Studies of the electron density at the nucleus and radial expectation values of the ground state for lithium-like systems from Z=11 to 18

The electron density at the nucleus ρ(0) and radial expectation values 〈rⁿ〉 (n=-2–10) of the ground state for lithium-like systems from Z=11 to 18 are calculated with the full core plus correlation wave functions. By using these obtained expectation values, accurate inequalities of radial expectation values derived by Gálvez and Porras [Phys. Rev. A 44, 144 (1991)] are examined and verified. The final results show that the full core plus correlation wave functions for lithium-like systems with higher nuclear charge are also accurate in the full configuration space and can give satisfactory electron density at the nucleus and radial expectation values.     

Charge density at the nucleus and radial behavior of ground state for lithium-like ions with Z = 21 to 30

By using the full-core plus correlation (FCPC) type wave functions, the accurate charge densities ρ(0) at the nucleus and the radial expectation values of the ground states for the lithium-like systems with Z = 21 to 30 are obtained. The determinantal conditions and the electron-nucleus cusp condition are used to calculate the inequalities of the upper and the lower bounds to ρ(0) with two or more expectation values. These inequalities, derived by Angulo and Dehesa [Phys. Rev. A 44 1516 (1991)], are verified to be also valid for these ions with higher nuclear charge. The present results show that the wave functions used in this paper are satisfactory in the whole configuration space for these ions with higher nuclear charge.     

类锂体系激发态的精确判据

利用Gálvez Porras关于原子体系电子在核处密度和径向期待值的精确不等式，分别建立了波函数的两套精确判据，它们是独立于能量判据之外的检验波函数精确度的判据. 以类锂体系激发态为研究对象，首先对1s2 3s态的电子在核处密度和径向期待值的上界进行了检查，然后对锂原子1s2 3s态在不同计算方法下由电子在核处密度上界定义的R6值和的上界定义的R4值分别进行了测试，同时还对锂原子双激发态的电子在核处密度和径向期待值的上界进行了检验. 研究表明这两套不等式都可作为原子体系各种能态波函数的精确判据. 关键词： 电子在核处密度 径向期待值 全实加关联 精确判据     

Energy and fine structure of the lithium isoelectronic sequence

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类锂体系激发态1s2 nd(n=3,4,5)精细结构和项能的理论计算

使用全实加关联(fullcorepluscorrelation缩写为FCPC)和里兹(Ritz)变分方法计算了类锂体系(Z=11—20)激发态1s2nd(n=3,4,5)的非相对论能量和波函数;包括动能修正、电子电子接触项、轨道轨道相互作用项以及Darwin项的相对论修正和质量极化项由全实加关联波函数的一阶微扰给出,量子电动力学(quantumelectronicdynamics缩写为QED)修正由有效核电荷方法和类氢公式计算;给出了高电离类锂体系激发态的激发能、精细结构和项能(termenergy),并 关键词： 类锂体系 全实加关联 精细结构 激发能     

The excitation energies and term energies of the excited states 1s2ns (n=3,4,5) and 1s2nf (n=4,5) of lithium-like systems of Z=11－20

In this paper, the full-core plus correlation (FCPC) and the Ritz method is extended to calculate the non-relativistic energies of 1s^2ns (n=3,4,5) and 1s^2nf (n=4,5) states and the wavefunctions of the lithium-like systems from Z=11－20. The mass-polarization and the relativistic correction including the kinetic-energy correction, the Darwin term, the electron－electron contact term, and the orbit－orbit interaction are evaluated perturbatively as the first-order correction. The contribution from quantum electrodynamic is also included by using the effective nuclear charge formula. The excited energies, the term-energy and fine structure, are given and compared with the other theoretical calculation and experimental results. It is shown that the correlative wave in the FCPC method embodies well the strong correlation between the 1s^2 core and the valence electron.     

On the accuracy of the wavefunctions calculated by LAPW method

The accuracy and the convergence properties of LAPW wavefunctions are studied using Be metal as an example. We show that radial part of thes-component of wavefunction inside the muffin-tin sphere differs substantially from the exact solution to the radial Schrodinger equation. We find that LAPW method underestimates the energy expectation value in the interstitial region. The inaccuracy of the well-converged wavefunctions occasionally produces significant errors in momentum matrix elements.     

