NMR studies of singlet-ground-state rare-earth ions in high-T c superconductors

Many of presently known high-T _c superconductors contain rare-earth (RE) ions with an even number of electrons in an unfilled 4f-shell (Pr³⁺, Tb³⁺, Ho³⁺, Tm³⁺). If the ground state of 4f-electrons is non-degenerate and separated from excited states by high enough energy intervals, one can observe the so-called “enhanced NMR” of RE nuclei at low temperatures. In the present paper some aspects of the enhanced NMR are analyzed in applications to the crystal and electron structure of high-T _c superconductors.     

Recombination channels of molecular ions He 2 + and electrons

The dependence of the intensities of atomic lines and molecular bands emitted in the afterglow of a helium discharge on the electron temperature is used to identify the processes in which states of He and He ₂ ^* are populated. It is established that the formation of He^* atoms (n = 3, 4) in decaying helium plasma occurs principally on account of the associative recombination of vibrationally excited He ₂ ⁺ ions and electrons. Analysis of the experimental reuslts leads to the conclusion that the distribution of the molecular ions He ₂ ⁺ over vibrational states is strongly nonequilibrium.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 67–72, February, 1984.It remains to thank N. P. Penkin for discussions and for his interest in the work.     

Spectroscopic study of the production of magnesium ions from the atomic metastable states 3s3p 3 P 0, 2 by electron impact

Spectroscopic studies of the production of MgII ions from atomic metastable states by electron impact in crossed atomic and electron beams were made. Cross sections for excitation of the strongest spectral transitions and their energy dependences were determined. The maximum value of the cross section for ionization with excitation of the 3² S _1/2–3² P _3/2 transition reached 2.4×10^?16 cm². Possible mechanisms of production of excited ions from metastable states and their contribution to the total ionization process are discussed.     

Exchange interactions in polynuclear complexes

We present detailed optical and magneto-optical data on Cs₃Cr₂Cl₉ as a single crystal containing only pairs of Cr³⁺ ions. Measurements have been carried out in a wide range of temperatures down to pumped helium and in the whole spectral region covering all singly and several doubly excited states. MCD helped considerably in resolving the absorption spectra into their numerous components, and proved especially useful in demonstrating the occurrence of a double excitation to ⁴ T ₂. It provides also parallel g factors for several excited terms.

The main conclusions of our work are: (i) all transitions are electric dipole allowed; (ii) transitions to singly excited doublet states are essentially promoted via a single ion mechanism; (iii) vibronic interaction must be invoked to understand the absorption data on sharp lines; (iv) the trigonal plus spin-orbit interaction competes favourably with exchange interaction to produce excited states splittings.

We present also a new non-phenomenological model to describe the splitting of the ⁴ A ₂Θ² E manifold under the combined effects of exchange, trigonal and spin-orbit interaction. This model includes no adjustable parameter. It leads to λ₀ ～ 180 cm^-1 and offers a good starting basis for a coherent interpretation of most of our experimental data.     

Copper Defects and Conductivity in Bi—Pb—Sr—Ca—Cu—O Glasses

Glass ceramics of the composition (Bi_0.8Pb_0.2)₄Sr₃Ca₃Cu₄O₈ prepared by the melt quenching technique and the crystalline phases produced by the rapid thermal annealing have been studied by electrical resistivity and electron paramagnetic resonance (EPR) measurements in the temperature range from liquid helium up to room temperature. The concentration of the EPR active Cu^2? paramagnetic centers decreases as conductivity increases for the glass ceramics and disappears after crystallization and the growth of superconducting phases, similar to bulk high-T_c superconductors. The KPR spectra of both glass and crystallized ceramics after short-time annealing indicate the coexistence of Cu^2? paramagnetic ions and the exchange coupled clusters.     

