Lipkin模型下最陡降法的理论计算

将由Ｃｉｏｓｌｗｓｋｉ提出和被文根旺推广了最陡下降法用于Ｌｉｐｋｉｎ可解模型，计算表明，用该方法对基态的近似计算可以达到任意精度，在相互作用较强的情况下，随着激发态能量的升高，所得激发态结果的精度将逐渐降低。该方法原则上原则上不受相互作用用强度的限制，在微扰论不适用的强相互作用不亦可得到满意的结果。该方法确实可望成为一种实用的量子力学计算方案。     

非相对论性和相对论性原子组态相互作用理论——激发能量和辐射跃迁几率

我们建立的非相对论性和相对论性原子组态相互作用理论计算方法可用来计算低度激发态的激发能量和辐射跃迁几率(包括允许跃迁和禁戒跃迁)。为了检查我们的计算程序,分别用两种方法计算了氦原子N=2激发态的激发能和相应的辐射跃迁几率。结果表明:非相对论性理论和相对论性理论计算结果基本一致。原子激发能量的精度为千分之几,振子强度的精度为百分之几。上述原子组态相互作用理论方法可用于计算任何原子或离化态原子。 关键词：     

He-HBr体系各向异性势及非弹性散射截面的理论研究

首先用BFW势函数形式拟合在CCSD(T)/aug-cc-pVQZ理论水平下计算的He-HBr相互作用能数据,得到了He原子与HBr分子各向异性势;并与ESMSV势进行比较,验证了拟合势的可靠性;然后采用公认的精确度较高的CC近似方法计算了He-HBr碰撞体系能量在150meV下He原子和HBr分子碰撞的转动激发微分截面和分波截面,总结了该碰撞体系非弹性散射截面的变化规律.研究表明:①拟合势较好地描述了He-HBr系统相互作用的各向异性特征;利用碰撞体系分子间势的量子化学从头计算结果,可解决势能参数难以确定的问题.②低激发态被激发的几率要远远大于高激发态被激发的几率;激发态越高,大角散射的几率越大.③尾部效应仅在低激发态中产生,高激发态不产生尾部效应.     

基于改进变分法对原子激发态精确波函数的研究

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.     

碱金属原子多极极化率的解析计算及其应用

通过考虑碱金属原子中的价电子在模型势中的运动, 给出了碱金属原子激发态(包括分立谱和连续谱)的波函数, 导出了碱金属原子的多极动态极化率的计算式中所涉及的矩阵元的解析表达式, 实现了碱金属原子多极动态极化率的解析计算. 作为应用, 利用范德瓦尔斯相互作用系数与动态极化率之间的积分关系, 计算了异核基态碱金属原子间的三体相互作用系数, 将计算结果与此前用稳定变分方法得到的结果进行了比较, 结果显示两者是一致的. 此工作为后续研究激发态碱金属原子间的相互作用奠定了基础.     

类Ne铜离子双电子复合过程辐射跃迁几率的MCDF计算

在组态相互作用的ｊ－ｊ耦合下，用相对论多组态Ｄｉｒａｃ－Ｆｏｃｋ（ＭＣＤＦ）方法计算类Ｎｅ铜离子（２９Ｃｕ１９＋）双电子复合过程的辐射跃迁几率。在计算中涉及了大量的双激发态的和单激发态的相对论组态函数，得出了所有可能的跃迁几率，精选得出最可能的跃迁结果。文中所使用的相对论ＭＣＤＦ方法克服了其他方法诸如在相对论效应、组态相互作用等方面的缺陷，从而获得了很好的结果。所得的结果可用于进一步计算类Ｎｅ铜离子的双电子复合系数     

原子-振子散射振转激发跃迁几率的理论计算

在相互作用表象中,利用角动量耦合理论,导出了原子-振子散射的含时量子计算公式,并计算了He-H₂体系的振转激发态-态跃迁几率和分散射截面。结果表明:(1)相互作用表象波函数在坐标空间中具有较高的定域性,随时间演化几乎不变形,因此在计算散射量时具有很高的精度,与标准的密耦合(CC)法的计算结果符合很好;(2)增加的振动部分对计算时间的影响取决于对一势能矩阵的积分,而在该积分中仅含基态的计算就能给出较为理想的散射截面,与CC法相比节省近一倍的计算时间。 关键词：     

快速傅立叶变换微磁学方法

提出了一种具有快速傅立叶变换的微磁学(FFTM)方法,并应用于二维纳米磁性系统.计算结果表明,利用该方法得到的结果与采用截短相互作用距离直接求和计算偶极相互作用能的方法得到的结果基本一致,同时其计算精度和计算速度得到很大的改善.结果证明FFTM方法能快速有效地计算包含远距离偶极相互作用的磁性系统的磁特性.     

类He双激发态3Pe和3De的能量、精细结构与跃迁率

本工作采用组态相互作用波函数计算了He和Be2+离子高位双激发态3Pe和3De的能量和精细结构,并计算相对论修正、质量极化、振子强度和跃迁率.我们采用新量子数集K、T、A分析双激发态里德伯系列的变化规则,计算结果与试验结果符合很好.     