V+20离子的能量和偶极振子强度

用全实加关联方法计算了类锂V+20离子 1s2nl(l=s,p, d;n≤9) 态的电离势和精细结构.依据单通道量子亏损理论, 确定了这三个Rydberg系列的量子数亏损.用这些作为能量的缓变函数的量子亏损,可以实现对任意高激发态(n≥10)的能量的可靠预言.用在计算能量过程中确定的波函数,计算了V+20离子1s22s-1s2np及1s22p-1s2nd (n≤9)跃迁的振子强度.将这些分立态振子强度与单通道量子亏损理论相结合,得到在电离域附近束缚态间的偶极跃迁振子强度以及束缚态-连续态跃迁的振子强度密度,从而将V+20离子的这一重要光谱特性的理论预言外推到整个能域.     

Quantum domain walls in the one-dimensional Ising model in a transverse field

Within the exactly soluble spin-$\text{1}\text{2}$ Ising chain in a transverse field, wavefunctions are identified which correspond to the domain wall-type solutions in the related classical model. For these wavefunctions the energy expectation values and longitudinal spin correlations are evaluated exactly. The results are used to comment on the relation between the quantum and classical domain walls.     

Relation between internal conversion coefficient and electron density at the nucleus for spin polarized Fe electrons

An ICC computation for the 14.4 keV transition in⁵⁷Fe has been made using relativistic wavefunctions derived from spin polarized UHF wave functions of atomic iron. It is shown that ICC and electron density at the nucleus are proportional for polarized s electrons as has been found already for unpolarized electrons.     

Energy and fine structure of 1s2np(n≤9) states for lithium-like systems from Z=11 to 20

A new variation method is extended to study the atomic systems with higher nuclear charges and in more highly excited states. The non-relativistic energies of 1s^2np (n≤9) states for the lithium-like systems from Z=11 to 20 are calculated using a full-core-plus-correlation method with multi-configuration interaction wavefunctions. Relativistic and mass-polarization effects on the energy are calculated as the first-order perturbation corrections. The fine structures are determined from the expectation values of spin-orbit and spin-other-orbit interaction operators in the Pauli－Breit approximation. The quantum-electrodynamics correction is also included. Our results are compared with experimental data in the literature.     

量子数n和l对束缚电子径向波函数的影响

利用Hartree-Fork平均自洽场理论,研究了主量子数n和角量子数l对束缚电子波函数影响的主要特征.原子实通常是致密、紧凑的,当n和l较大时价电子的行为将与相应的氢原子电子相似;在靠近核的原子实区域,原子实的影响使价电子径向波函数节点的位置几乎重合.在近核区域离心势可对电子产生很大影响:小l电子只能轻微地贯穿到原子实的较深区域,对大l电子离心势将阻止其深入到离核很近的原子实内;离化度较高时离心势的作用相对减弱,电子深入到原子实内的可能性较大.     

Mn22+离子1s22s-1s2np的偶极跃迁能和振子强度

用全实加关联方法计算了类锂Mn22 离子1s22s-1s2np(2≤n≤9)的偶极跃迁能和振子强度.1s2np(2≤n≤9)态的精细结构通过计算自旋-轨道与自旋-其他轨道相互作用算符的期待值确定.依据单通道量子亏损理论,确定了Rydberg系列1s2np的量子数亏损.从而可以用这些作为能量的缓变函数的量子亏损,实现对任意高激发态(n≥10)的能量的可靠预言.将这些分立态振子强度与单通道量子亏损理论相结合,得到在电离阈附近束缚态-束缚态跃迁振子强度以及束缚态-连续态跃迁的振子强度密度,从而将Mn22 离子的这一重要光谱特性的理论预言外推到整个能域.     

