Three-Parameter Wave Functions for ns2-Orbitals in Alkali—Metal Negative Ions

A three-parameter variational wave function is used to describe the binding energy of alkali—metal negative ions using a two-electron system in the ns²-state. Each electron is described by a modified screened hydrogenic wave function involving two free screening parameters denoted by c and a in addition to the core-screened nuclear charge, . The model is applied to lithium, sodium, potassium, rubidium, and cesium anions, where the optimum values of the variational parameters are deduced through fitting the optimized energy to the available experimental values. It is also applied to group-II isoelectronic neutral atoms of Be, Mg, Ca, Sr, and Ba. The results of our calculation are compared with other two-electron methods.     

Debye屏蔽自洽势下Au50+离子的能级与振子强度

以惯性约束聚变实验中感兴趣的金的类铜离子(Au⁵⁰⁺)为例，讨论了等离子体中自由电子对复杂原子中电子行为的影响.采用受Debye屏蔽的Hartree-Fock-Slater自洽势，计算了Au⁵⁰⁺离子的主量子数n从1到7的28个本征态，得到了对应于一系列Debye长度Λ的能量本征值E_nl，即轨道束缚能，和能级之间的光学振子强度.与类氢情况相似：自由电子的屏蔽作用使所有能级均从无屏蔽时的位置向连续态移动，即电离限下移；对于每个能量本征态(n, 关键词：     

Atoms with vacancies

Methods of orthogonalization of the wave function for an atom with vacancies in the s shell and the energetically lower state for ns(n + 1)s²-type configurations are considered. Non-orthogonal radial orbitals are used. An equation is obtained for the overlap integral for atomic wave functions in terms of single-electron radial orbitals. The parameters of the generalized hydrogenic analytic variational radial orbitals and the energies of F, Ne⁺, and Na²⁺ in the configuration 1s2s²2p⁶ are determined. Results are compared to calculations from other authors and experimental values, demonstrating that the approximation is good for calculating atoms with vacancies.     

Binding energy of a screened donor in a spherical quantum dot with a parabolic potential

A wavefunction is proposed for calculating the ground-state energy of a screened donor in a spherical quantum dot under a parabolic potential by a variational method. The donor is taken to be at the center of the quantum dot. Results are presented for four values of the screening parameter by the proposed wavefunction as well as for the hydrogenic donor case by a wavefunction used by Xiao et al.. To assess the accuracy of the results, ‘exact’ energies are also obtained by numerical integration of the Schrödinger equation. It is shown that the proposed wavefunction gives very good results in all cases including the hydrogenic donor case.     

New screening coefficients for the hydrogenic ion model including l-splitting for fast calculations of atomic structure in plasmas

New screening coefficients are given for calculating the energy levels of many-electron atoms in the hydrogenic ion approximation including l-splitting. This model allows fast computation of various atomic parameters (one-electron energies, ionization potentials, etc.) for all ionization stages of any element with no restriction concerning the maximum nl subshell. Part of the screening coefficients have been obtained from numerical fits over a large data base containing ionization potentials and excitation energies of ions. The others have been extrapolated by means of regularities deduced from the adjustment procedure. The mean and root mean square errors are better than 5% and 16.2%, respectively, for the 15 636 data considered. Some properties of the new screened hydrogenic model are studied, such as the filling competitions between several subshells of the lanthanides. The meaning of one-electron energies available from the total ion energy is discussed and the status of the self-screening term in plasmas in local thermodynamic equilibrium is briefly addressed. These notions are of great importance for coherence between the statistical treatment of such media and the calculation of their spectral properties.     

Doubly-Excited 1,3 P o States of H− Interacting with Screened Coulomb (Yukawa) Potentials

We have investigated the doubly excited 2s2p ³ P ^o and 2s3p ¹ P ^o resonance states of H⁻ embedded in a model plasma environment. Plasma effects are taken care of by using a screened Coulomb (Yukawa-type) potential. Correlated wave functions are used to represent the correlation effect between the charged particles. The density of resonance states has been calculated using the stabilization method. The calculated resonance energies and widths for various screening parameters are reported.     

