Study of the energy level structure for the isoelectronic series of scandium-like ions

The structure of the energy level system for 39 ions of the scandium isoelectronic sequence is studied on the basis of the relativistic self-consistent field method taking into account the configuration interaction. The Dirac-Fock equations are solved with subsequent diagonalization of the energy matrix. The ground-state ionization potentials are determined for each ion. The energy levels corresponding to the 3d4s ², 3d ²4s, and 3d ₃ configurations are also calculated. The obtained energy values are compared with the experimental data as well as with the results of calculations carried out by other authors.     

Polarization correlations in the two�Cphoton decay of hydrogen�Clike ions

Polarization properties of the photons emitted in the two?Cphoton decay of hydrogen?Clike ions are studied within the framework of the density matrix and second-order perturbation theory. In particular, we derive the polarization correlation function that gives the probability of the (two?Cphoton) coincidence measurement performed by polarization?Csensitive detectors. Detailed calculations of this function are performed for the 2s _1/2 ??1s _1/2 transition in neutral hydrogen as well as Xe^53?+? and U^91?+? ions. The obtained results allow us to understand the influence of relativistic and non?Cdipole effects on the polarization correlations in the bound?Cbound two?Cphoton transitions in heavy ions.     

Temperature dependence of the disorientation cross section σ 1 2/(1) in rubidium-rare gas collisions

The cross sections for the collision induced transfer²P_1/2m_j=1/2 → m_j = ?1/2 optically polarized Rb-vapour has been measured for collisions with He, Kr and Xe in the temperature range 30 °C → ～ 400 °C. The measurements were done by observing the degree of polarization in the fluorescent light emitted by the Rb-vapour. To avoid hyperfine structure effects, the nuclear spin was decoupled with a magnetic field. Calculations are presented in the temperature range 20 K → 1000 K using a semiclassical treatment and the Pascale Vandeplanque potentials. In the case of helium theoretical and experimental results are at variance, whereas for krypton and xenon satisfactory agreement is obtained. For the heavy rare gases the importance of trajectory effects, notably orbiting, becomes apparent.     

Transverse single spin asymmetry measurements at STAR

Transverse single spin asymmetries A _N are expected to be sensitive to par-ton polarization and orbital angular momentum contributions to the nucleon spin. Significantly large A _N has been observed in different collision systems such as semi-inclusive deep inelastic scattering (SIDIS) and polarized proton-proton (pp) collisions, indicating a dominant contribution of partonic interactions in the non-perturbative regime. Therefore it’s critical to measure A _N in various channels of polarized pp collisions in order to complement SIDIS data and to constrain theoretical models. We report STAR asymmetry measurements on mid-rapidity hadron-jet and di-hadron correlations at √s = 200 GeV and forward rapidity inclusive hadron production at √s = 500 GeV polarized pp collisions.     

On the relativistic theory of tunneling

A relativistic generalization of the semiclassical theory of tunneling and multiphoton ionization of atoms and ions in the field of a high-intensity electromagnetic wave with linear, circular, and elliptic polarization is constructed. The exponential factor in the ionization probability is calculated for arbitrary values of adiabaticity parameter γ. In the case of low-frequency laser radiation, an asymptotically exact formula is derived for the ionization rate of the s atomic level, including the Coulomb, spin, and adiabatic corrections and the preexponential factor.     

On the relativistic equation for particles with spinj in the 2[2j+1] — component formalism

The equation describing a relativistic particle with spinj and massm by a 2[2j+1] component wave function is derived using the method of boost transformations. The formalism developed in this paper allows us to find the wave functions satisfying the equation obtained and to construct the relativistically invariant quantities from these functions in an easy way. For the case of spin 3/2 the unitary equivalence with earlier results is demonstrated.     

Relativistic Hartree-Fock energies and oscillator strengths for some ions with ns2np (n=4minus;6) ground-state configuration

The lowest s and p levels in the spectra of ions isoelectronic with gallium, indium and thallium Ge(II) through Se(IV), Sn(II) through Te(IV), Pb(II), and Bi(III) are studied using the relativistic single-configuration Hartree-Fock method. The ionization energies, fine structure intervals, sharp series line-strength ratios, and oscillator strengths are computed and compared with experiments. Deviations in line-strength ratios from statistical ratios are discussed. The influence on oscillator strengths of valence- core electron correlations (core polarization) is included within the single-configuration scheme and is investigated. It is found that, for sharp series transitions, core polarization is less important in ions isoelectronic with Ga, In, and Tl than in neutral systems and both core-polarization-corrected and uncorrected oscillator strengths agree with experiments within experimental errors. This good agreement proves that, for sharp series transitions, the relativistic single-configuration Hartree-Fock method yields acceptable results.     