Doubly excited 2s2p 1,3P1 resonances in photoionization of helium

The multi-configuration Dirac-Fock（MCDF） method is implemented to study doubly excited 2s2p ^1,3P₁ resonances of the helium atom and the interference between photoionization and photoexcitation autoionization processes.In order to reproduce the total photoionization sprectra,the excited energies from the ground 1s^{2 1}S₀ state to the doubly excited 2s2p ^1,3P₁ states and the relevant Auger decay rates and widths are calculated in detail.Furthermore,the interference profile determined by the so-called Fano parameters q and ρ² is also reproduced.Good agreement is found between the present results and other available theoretical and experimental results.This indeed shows a promising way to investigate the Fano resonances in photoionization of atoms within the MCDF scheme,although there are some discrepancies in the present calculations of the 2s2p ³P₁ state.     

Effect of electrons of the multiply charged ion core on single-electron capture

The population of various electronic states of particles that arise during the capture of a single electron in hydrogen and helium atoms, as well as hydrogen molecules, by Ar³⁺ and Ne³⁺ ions with an energy of several kiloelectronvolts was studied by collision spectroscopy, viz., precision analysis of kinetic energy variation for ions formed as a result of interaction between ions and atoms. It is shown that single-electron capture in many cases is a multielectron process accompanied by the rearrangement of a multiply charged ion core. It is found that the triply charged Ne³⁺ ions formed as a result of ionization of Ne atoms by electron impacts are formed mainly in metastable states. The population of excited states of particles during their multiple ionization should be taken into account in determining the characteristics of various particles by the appearance potential method. Collision spectroscopy can be used for analyzing the metastable ion impurities in ionic beams.     

Screened self-energy correction to the 2<Emphasis Type="Italic">p</Emphasis><Subscript>3/2</Subscript>-2<Emphasis Type="Italic">s</Emphasis> transition energy in Li-like ions

We present an ab initio calculation of the screened self-energy correction for 1s² 2p_3/2 and 1s² 2s states of Li-like ions with nuclear charge numbers in the range Z = 12?100. The evaluation is carried out to all orders in the nuclear strength parameter Zα. This investigation concludes our calculations of all two-electron QED corrections for the 2p_3/2-2s transition energy in Li-like ions and thus considerably improves theoretical predictions for this transition for high-Z ions.     

Ionization of hydrogen and helium atoms by highly charged fast ions in collisions with small momentum transfer

Ionization of hydrogen and helium atoms is studied for the case of “soft” collisions with highly charged fast ions with v≲Z≪v² and v≫v ₀, where Z is the ion charge, v is the collision velocity, and v ₀∼1 is the characteristic velocity of the electron in the ground state of the atom. Analytical expressions are derived for the singly and doubly differential cross section for ionization of a hydrogen atom accompanied by the ejection of a slow electron v _e≲v ₀, where v _e is the velocity of the ejected electron with respect to the recoil ion). The results are generalized to the case of single ionization of helium. It is shown that soft collisions provide the main contribution to the hydrogen ionization cross section and for all practical purposes determine the cross section for single ionization of helium. The asymmetry in the angular distribution of the ejected slow electrons and the properties of momentum exchange in such collisions are discussed. Finally, a formula for the cross section for single ionization of helium is proposed. Zh. éksp. Teor. Fiz. 112, 1966–1977 (December 1997)     

Kinetics of luminescence induced by sputtering metallic cadmium by a pulsed fast electron beam in helium

Results of an experimental study of the kinetics of luminescence observed when a metallic cadmium foil is bombarded in a helium medium by a 3-ns pulsed beam of 150-keV fast electrons are reported. The foil was irradiated at gas pressures from 76 to 2280 Torr. At a foil temperature of T = 240° C, the de-excitation time of the Beitler levels of the Cd II ion was measured as a function of the buffer gas pressure and the constant of collision quenching of the 5s22D_5/2 level of Cd II by He atoms was determined as k ≈ 3 × 10^-29 cm⁶/s. The experimental data were compared with calculations performed for the gas—vapor mixture in order to find the fraction of excited Cd II ions in the 5s²2D_5/2 state produced directly as a result of sputtering of metallic cadmium by high-energy electrons and by components of the helium plasma. At a helium buffer gas pressure of P ≤ 2.5 atm and a temperature of the cadmium target of T = 240° C, the value of this quantity was found to be α = 0.28 + 0.23P (where P is the helium pressure in atmospheres).     