Donor electron in a quantum well under the influence of an electric field

The ionization energies and the polarizabilities of a donor in an isolated well of a quasi two dimensional (Q2D) GaAs/Ga_1−x Al _x As heterostructure have been obtained for different well widths including electron-lattice coupling. A wave function that properly reduces to the hydrogenic function in the limiting case has been used. For fields of the order of 10⁵ V/m, the ionization energies decrease slightly with electric fields for all well widths (10 nm to 50 nm) studied. Also for a given electric field, as the well width increases, the ionization energy decreases. For fields of the order of 10⁷ V/m and for smaller well widths (<10 nm), the ionization energy generally increases with electric field. The results also show that for electric fields of this order, no donor bound state associated with the lowest subband is possible for well widths greater than 20 nm. The polarizabilities estimated using the expression for the dipole operator show that as the well width increases, the polarizability values also increase and do not show any abnormal behaviour.     

低能电子碰撞He+(e,2e)反应绝对三重微分截面的理论研究

利用Berakdar和Briggs对BBK波函数Sommerfeld参数的修正结果，即考虑第三个粒子存在对两个粒子间相互作用的影响，考虑了入射道的库仑相互作用及出射粒子的交换对称性，计算了在共面等能分配几何情况下低能电子碰撞He⁺(e,2e)反应绝对三重微分截面.结果表明，入射道库仑场对较低的入射能量及小的碰撞参数的三重微分截面影响较大. 关键词：     

An analysis of the effect of nitrogen and a screened (by free carriers) Coulomb field on the binding energy of hydrogenic shallow donors in GaInAsN

The effect of nitrogen concentration on the screening with free carriers and binding energy of hydrogenic shallow donors in GaInAsN alloys is investigated. The binding energy is calculated using a novel algebraic model which was proposed recently by Gönül et al. (2006) [16], in order to find an analytical solution to the screened Coulomb potential. The results show that the nitrogen concentration is a strong factor in producing a screening field of free carriers and in affecting the binding energy of hydrogenic shallow donors.     

Relativistic correction to the dipole polarizability of a hydrogenic ion

The first relativistic correction of orderα ² to the dipole polarizability of a hydrogenic ion has been investigated by using mean excitation energy of the ion within the second-order perturbation theory. The density-dependent mean excitation energy is estimated via Bethe theory for the stopping cross section for a moving point charge interacting with the hydrogenic ion. In this approach only the unperturbed Dirac wavefunctions are required to evaluate the appropriate matrix elements. The first relativistic correction turns out to be − (13/12)(αZ)². This has the correct sign and is within 5% of the exact result which is −(28/27)(αZ)².     

Differential oscillator strengths and dipole polarizabilities for transitions of the helium sequence

The dipole radial integral for an initial discrete 1s state and a final continuum state has been calculated under the screened hydrogenic model. In this model, single-electron hydrogenic wave functions are employed and the initial and the final states are treated by two different effective-charge parameters. Numerical values of differential oscillator strengths for transitions from 1s 21S to the continuum for the helium sequence ions are obtained. Also calculated are the dipole polarizabilities, which are found to be in excellent agreement with the results of other authors.     

A screened hydrogenic model using analytical potentials

The screened hydrogenic model and analytical potentials are tools widely used for atomic calculation of dense plasma physics. In this paper, we present a simple method to obtain screened hydrogenic energy levels and wave functions from analytical potentials for ions. Atomic data obtained using this model are compared satisfactorily with results of similar models and of more sophisticated self-consistent codes.     

Binding energy of hydrogenic impurity in multi-quantum-dot structure

In this paper, we perform a theoretical study, using a variational method, of the binding energy of ground state for hydrogenic impurity in the multi-quantum-dot structure. It is found that the binding energy is not only as a function of the size of the system in the x–y plane, but also the barrier thickness and the width of a dot in the z direction. Especially, when the barrier thickness is equal to the width of a dot, there are two peaks in the behavior of the binding energy as a function of the barrier thickness. All these behaviors of the binding energy are determined by the competition between the localization effect of the wave function and the tunneling effect of the wave function due to an increase or decrease in the barrier thickness and the width of a dot. Moreover, we also investigate the behavior of binding energy with different impurity position.     

Theoretical study on behaviors of 1s22s-1s2np transition for Co24+ ion in the whole energy region

Non-relativistic energies of 1s²2s and 1s² np (n⩽9) states for Co²⁴⁺ ion are calculated by using the full-core plus correlation method. Our results of 1s²2s and 1s²2p states agree well with the high-precision results of Yan et al. Based on calculating the first-order corrections to the energy from relativistic and mass-polarization effects, we estimate the higher-order relativistic contribution and QED correction to the energy under a hydrogenic approximation. The transition energies, wavelengths and oscillator strengths for the 1s²2s−1s² np (n⩽9) transitions of this ion are calculated. The results agree with the experimental data available in literature satisfactorily. By combining with quantum defect theory, our theoretical predictions on the energy and oscillator strength of this ion are extrapolated to the whole energy region including continuous states.     

