We have also compared the results with that of hydrogen atom .Our calculations certify the validity of the closed orbits theory and make some improvement upon it, and imply that the core-scattering effects is important.In the case of He Rydberg atom, our works are not only the extension but also the validation and supplement for the closed-orbit theory. So fa更多还原