Recombination of U89+ ions with free electrons at the ESR

After an extended upgrading period at the Experimental Storage Ring (ESR) of the GSI in Darmstadt, an experiment on recombination of lithium-like uranium has been carried out. A 107.1 MeV/u U⁸⁹⁺ beam with up to 500 μA effective current was stored and cooled. In addition to measurements of radiative recombination (RR) and dielectronic recombination (DR) with high energy resolution in the range of 0–90 eV, the diagnostic properties of DR have been utilized to characterize the new cooler setup. Preliminary experimental results for the 1s²2p_3/25ℓj(j=3/2,5/2) resonance manifolds are presented and compared with theoretical predictions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Calculation of the binding energy of a highly excited electron in heavy Be-like ions

The binding energy of a highly excited electron (n=20–50, where n is the principal quantum number) in the Be-like ions Au⁷⁵⁺, Pb⁷⁸⁺, Bi⁷⁹⁺, and U⁸⁸⁺ is calculated in order to determine the energy of the 2p _1/2-2s transition from experiments on dielectronic recombination in Li-like ions. A formula approximating the calculated data with an error not exceeding 0.04% is proposed.     

Dielectronic recombination rate coefficients for the Ni ${\sf I}$ isoelectronic sequence

Ab initio calculations of the total dielectronic recombination (DR) rate coefficients for thirteen ions along the NiI isoelectronic sequence in the ground state (Kr⁸⁺, Mo¹⁴⁺, Ag¹⁹⁺, Sn²²⁺, Xe²⁶⁺, Nd³²⁺, Gd³⁶⁺, Yb⁴²⁺, W⁴⁶⁺, Au⁵¹⁺, Pb⁵⁴⁺, At⁵⁷⁺, and U⁶⁴⁺) have been performed using the flexible atomic code. The level-by-level calculations are performed for evaluating the DR contributions through the relevant Cu-like autoionizing inner-shell excited 3l¹⁷4l^′n^′′l^′′ and 3l¹⁷5l^′n^′′l^′′ configuration complexes with n^′′ ≤15, which are associated with Δn=1 and Δn=2 core-excitations, respectively. The usual (n^′′)^-3 scaling law is found to be invalid for low-Z ions. A level-by-level extrapolation procedure is employed to obtain the contributions through higher n^′′ complexes. The decays to autoionizing levels followed possibly by radiative cascades could enlarge the rates at relatively high temperature by a factor up to about 23%. For the whole isoelectronic ions the contributions from 3s²3p⁶3d⁹ 4l^′n^′′l^′′ dominate the total DR rates while the contributions from the 3s²3p⁶3d⁹ 5l^′n^′′l^′′ configuration complexes are about 10-20% at relatively high temperature. On the basis of the calculated results, a general analytic formula for the total DR rate coefficients of all the ions with 36≤Z ≤92 along the NiI isoelectronic sequence is constructed. The comparisons of the rates obtained from the general formula with those from the detailed calculations show that the formula is of high precision, generally better than 3% accuracy for electron temperatures kT≥0.1E_I, where E_I is the ionization energy of the Cu-like ion. The present DR rates at temperature above 1.0E_I are larger than the previously published data by a factor above 30%. The commonly used semiempirical formula proposed by Burgess and modified by Merts may overestimate the rates at high temperature by a factor of about 2 for low-Z ions.     

Quadratic spherical bessel functions and the inverse scattering problem

In the course of inverting the partial-wave Born approximation, a new expression for the inverse function ofj _l ² (ρ) was obtained. Using this result, one can also derive two expressions involving the binomial coefficients. Finally, a particular differential operator whose effect onj _l ² (ρ) was previously investigated by Mavromatis and Jalal is shown to have similar effects onn _l ² (ρ) andn _l (ρ)j _l (ρ).     