Exact formulas and phase-integral formulas,not involving wavefunctions,for expectation values pertaining to general potentials

An exact formula for quantal expectation values associated with bound states in a general potential is derived. The formula does not contain wavefunctions, but is expressed in terms of derivatives, with respect to an auxiliary parameter and with respect to the energy, of a function appearing in an exact quantization condition. Replacing the exact quantization condition by a phase-integral quantization condition (which in some cases may be exact as well), one obtains a useful formula for calculating quantal expectation values, without the use of wavefunctions, for any potential for which a phase-integral quantization condition is known. Explicit phase-integral formulas are given for the case of a single-well potential.     

类锂体系(Z=21—30)基态1s22s电离能和相对论项能的理论计算

使用全实加关联方法和里兹(Ritz)变分方法计算了类锂体系(Z=21—30)基态1s²2s的非相对论能量和波函数；包括动能修正、电子-电子接触项、轨道-轨道相互作用项以及Darwin项的相对论修正和质量极化项由全实加关联波函数的一阶微扰给出，量子电动力学修正QED(quantum electronic dynamic)由有效核电荷方法和类氢公式计算；给出了中等核电荷的高电离类锂体系基态的电离能、相对论效应的项能(term energy)，并将计算结果与实验数据进行了比较，表明FCPC 关键词： 类锂体系 全实加关联 电离能 项能     

类锂体系(Z=11～20) 1s~24s -1s~2np(5≤n≤9)跃迁能和振子强度的理论计算

利用全实加关联的方法计算类锂体系(Z=11～20) 1s~24s -1s~2np(5≤n≤9)的跃迁能, 将相对论效应(电子动能的相对论修正,Darwin项,电子-电子接触项以及轨道-轨道相互作用)和质量极化效应作为微扰,计算了它们对体系能量的修正.利用得到的波函数和跃迁能计算了核电荷Z=11~20的类锂离子的1s~24s -1s~2np(5≤n≤9)偶极跃迁的长度、速度和加速度三种规范下的振子强度,与现有的实验数据比较,结果符合得很好.     

Sc+18离子的跃迁能和振子强度

用全实加关联方法计算了Sc⁺¹⁸离子1s²2s--1s²np (2≤n≤9) 和1s²2p--1s²nd (3≤n ≤9)的跃迁能和振子强度。1s²np和1s²nd 态的精细结构劈裂通过计算自旋-轨道及自旋-其他轨道相互作用算符的期待值加以确定。还得到了这两个里德堡系列的量子亏损（作为能量的函数）。依据三种规范的振子强度公式得到的计算结果相当好的一致。将这些计算结果与量子亏损理论相结合，进一步得到电离阈附近的分立态-分立态跃迁的振子强度和分立态-连续态跃迁的振子强度密度。     

Rotational and vibration-rotational intensities of CS isotopes

Rotational and vibration-rotational intensities (dipole-moment matrix elements and Einstein A coefficients) have been calculated for the four most abundant isotopes of CS for the following sets of rotational and vibrational quantum numbers: J′ − J = ±1 for 0 ≤ J′ ≤ 200, and 0 ≤ v′ − v ≤ 4 for 0 ≤ v′ ≤ 20. The transition moments were calculated using both a series expansion and a Padé approximant representation for the dipole-moment function obtained from ab initio calculations and numerical vibration-rotational wavefunctions computed via a solution of the radial Schrödinger equation with accurate RKR potential-energy functions. Representative numerical results for bandhead positions and dipole-moment matrix elements of vibration-rotational transitions of ¹²C³²S are presented and compared with experimental and theoretical results of other workers. Explicit results are also given for a number of lines in the pure rotational band of CS that are of interest to radio astronomers.     

Oscillator strengths for 2 ^2P-n ^2D transitions of lithium-like systems with Z=11 to 20

The dipole-length, velocity and acceleration absorption oscillator strengths for the 1s^22p－1s^2nd(3≤n≤9) transitions of the lithium-like systems with Z=11 to 20 are calculated using the energies and the multiconfiguration interaction wavefunctions obtained from a full core plus correlation method. The agreement between the f-values calculated from the length, velocity and acceleration formulae is excellent. Our results agree closely with the experimental data available in the literature. Combining these discrete oscillator strengths with the single-channel quantum defect theory, the discrete oscillator strengths for the transitions from 1s^22p state to highly excited states (n≥10) and the oscillator strength densities corresponding to the bound-free transitions are obtained.