类He双激发态3p^e和^3D^e的能量、精细结构与跃迁率

本工作采用组态相互作用波函数计算了He和Be^2 离子高位双激发态^3P^e和^D^e的能量和精细结构，并计算相对论修正、质量极化、振子强度和跃迁率。我们采用新量子数集K、T、A分析双激发态里德伯系列的变化规则，计算结果与试验结果符合很好。     

The single-determinant approximation with a local potential for excited states

The specific features of the calculations of the electronic structure in the approximation of a local exchange potential that is identical for all the electrons involved are considered. An optimized effective potential method is proposed for calculating the energies of excited electronic states of the same symmetry. A single-particle Schrö dinger equation is derived for an excited state whose orbitals are described by a single-determinant wave function orthogonal to the ground state. The equations determining the local potential for excited states are obtained within the variational approach. The solution to these equations is analyzed in the framework of the parameterized representation of the effective potential. The efficiency of the proposed method is demonstrated by calculating the energies of three excited states of the same symmetry for a HeH molecule. The difference between the results obtained by the Hartree-Fock method and the method proposed in this paper is equal, on average, to 0.05%. A comparison with the results obtained from precise calculations based on the configuration interaction method shows that the accuracy in determining the energy of the excited states by the optimized effective potential method is comparable to the accuracy in calculating the energy of the ground state.     

A priori calculations of hyperfine interactions in highly ionized atoms: g-factor measurements on aligned pico-second states populated in nuclear reactions

Calculations of hyperfine interaction strength and life-times of states in highly ionized atoms, using the GRASP atomic structure package, are reported. The calculations aim at providing calibration for Recoil-in-Vacuum nuclear excited state g-factor measurements. The method is outlined and results compared with experiment. Inclusion of decay of higher electronic states is discussed.     

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Using the fully relativistic configuration interaction (RCI) method and the multi-configuration Dirac-Fock (MCDF) method and taking quantum electrodynamical (QED) effect and Breit correction into account, wavelengths, transition probabilities and oscillator strengths were calculated for electric dipole (E1) transitions and magnetic dipole (M1) transitions in Au⁵⁰⁺ ion. The obtained energy levels of some excited states and wavelengths of transitions in Au⁵⁰⁺ ion from the method were compared with other theoretical and experimental results, and a good agreement with other results was shown. The calculated transition probabilities and oscillator strengths in E1 transitions using the velocity and length gauges respectively confirmed the accuracy of our calculations. The calculation results indicated that for high-Z highly ionized atom, some forbidden transitions could be very important.     

Nuclear polarization in muonic atoms of deformed nuclei

The treatment of nuclear polarization correction in muonic atoms belonging to deformed nuclei is analyzed. The geometrical factors involved are expanded into a series of multipoles and the exact expansion coefficients are calculated. It is shown that, using reasonable assumptions about the nuclear spectrum, the nuclear polarization correction may be expressed as a shift of all hyperfine components plus a renormalization of the even multipole hyperfine interaction constants. All nuclear excited states contribute to the shift, but the ground-state rotational band gives an over-whelming contribution to the multipole moment renormalization. The effect of the ground-state band is analyzed in detail. The radial coefficients are calculated and an approximate formula, applicable over a broad range of atomic numbers and deformations, is obtained. By comparing our results with exact calculations we conclude that this part of the nuclear polarization correction may be calculated with accuracy better than 10 %.     

Local forces and the 16O reaction matrix

It is demonstrated that the G-matrix elements obtained from a solution of the Bethe-Goldstone equation for finite nuclei and a given NN interaction can be very well approximated by an effective local interaction. The local approximation is determined from the reaction matrix in nuclear matter using the same realistic NN interaction. The comparison is performed on the level of RPA calculations for the excited states in ¹⁶O. Very good agreement is found between the results for both interactions except for scalar-isoscalar states. It is shown that this is due to the energy dependence of the reaction matrix and can be cured rather easily. A comparison with experiment for isovector states is very satisfactory.     

The use of the CNDO method in spectroscopy : Naphthalene and the breakdown of the pairing theorems

It is shown that CNDO/S calculations provide 6 significant figures of accuracy in the energies of configurations, and 4 significant figures after configuration interaction. The pairing theorem is shown not to hold in the CNDO/S method since all F_μν are calculated and since the F_μμ are not constant. It is further shown that the degeneracies required by the pairing theorem are not even approximated in naphthalene. Finally, using absorption and emission spectroscopic measurements, including triplet-triplet and excited singlet-singlet absorptions, the spectroscopic states of naphthalene are discussed in detail.     

A CASCI-MRMP method based on Kohn—Sham orbitals

Kohn-Sham orbitals are used in the previously proposed CASCI-MRMP scheme (a multi-reference M?ller-Plesset (MRMP) method with a complete active space configuration interaction (CASCI) reference function). That is, the CASCI wave function was constructed using the Kohn-Sham orbitals and used as a reference function of the MRMP to incorporate the remaining dynamical correlation. The scheme was applied to the potential curves of the ground and low-lying excited states of N₂, the potential curve of the ground state of CO, the barrier height of the H₂CO → H₂ + CO reaction, the valence π-π? and Rydberg excited states of benzene, and the low-lying excited states of ozone. Good agreement between the theory, experiment, and some benchmark calculations was obtained. The various orbitals which are investigated here do not give very different results. Rather, the choice of active space makes a considerable difference, and in particular the perturbation calculation is proved to be very important.     

Shape mixing as an approximation to shell model24Ne

Band mixing calculations have been done for²⁴Ne including the two degenerate prolate and oblate Hartree-Fock states and also some particle-hole excited states in the projection formalism using an interaction obtained by Preedom and Wildenthal. The energy spectrum agrees very well with the experimental results as well as the exact shell model calculations. Thus the band mixing calculations provide a good approximation to the lengthy exact shell-model calcuations. In addition they offer a physical insight into the collective nature of the nucleus as nuclear states are described in terms of only a few ‘intrinsic’ states.