Autoionization cross section of lithium atoms excited by electron impact

We measure the full autoionization cross section of lithium atoms excited by electrons in the energy range from the first autoionization threshold at 56.39 to 600 eV. Data are obtained by determining the total intensity of electron spectrum of autoionization states 1sn ₁ l ₁ n ₂ l ₂ detected at the “magic” observation angle of 54.7°. The cross section behavior is characterized by a sharp increase to a maximum value of 1.7 × 10⁻¹⁸ cm² in the energy interval of 56.4–60 eV and a subsequent monotonic drop to a value of 10⁻¹⁸ cm² at 600 eV. We have discovered a “thin” cross section structure that reflects the presence of strong resonances of Li⁻ ions in the near-threshold area of excitation of the lowest energy autoionization states (1s2s2)2S, (1s2s2p)⁴ P, 1s(2s2p ³ P)² P), and 1s(2s2p ¹ P)² P. We have established that the contribution of autoionization to the absolute cross section of single ionization of lithium atoms does not exceed 4%. We perform a comparative analysis of the data with analogous data for potassium and cesium atoms.     

A Derivative Formula for the Free Energy Function

We consider bond percolation on the Z ^d lattice. Let M _n be the number of open clusters in B(n)=[−n,n] ^d . It is well known that E _p M _n /(2n+1) ^d converges to the free energy function κ(p) at the zero field. In this paper, we show that s²_p(M_n)/(2n+1)^d\sigma^{2}_{p}(M_{n})/(2n+1)^{d} converges to −p(1−p)κ′(p).     

Recombination measurements at low energies with Au49+,50+,51+ at the TSR

Recombination of Au⁴⁹⁺, Au⁵⁰⁺, and Au⁵¹⁺ ions has been studied at the TSR. With Au⁵⁰⁺ ions a storage lifetime of only 2 to 4 s was observed with the magnetically expanded electron beam of the cooler at a density of n_e = 10⁷ cm^-3. This short storage time is a consequence of the highest recombination rate coefficient ever observed with an atomic ion (1.8·10^-6 cm³ s^-1 at zero relative energy E_rel = 0 between electrons and ions). At about 30 meV a huge dielectronic recombination resonance is found with a record small width of only about 15 meV. Such resonances fortuitously occurring near E_rel=0 are probably the main reason for the enhanced recombination rates observed with Au⁵⁰⁺, with Pb⁵³⁺ (in a recent experiment at LEAR) as well as with other complex ions. For Au⁴⁹⁺ and Au⁵¹⁺ the recombination rates are smaller by an order of magnitude. This revised version was published online in August 2006 with corrections to the Cover Date.     

DFT study on size-dependent geometries, stabilities, and electronic properties of AunM2 (M = Si, P; n = 1–8) clusters

The ab initio method based on density functional theory at the PW91PW91 level has been employed to systematically study the structures, stabilities, electronic, and magnetic properties of gold clusters with or without silicon/phosphorus doping. The optimized geometries show that the most stable isomers for Au _n Si₂ and Au _n P₂ (n = 1–8) clusters prefer a three-dimensional structure when n = 2 and n = 3 upwards, respectively, and they can be viewed as grown from the already observed Au _n−1M₂ (M = Si, P). The relative stabilities of calculated Au _n M₂ (M = Si, P) clusters have been analyzed through the atomic average binding energy, fragmentation energy, second-order difference of energy, and HOMO-LUMO gap. A pronounced odd-even alternative phenomenon indicates that the clusters with even-numbered valence electrons possess a higher stability than their neighboring ones. For both systems, natural population analysis reveals that electronic properties of dopant atoms in the corresponding configuration are mainly related to s and p states. We also investigated magnetic effects of clusters as a function of cluster size, however, their oscillatory magnetic moments were found to vary inversely to the fragmentation energy, second-order difference of energy, and HOMO-LUMO gap.     

Mechanism and kinetics of the diffusion of gold in silicon

The diffusion of Au in Si is known to take place via the interchange of Au atoms between substitutional (Au _s ) and interstitial (Au _i ) sites. So far it has generally been believed that this interchange involves lattice vacancies (V) and that it occurs via the Frank-Turnbull mechanism V+Au _i ⇆Au _s . It is stated in the literature that this model explains the observation that the Au _s concentrationC _s ^m in the centre of Au-diffused Si wafers increases with timet according to . We show that this statement is incorrect, i.e., the Frank-Turnbull model cannot account for the law. Such a dependence is expected in the case of Si wafers with a sufficiently low density of internal sinks for self-interstitials if the Au _i −Au _s interchange is controlled by the so-called kick-out mechanism Au _i ⇆Au _s +1. Since this mechanism involves self-interstitials (I) the present result is in accordance with the fact that under high-temperature equilibrium conditions the dominating intrinsic point defects in Si are self-interstitials and not vacancies as in Ge or metals.     