Two-step excitation of Rb atoms on He nanodroplets

We present the first sequential laser excitation of atom-doped helium nanodroplets. Rubidium atoms on the surface of helium nanodroplets are selectively excited with a continuous wave laser to the 5²P_1/2 state so as not to desorb from the nanodroplets. From there they are excited by a laser pulse to the 5²D state; a laser-induced fluorescence (LIF) spectrum is recorded by monitoring the 6²P ?\rightarrow 5²S_1/2 emission. The LIF spectrum differs from that of the two-photon one-color direct excitation spectrum 5²D ?\leftarrow 5²S_1/2, indicating that the system does relax vibrationally during the lifetime of the 5²P_1/2 state. To model the LIF spectra we use calculated energy levels of the Rb atom as a function of its distance R from the center of the helium nanodroplet. The Franck-Condon factors of the resulting potential energy curves agree with the experimental spectra. In the future the 5²P_1/2 state can be used as a springboard to reach high-lying ²S and ²D states, and possibly create an artificial super-atom.     

g factor of the [(1s)2(2s)22p]2P3/2 state of middle-Z boronlike ions

Theoretical g-factor calculations for the first excited ²P_3/2 state of boronlike ions in the range Z=10–20 are presented and compared with the previously published values. The first-order interelectronic-interaction contribution is evaluated within the rigorous quantum electrodynamics (QED) approach in the effective screening potential. The second-order contribution is considered within the Breit approximation. The QED and nuclear recoil corrections are also taken into account.     

Relaxation times for establishing steady state populations in optically thin helium plasmas

Population densities of HeI and HeII excited states are calculated from a collisional radiative model for non-LTE optically thin helium plasmas. Effect of direct ionisation-excitation of HeI to HeII states on the population density of HeII states is shown. Relaxation times for HeI states calculated from the CR model is reported forT _e from 3 to 18 eV andn _e from 10⁹ to 10¹⁶ cm⁻³. Part of a research project supported by the Department of Atomic Energy.     

Reactions of excited atoms and molecules with atoms and molecules

Ionizing collisions of long lived excited particles with atoms and molecules are studied by a cross beam technique. For the first time reactions of atoms in high Rydberg states are included in the investigation. In this paper we report relative cross sections for the production of the ions RH⁺, RH ₂ ⁺ , and H ₂ ⁺ by collisions of excited rare gas atoms R^* with H₂. With HD as the target molecule the isotope effect for the production of RD⁺ and RH⁺ has been determined. In the case of argon and krypton, ions are produced only by the high Rydberg states, whereas in the case of helium and neon only the metastable states contribute to a measurable extent. The data indicate, that the reaction mechanism is different in principle for metastable and highly excited atoms. Simple models are proposed to explain the experimental results.     

Scaling of cross-sections for asymmetric (e, 3e) process on helium-like ions by fast electrons

An approximate simple scaling law is obtained for asymmetric (e, 3e) process on helium-like ions for double ionization by fast electrons. It is based on the equation (Z ^′3π) exp[-Z(r₁ + r₂)],Z′ = Z – (5/16) for ground state wave function of helium-like ions and Z^′2 scaling of energies. The scaling law is found to work very well if the lower energy electron is ejected along the momentum transfer direction and the other one is ejected in the opposite direction. It also works quite well if this electron is ejected within about 90° of the momentum transfer direction with the other electron going in the opposite direction. The scaling law becomes increasingly accurate as the target nuclear charge and the energy increase.     

