基于改进变分法对原子激发态精确波函数的研究  

Accuracy study for excited atoms(ions):A new variational method

作　　者：熊庄[1,2] 汪振新[1,2] Naoum C.Bacalis 

机构地区：[1]东南大学空间科学与技术研究院,南京210096 [2]东南大学能源热转换及其过程测控教育部重点实验室,南京210096 [3]Theoretical and Physical Chemistry Institute,National Hellenic Research Foundation,Vasileos Constantinou 48,GR-116 35 Athens,Greece

出　　处：《物理学报》2014年第5期113-123,共11页Acta Physica Sinica

基　　金：国家自然科学基金重大研究计划(批准号:91334205);国家自然科学基金联合基金(批准号:11178008)资助的课题~~

摘　　要：传统的利用变分原理求解Schrfidinger方程获得原子激发态波函数的方法是基于HUM理论(HylleraasUndheim and MacDonald theorem),在有限的N维Hilbert空间中,通过求解久期方程的高阶根获得激发态的近似波函数.在我们前期的工作中已指出,由于HUM方法的几个内禀缺陷限制,它将导致在相同的函数空间中,由传统变分法得到的激发态波函数的‘质量’远差于足够好的基态波函数.进一步地,为了避免基于HUM方法的变分缺陷,本文提出了新的变分函数,并证明其试探激发态波函数在其本征态处具有局域极小值,因而可以通过变分极小无限制的逼近该本征态.在此基础上,利用广义的Laguerre类型轨道(GLTO)在组态相互作用的框架下,分别编写了基于传统HUM理论和新变分函数的关于求解原子近似波函数的计算程序,并且利用该程序计算了氦原子(He)在1S(e),1P(o)态下相应的基态及激发态近似波函数及对应的能量值和径向平均值,并与已有文献中结果进行比较,计算结果显示了HUM理论的缺陷及新变分函数优越性,并就进一步提高激发态的精度指明了方向.For the computation of excited states, the traditional solutions of the Schrfiedinger equation, using higher roots of a secular equation in a finite N-dimensional function space, by the Hylleraas-Undheim and MacDonald（HUM） theorem,we found that it has several restrictions which render it of lower quality, relative to the lowest root if the latter is good enough. In order to avoid the variational restrictions, based on HUM, we propose a new variational function and prove that the trial wave function has a local minimum in the eigenstates, which allows to approach eigenstates unlimitedly by variation. In this paper, under the configuration interaction（CI）, we write a set of calculation programs by using generalized laguerre type orbitals（GLTO） to get the approximate wave function of difierent states, which is base on the HUM or the new variational function. By using the above program we get the approximate wave function for1S（e）,1P（o）state of helium atoms（He） through the difierent theorems, the energy value and radial expectation value of related states. By comparing with the best results in the literature, the theoretical calculations show the HUM＇s defects and the new variational function＇s superiority, and we further give the direction of improving the accuracy of excited states.

关 键 词：变分法 激发态波函数 变分函数 组态相互作用 

分 类 号：O562[理学—原子与分子物理]