Observation of Δn=1 dielectronic recombination resonances of boronlike argon

We report here an observation ofn=1 dielectronic recombination resonances of boron-like argon in the energy region 140–195 eV. With the cooler's electron beam as a target, a resolution of approximately 0.6 eV FWHM was obtained in the observed energy range. The energies of the doubly excited states were estimated with a Hartree-Fock calculation, which indicates that the observed resonances are from Ar¹³⁺(1s²2s²2p) to Ar¹²⁺(1s²2s²3l3l) and Ar¹²⁺(1s²2s2p3l3l) transitions.     

Resonances in Muon Transfer from Muonic Hydrogen to Oxygen and Neon

The influence of resonances on the muon transfer processes from muonic hydrogen to oxygen and neon (pμ)_1s + O⁸⁺ → p + (μO)_nl⁷⁺ and (pμ)_1s + Ne¹⁰⁺ → p + (μNe)_nl⁹⁺ is considered using the Smith lifetime matrix formalism. It is shown that the existence of a long lived resonance in the case of Ne induces a stronger dependence on collision energy of the muon transfer cross-section for this system. Present address: Chemistry Department, Vancouver University, Vancouver, BC V6T 1Z3, Canada     

Near-IR laser inelastic electronic light scattering spectroscopy on transitions between ground and excited states of acceptor centers in GaAs and InP crystals

We report the development of a method for recording the low-temperature (T=6 K) near-IR inelastic light scattering spectra and the observation of electronic scattering on the transitions 1s _3/2(Γ₈) → 2s _3/2(Γ₈) between the ground and excited states of different shallow acceptor centers in a n-type semi-insulating crystal si-GaAs (n=1.0 × 10⁸ cm⁻³) and in a doped p-InP crystal (p=3.6×10¹⁷ cm⁻³). Moreover, a new line, associated with the transition 1s _3/2(Γ ₈) → 2p _3/2(Γ₈) and due to a dielectric local mode, recorded for the first time in the spectra of narrow-gap semiconductors, was found in the residual-frequency band in the p-InP spectrum between TO(Γ) and LO (Γ) phonons. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 334–339 (10 March 1998)     

Detection of trielectronic recombination of In<Superscript>+</Superscript> ion

The trielectronic recombination of an In⁺ (4d ¹⁰5s ^{2 1} S ₀) ion in collisions with slow electrons, including the two-electron excitation of the 5s2 core of the ion with the simultaneous capture of the triply excited 5p ³ intermediate autoionizing state with its subsequent radiative stabilization 5p ³ → 5s5p ² + hν has been detected and experimentally examined for the first time. The maximum effective cross section of trielectronic recombination is 1.6 × 10⁻¹⁶ cm², which is comparable to the effective cross sections for both dielectronic recombination and electron excitation of the In⁺ ion.     

Time-and-energy resolved measurement of the cascaded Auger decay in krypton

The cascaded Auger decay following ionization or excitation with 94 eV soft-X-ray pulses from the 3d subshell in krypton has been energy-and-time-resolved for the first time. The decay time of the 4s ⁻¹4p ⁻² nl → 4p ⁻³ + e and/or 4s ⁻¹4p ⁻¹ nl → 4p ⁻² + e transition is measured to be 74 ± 20 fs. Furthermore, our data shows that the electrons with a kinetic energy around 25 eV (generally assigned as 3d ⁻¹ np → 4s ⁻² n′p + e) emitted after core excitation are emitted in a second decay step suggesting an alternative assignment of the form 4s ⁻² np 4p ⁻² + e.     

