All-order transition amplitudes in many-electron atoms

All-order expressions for transition amplitudes are obtained from the exact re-summation of three-operator perturbation series. They are formulated in terms of continued fractions where the role played by the non-central part of the many-electron atom potential is shown explicitly.     

多电子原子能量的相对论修正

以Breit-Pauli哈密顿的球张量形式为基础,借助不可约张量理论,建立了计算多电子原子能量的相对论修正的一种解析理论形式,导出了多电子原子相对论修正项(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项和轨道-轨道相互作用项)在斯莱特表象中的矩阵元的解析表达式,完成了所有角向积分和自旋求和计算.利用所建立的理论,对类锂体系(1s)2(2p)2P态能量的相对论修正进行了具体计算.     

Relativistic theory of parity violation in many-electron atoms

We present a theoretical framework for the calculation of parity-mixing effects of the weak interaction in many-electron atoms which is based on first principles. The starting point is an external-field no-pair Hamiltonian H₊ which allows for a consistent treatment of effects coming from virtual electron-positron pairs and can be used as a basis for a systematic program of calculations. We show that the matrix element $\text{M}$ for parity-violating E1 transitions, given by quantum electrodynamics, gets an appreciable contribution $\text{M}$^pair from states involving an extra electron-positron pair. However on eliminating the velocity operator α in favor of the length operator iωr, we find cancellations which result in an accurate formula for $\text{M}$ involving only the positive-energy N-electron eigenstates of H₊ as intermediate states and the length form, iωr · ?, of the dipole operator. We discuss the implications of our results for calculations of amplitudes for parity-violating radiative E1 transitions in many-electron atoms. Our analysis includes a study of the effects coming from the weak electron-electron interaction as well as those arising from the weak electron-nucleus interaction.     

Relativistic polarization potential of a many-electron atom

An effective approximate calculation of the exchange-polarization second-order diagrams in the Rayleigh-Schrödinger perturbation theory with the use of the relativistic Thomas-Fermi approximation is described and used to obtain a new relativistic expression for the effective two-particle polarization interaction potential in a many-electron atom.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 5–9, January, 1990.     

Electron loss of heavy many-electron ions in relativistic collisions with neutral atoms

Electron-loss processes arising in collisions of heavy many-electron ions (like U²⁸⁺) with neutral atoms (H, N, Ar) are considered over a wide energy range including relativistic energies. Various computer codes (LOSS, LOSS-R, HERION, and RICODE), created for calculation of the electron-loss cross sections, and their capability are described. Recommended data on the electron-loss cross sections of U²⁸⁺ ions colliding with H, N, Ar targets and predicted lifetimes of U²⁸⁺ ion beams in accelerator are given. Calculated electronloss cross sections are compared with available experimental data and other calculations.     

Test of the many-electron theory of atoms in an exactly solvable model

The many-electron theory of ground states of Sinano?lu is tested on an exactly solvable model. The many electron theory wave functions and energies reproduce closely the exact solutions.     

New analytical independent-particle model potential for atoms

A new analytical, independent-particle model potential with four shell-independent parameters is proposed, which is suitable for high, medium, and low Z atoms. The four parameters are determined for 101 atoms from Li to Lr by fitting the results of the X _a method found in the literature. The average fitting error 0.675% of the new potential for the 101 atoms is far better than 3.92% of the widely used Green’s potential. The radial Schrödinger equation with the new potential is solved by using Numerov’s numerical method for 7 typical atoms: Ne, Ca, Zn, Zr, Sn, Yb, and Th. The energy eigenvalues, radial wave functions, and atomic ground-state energy are in good agreement with the results of the X _a method. The new potential here shows greater flexibility and better accuracy compared with the Green’s potential.     

四参数解析有效势在原子结构计算中的应用

在原子结构的计算中,势函数的选取对计算结果起着非常重要的作用.解析形式的势函数能极大的减小原子结构的计算量.本文提出了一种新的解析有效势,包含四个壳层独立的参数,参数的值通过拟合参数化优化有效势(POEP)方法的数值结果得到.运用该势函数对中性原子进行了计算,通过求解薛定谔方程,得到了电子轨道能和总能,并与Green和POEP方法的结果进行了比较.结果表明新的四参数有效势是一种简单性、适用性、准确性都很高的势函数.     

四参数解析有效势在原子结构计算中的应用

在原子结构的计算中,势函数的选取对计算结果起着非常重要的作用。解析形式的势函数能极大的减小原子结构的计算量。本文提出了一种新的解析有效势,包含四个壳层独立的参数,参数的值通过拟合参数化优化有效势(POEP)方法的数值结果得到。运用该势函数对中性原子进行了计算,通过求解薛定谔方程,得到了电子轨道能和总能,并与Green和POEP方法的结果进行了比较。结果表明新的四参数有效势是一种简单性、适用性、准确性都很高的势函数。     

Four-parameter analytical local model potential for atoms

Analytical local model potential for modeling the interaction in an atom reduces the computational effort in electronic structure calculations significantly. A new four-parameter analytical local model potential is proposed for atoms Li through Lr, and the values of four parameters are shell-independent and obtained by fitting the results of X_a method. At the same time, the energy eigenvalues, the radial wave functions and the total energies of electrons are obtained by solving the radial Schr?dinger equation with a new form of potential function by Numerov's numerical method. The results show that our new form of potential function is suitable for high, medium and low Z atoms. A comparison among the new potential function and other analytical potential functions shows the greater flexibility and greater accuracy of the present new potential function.     

Anisotropic potential energy functions for carbon atoms in graphite

Recent experimental studies of the scattering of He atomic beams by graphite have shown that the electronic anisotropy of the C atoms must be taken into account in calculating the interaction between a graphite lattice and an external He atom. The empirical compressibility of graphite is used to determine an appropriate value for the polarizability of graphite C atoms parallel to the graphite c axis, a parameter needed to calculate He-graphite interaction potentials.     

Parametrization of the hybrid potential for pairs of neutral atoms

The hybrid form is a combination of the Rydberg potential and the London inverse-sixth-power energy. It is accurate at all relevant distance scales and simple enough for use in all-atom simulations of biomolecules. One may compute the parameters of the hybrid potential for the ground state of a pair of neutral atoms from their internuclear separation, the depth and curvature of their potential at its minimum, and from their van der Waals coefficient of dispersion C₆.     

Correlated basis functions for the many-electron problem

The method of correlated basis functions is applied to the electron system in a metal. To overcome the twofold difficulty of large particle number and long-range Coulomb interaction in metals, a new optimal cluster decomposition for arbitrary correlated wave functions is derived. With this method, not only ground-state properties, but also thermal averages and response functions can be calculated from a given set of correlated basis functions. The appropriate synthesis of correlated wave functions including physically expected properties of subsystems as for instance partially filled inner shells in transition metals is discussed in detail.     

Large-scale semidefinite programming for many-electron quantum mechanics

The energy of a many-electron quantum system can be approximated by a constrained optimization of the two-electron reduced density matrix (2-RDM) that is solvable in polynomial time by semidefinite programming (SDP). Here we develop a SDP method for computing strongly correlated 2-RDMs that is 10-20 times faster than previous methods [D.?A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. We illustrate with (i) the dissociation of N(2) and (ii) the metal-to-insulator transition of H(50). For H(50) the SDP problem has 9.4×10(6) variables. This advance also expands the feasibility of large-scale applications in quantum information, control, statistics, and economics.