On the mechanisms of formation of excited hydrogen atoms in a decaying helium-hydrogen plasma

We spectroscopically studied the population of the excited hydrogen atomic states with the principal quantum numbers n=3 and 4 in a decaying plasma produced by a pulsed discharge in a mixture of helium (p=40.4 Torr) with a small amount of hydrogen ([H₂]≈10¹² cm^?3). Experiments on recording the response of the spectral line intensities to a short-duration electron temperature perturbation revealed the contribution of electron-ion recombination to the population of the H*(n=3) states in the early afterglow. The ions produced by collisions of hydrogen molecules with metastable He(2³ S ₁) atoms, whose density decreases relatively rapidly with time in the decaying plasma, were assumed to be involved in this process. No population of the H*(n=4) atomic levels due to electron-ion recombination was found. Our experimental results are consistent with the conclusions of previous studies that excitation transfer during collisions of metastable helium molecules with hydrogen molecules plays a major role in the population of the excited hydrogen atomic states both with n=3 and with n=4 during most of the afterglow.     

Multi-band spectral structure and kinetics of the third continua in Ar,Kr and Xe gases excited by a pulsed discharge

Time-resolved VUV-UV emission of Ar, Kr, and Xe gases (Rg), excited by a pulsed discharge, have been measured to clarify the origin of the 3rd continua. Several detected continuum bands exhibit very different time behaviors due to various atomic (ionic) precursors and plasma kinetics. Imaging experiments with ns-gated ICCD camera have shown that the 2nd continua (Rg₂^*) and Rg^* lines emit uniformly in the positive column of the discharge. However, the 3rd continua and Rg^+* lines were excited exclusively in the negative glow zone, where high-energy electrons are injected from the cathode layer. The multi-band structure of the 3rd continua has been connected with Rg²⁺ ions produced in the ground and different excited states. These precursors lead to the formation of several bound states Rg₂^2+*, which decay radiatively to the repulsive states (Rg⁺ + Rg⁺), where Rg⁺ ions can be on ²P_3/2, ²P_1/2 levels due to spin-orbit coupling. The rate constants for the formation of Rg₂²⁺ excimers in three-body reaction and two-body collisional quenching of Rg^2+∗ ions have been determined from the time behaviors of emission. The quenching of Rg^2+∗ ions is explained by the level crossing between bound (Rg^2+* + Rg) and repulsive (Rg²⁺ + Rg) potential curves.     

Fine-structure effects in relativistic calculations of the static polarizability of the helium atom

We use the relativistic configuration-interaction method and the model potential method to calculate the scalar and tensor components of the dipole polarizabilities for the excited states 1s3p ³ P ₀ and 1s3p ³ P ₂ of the helium atom. The calculations of the reduced matrix elements for the resonant terms in the spectral expansion of the polarizabilities are derived using two-electron basis functions of the relativistic Hamiltonian of the atom, a Hamiltonian that incorporates the Coulomb and Breit electron-electron interactions. We formulate a new approach to determining the parameters of the Fuss model potential. Finally, we show that the polarizability values are sensitive to the choice of the wave functions used in the calculations. Zh. éksp. Teor. Fiz. 115, 494–504 (February 1999)     

Hund's rules and the interpretation and common misinterpretation of energy differences

With a Z expansion formalism which is exact in non-relativistic quantum mechanics it has been shown that for multiplets of neutral atoms and of many positive ions the state of the highest energy has the lowest expectation value for the interelectronic repulsion energy. This reversed order of the repulsion energy occurs for cases which obey Hund's first rule as well as for cases which obey the second of Hund's rules. It can be shown that the energy differences are in all cases dominated by the difference in electron nuclear attraction energy and not by the difference in electron repulsion energy.

The lowest ¹Π _u and ³Π _u states of the H₂ molecule have similar features. At many internuclear distances, including the equilibrium ones, the ¹Π _u state has the highest energy but the lower kinetic energy and electron repulsion energy but again the higher electron nuclear attraction energy. These results contradict clearly the usual theories for energy differences between spectroscopic states in atoms and molecules.     

Comparison of vibrational population of excited ions formed in penning ionization determined by electron spectroscopy and fluorescence measurement

The electron spectroscopical determination of the primary distribution of vibrational levels of the HCl⁺ and HBr⁺ ions in the excited A²Σ⁺ states, formed in Penning ionization by helium metastables, has shown that the vibrational distribution determined by fluorescence measurement is altered by post-ionization relaxation effects.