Properties of the Positronium Negative Ion Interacting with Exponential Cosine-Screened Coulomb Potentials

The positronium negative ion (Ps ⁻) in exponential cosine-screened Coulomb potentials (ECSCP) has been theoretically investigated. Using highly correlated wave functions with 525 terms we report binding energies, annihilation rates and several other parameters for various values of the screening parameter. Our reported results for the unscreened case are in nice agreement with some of the most accurate results in the literature. Further we make a comparative study of the properties of Ps ⁻ in ECSCP with the corresponding properties in screened Coulomb potential (SCP). To the best of our knowledge, such a study on Ps ⁻ in ECSCP is carried out for the first time in the literature.     

Exact polarizability of low-dimensional excitons

Wannier excitons polarized by a static electric field and confined to low-dimensional structures are studied. Effective non-integer dimensions are included by considering hydrogenic states in α-dimensional space, with α as a parameter. Exact expressions for lowest order energy and wave function corrections are obtained as a function of α. For the 1s state, we demonstrate that the exciton polarizability decreases with reduced dimensionality and eventually vanishes as (α−1)⁴ as the 1D limit is approached. The low-dimensional 2s and 2p polarizabilities are also decreased but remain finite in the 1D limit.     

Screening of the electron-hole interaction in quantum well structures

Recent optical non-linearities in GaAs/Ga_1?xAl_xAs quantum well structures have been attributed to the screening of the electron-hole interaction in such structures by the free carriers created. We here present the results of a variational calculation of the ground state energy of an electron-hole pair confined to move in two dimensions when screening of the Coulomb interaction between the electron-hole pair by the free carriers present is taken into account by using the screened potential obtained by Stern and Howard for hydrogenic impurities in semiconducting inversion layers. It is found that the binding energy of the 2D exciton decreases less rapidly with the screening parameter than is the case for a 3D exciton and that the 2D exciton remains bound even for large values of the screening parameter. This is in contrast to the case in bulk semiconductors where the electron-hole pair no longer bind into an exciton when the screening length of the free carriers becomes less than the Bohr radius of the exciton.     

Wavelength and oscillator strength of dipole transition 1s<Superscript>2</Superscript>2p—1s<Superscript>2</Superscript><Emphasis Type="Italic">n</Emphasis>d for Mn<Superscript>22+</Superscript> ion

The transition energies, wavelengths and dipole oscillator strengths of 1s²2p—1s² nd (3⩽n⩽9) for Mn²²⁺ ion are calculated. The fine structure splittings of 1s² nd (n</9) states for this ion are also evaluated. In calculating energy, the higher-order relativistic contribution is estimated under a hydrogenic approximation. The quantum defect of Rydberg series 1s² nd is determined according to the quantum defect theory. The results obtained in this paper excellently agree with the experimental data available in literatures. Supported by the National Natural Science Foundation of China (Grant No. 10774063)     

L-shell internal excitation accompanyingL-capture

TheL-shell internal excitation accompanyingL-capture has been treated relativistically by the use of hydrogenic wave functions. Numerical calculations for the nuclides³⁷Ar,⁵⁵Fe,⁷⁷Ge,¹³¹Cs,¹⁵⁷Tb,¹⁶⁵Er,¹⁷⁹Ta and¹⁹³Pt have been performed for the first-time. The present calculations show that doubleL _i-hole production probability decreases with increasing atomic number and it is almost independent of transition energy for a particular shell. Possible experiments to detect this phenomenon in atoms for whichK-K processes are energetically forbidden are discussed briefly.     

Negative muon capture in3He

We compute the partial capture rate of negative muons in³He by following the analysis of Peterson to include the relativistic corrections and the exchange effects, for various values of theg _p /g _A ratio. We also calculate the total capture rate. The ground state of³He is assumed to be spherical. The radial dependence of the ground state wave function is taken to be (a) one parameter Irving function, (b) a modified three-parameter Irving function and (c) a function having ‘soft-core’, whose parameters have been fixed in a variational calculation of the binding energy of the triton using a non-local momentum-dependent potential involvingp ² terms. The calculated values of the capture rates are compared with the experimental data to find a value for theg _p /g _A ratio.