Some perturbation calculations for 1s2p, 1s 22p,and 1s 22s

The Dalgarno interchange theorem is used, together with the U function approach, to evaluate the first order perturbation corrections to <r ₁ ^-1+r ₂ ^-1> and <r ₁ + r ₂> for the two-electron states 1s2p ¹ P and 1s2p ³ P. The results for <r ₁ + r ₂> are extended by using a screening approximation, and are compared with the results of accurate variational calculations. The first order perturbation correction to spin-weighted expectation values of type <ΣV(r_j )s_zj > is given for the three-electron states 1s ²2p ² P and 1s ²2s ² S. The case V(r_j ) = r _j ^-1 is treated in detail.     

Photoionization of the ground1 S e and twenty lowest excited states of the Ne-like Fe16+

TheR-matrix method is used to calculate cross-sections for the photoionization of Ne-like Fe¹⁶⁺ from ground 2s ²2p ⁶¹ S ^e and excited states belonging to 2s2p ⁶ 3l and 2s ²2p ⁵ 3l configurations. Configuration interaction wavefunctions are used to represent two target states of Fe¹⁷⁺ ion retained in theR-matrix expansion. The cross-sections are obtained as a function of kinetic energy (ε _k) of the ejected electron from 10 to 24 Ry. For low kinetic energy the cross-sections show series of Rydberg states which converge onto² S ^e threshold Fe¹⁷⁺. The calculations are carried out in the LS coupling.     

高离化态金离子的辐射复合及其退激发过程的理论研究

利用基于多组态Dirac-Fock方法的程序包GRASP92和RATIP以及最新发展的RERR06程序,详细计算了高离化态金离子(类镍Au51+、类铜Au50+和类锌Au49+)俘获一个自由电子到nl(n=4—8,l=0—3)壳层的辐射复合谱以及相应的辐射退激发谱.理论计算的辐射复合谱很好地重现了实验谱.研究结果表明:对类镍Au51+、类铜Au50+和类锌Au49+而言,将一个自由电子俘获到n=4壳层的概率最大;在辐射复合过程之后,处在n=4壳层的俘获电子的辐射退激发谱线最强,并且体现了整个辐射退激发谱的主要特征.     

Enhancement of Dielectronic Recombination by External Electromagnetic Fields

The enhancement of the dielectronic recombination rate of lithiumlike Ne⁷⁺ and O⁵⁺ ions by external electromagnetic fields has been measured at the storage ring CRYRING. The energy range covered all 1s ²2pnl dielectronic recombination resonances attached to the 2s→2p core excitation. Electric fields up to 1436 V/cm were applied in the Ne⁷⁺ experiment and the saturation of the enhancement with increasing electric field could clearly be seen. In the O⁵⁺ experiment the enhancement was studied as a function of the Rydberg quantum number n.

     

类氖等电子系列离子基态的双电子复合速率系数研究

使用全相对论组态相互作用方法, 能级-能级细致计算了0.1 E_I ≤ kT_e≤ 10 E_I (E_I是类钠离子基态的第一电离能) 温度范围内类氖离子基态双电子复合(DR)速率系数, 双激发自电离能级考虑了(2s2p)⁷3ln'l', (2s2p)⁷4l4l' 以及(2s2p)⁷4l5l'组态. 对于(2s2p)⁷3ln'l'双激发自电离组态, 轨道角量子数l' >8 的(2s2p)⁷3ln'l'双激发自电离态对双电子复合速率系数的贡献可以忽略不计; (2s2p)⁷3ln'l'双激发自电离组态的高里德堡态对双电子复合速率系数的贡献满足 n'^-3组态-组态外推法, 并且核电荷数越大, 趋于n'^-3标度的n'值越小; 对细致能级计算得到的类氖离子基态的总DR速率系数进行了拟合, 得到类氖离子基态的总DR速率系数随核电荷数 Z和电子温度变化的经验公式, 该拟合公式与细致计算结果的偏差在2%以内, 能较准确的计算任意核电荷数Z的类氖离子在0.1E_I ≤ kT_e ≤ 10E_I电子温度范围的DR速率系数. Burgess-Merts(BM)近似公式不适用于估算低温(kT_e<0.3 E_I)类氖离子的DR速率系数, 在高温(kT_e>2E_I)时, 类氖离子的DR速率系数可以用BM近似公式表示.