用TDDFT方法计算钠原子激发态和氢分子高阶谐振的产生

【作者】 顾斌；

【导师】 曾祥华；

【作者基本信息】 扬州大学 ， 凝聚态物理， 2005， 硕士

【摘要】 正在发展中的含时密度泛函理论(TDDFT)由于其物理思想明确、理论基础严密、计算实现便利、适用范围广泛而备受关注,并有望成为处理多电子系统线性和非线性含时响应行为的标准工具。 对原子分子激发态的研究为人们展示了丰富的物理现象,过去几十年中人们发展了许多有效处理激发态问题的高阶方法,如组态相互作用法,量子蒙特卡罗方法,格林函数方法等等。但由于它们计算复杂、计算量较大,只适用于很小的系统激发态的精确求解。含时密度泛函的线性响应理论为人们提供了方便求解激发态的新思路。 本文采用含时密度泛函方法,结合赝势模型和交换相关作用的局域密度近似,用Petersilka线性响应函数理论成功求解了钠原子多个激发态的能级。计算得出的钠原子光谱与实验数据符合较好,其中主线系四条谱线波长的相对误差低于0.6%。结果验证了含时密度泛函理论处理激发态问题的有效性。 随着强激光技术的发展,激光与原子分子相互作用的研究已经成为物理学中一个新的热点。实验表明在超强超短激光脉冲的作用下,原子分子会出现一系列微扰理论无法解释的新现象。其中高阶谐振的产生,由于可以作为产生真空远紫外线和软X射线的可能途径,受到人们的极大关注。对原子分子高次谐波产生的研究可以系统地促进非微扰理论的建立和发展,使人们更好地理解强激光场中新的物理现象和物理机制,同时又为设计简便的高频相干激光源提供理论依据。人们通常用含时薛定谔方程描述激光和原子分子相互作用的简化模型。但是随着系统电子数和自更多还原

【Abstract】 The developing time-dependent density-functional theory (TDDFT) has been attracting more and more attention since its intrinsic advantages, such as explicit physical conception, rigorous basis in theory, convenience in application and general applicability. It is hopeful to become a general method to deal with both linear and non-linear response of multi-electron systems.The studies of excited states of atoms and molecules have opened out many colorful physical pictures. In the past decades, many efficient high level methods, such as configuration interaction method, quantum Monte Carlo simulations and the Green function method, have been developed to deal with the excitation of electrons. While these methods describe electronic excitations properly, they are usually limited to deal with very small systems because of their complication and high computational demands. An alternative efficient approach is to consider the linear response methods based on TDDFT.In this thesis, according to the Petersilka linear response theory which is based on TDLDA, combining with the pseudo-potential model, several excited states of sodium atom are calculated in detail. The resulted sodium spectra consist with the experimental data very well, with a less than 0.6% relative error of the principal series, which show a good evidence for the TDDFT application to the description of the excited system.Recently with the development of laser technology, the subject of interactionbetween strong laser and atoms, molecules has become a new hot topic. When atoms and molecules are radiated by ultra intense laser pulse, a series of new non-linear phenomena which can’t be interpreted by perturbation theory appears. The most attractive one is high order harmonic generation (HHG), which can be used as a source of extreme ultraviolet (XUV) and soft X-ray lasers. The importance of studying HHG consists in two aspects. Firstly it can accelerate the development of non-perturbation theory and contribute to the further understanding of strong laser induced new phenomena and the underlying new physical mechanism. Secondly it may provide theory background for the development of simple and cheap short wavelength coherent light generators.The popular theoretic methods to describe the simplified interaction of laser-atoms and molecules are based on time-dependent Schrodinger equations (TDSE). As the number of electrons and the degree of freedom increase, the solutions of the TDSE go beyond current computational ability. However, according to TDDFT, if the electronic density is taken as the principle variable the degree of freedom will remain very small, despite the increase of the number of particles. In this thesis, the HHG of hydrogen molecule radiated by an ultra strong femto-second laser pulse are simulated by the TTDFT method with the general gradient approximation (GGA) of the exchange-correlation energy. The results indicate that the HHG spectrum of H2 has a "Decrease-Plateau-Cutoff’ structure, which is similar to the typical atom HHG spectrum; when the polarization of laser is perpendicular or parallel to the molecule axis, there is a kind ofselective phenomena of the order number of HHG, which may be induced by the symmetry of H2 molecule. Compared with the result of one dimension soft Coulomb model, the peak region of the transform ratio both locate between 9th to 19th orders; the cutoff order of TDDFT result is smaller than the classical model. We also find that the difference in the polarization direction may change the cut-off order and spectrum intensity of HHG. Further research about the HHG of H2 and other molecules radiated by lasers with different parameters and how to interpret the physical mechanism underlying the phenomena with the evolution of the electronic density are carrying out.The basic works in this thesis may lead us to explore more interesting and fascinating strong laser induced excitation and nonlinear response of atoms and molecules.更多还原