Spin-polarized relativistic calculations on highly ionized molybdenum

The energies of K_α X-ray satellite lines of molybdenum ionized to different degrees in the L shell with closed and open outer shells (n=3,4 and 5) are reported in this work. The calculations have been carried out using Xα method with spin-polarized single configuration relativistic Dirac-Fock wavefunctions. Calculations have also been carried out with un-polarized relativistic wavefunctions. The effect of relativistic spin exchange potential on the total energies of the various states ionized to different degrees in the inner and outer shells are analyzed. As the transition assignments in the spin-polarized treatment of atomic orbitals take into account the spin orientations of the electrons in the initial and final states, the present calculations elucidate the significance of this technique in giving unique spin-dependent transition assignments to experimental energies.     

The ground-state magnetic moments of odd-mass Hf isotopes

In this paper the Quasiparticle-Phonon Nuclear Model (QPNM), based on QRPA (Quasiparticle Random Phase Approximation) phonons, has been utilized to investigate spin polarization effects on the groundstate magnetic properties such as intrinsic magnetic moment (g _K ) and effective spin gyromagnetic factor (g _s ^eff. ) of odd-mass deformed ^165–179Hf isotopes with K > 1/2. Investigations of the spin polarization effects of the even core on the magnetic moments show that the spin gyromagnetic factors (g _s ) of the nucleons in the nucleus differ noticeably from the corresponding values for free nucleons and that the spin-spin interactions play an important role in the re-normalization of g _s factors of the odd-mass ^165–179Hf isotopes. In addition, some theoretical predictions are presented for the magnetic moments of ¹⁶⁵Hf, ¹⁶⁷Hf, and ¹⁶⁹Hf, whose ground state magnetic moments haven’t been experimentally determined yet.     

Direct observation of resonant four-photon parametric mixing conditioned by the difference of atomic multipole relaxation rates

Experimental evidence of previously predicted relaxation induced parametric processes is presented. Parametric interaction of orthogonal linearly polarized waves has been observed in the 2s₂-2p₁ (j = 1 → j = 0) Ne transition under λ = 1.52 μm He-Ne laser pumping. Coherence transfer between Zeeman sublevels eliminates the ban of the parametric interaction of orthogonal linearly polarized waves. This transfer is connected with collisions and photon-trapping processes resulting in the difference between relaxation rates of the electric quadrupole and magnetic dipole moments of the Ne atoms in the 2s₂ level.     

Experimente und Berechnungen zur Hyperfeinstruktur der 3d 9 5g-Konfiguration im Kupfer II-Spektrum

The 3d ⁹ 5g-configuration in the Cu II-spectrum is an example for extreme(j _d l _g )K-coupling. It is shown how under these circumstances experimental hyperfinestructure separations can be explained and calculated by means of the concept of intermediate coupling between two basic coupling schemes. The basic schemes used are built on the vectorK coupled either to the spins of the outer 5g-electron or to the nuclear spinI. The value of the experimental magnetic separation factorya _j (3d) can be understood as the consequence of the core polarization of the inners-electrons by the spin of the unfilled 3d-shell. — The measured effective spin-orbit-constantζ _5g is three times larger than the theoretical result. Reasons for this discrepancy will be discussed.     

Polarization transfer in deuteron stripping reactions

Polarization phenomena involving the spins of a and b in the A(a, b)B reaction are discussed using a complete set of irreducible tensors carrying definite spin transfer. The linear model independent equations relating the cross section and the polarization observables with these tensors are shown to be particularly appropriate for the study of spin dependent interactions, preferentially associated with particular values of spin transfer. The DWBA theory of polarization transfer in deuteron stripping reactions is thoroughly discussed and among the 17 polarization observables we distinguish those likely to be more sensitive to spin dependent distortion, to have stronger deuteron D-state effects, to exhibit the sign-rule j-dependence and other forms of j-dependence. For certain deuteron polarizations, when the spin transfer is pure $\text{s =}\text{1}\text{2}$, it is shown that deuteron stripping reactions are transparent to vector polarization transfer and the outgoing nucléon polarization independent of scattering angle and deuteron energy. DWBA calculations including contributions from spin transfer $\text{3}\text{2}$ through the deuteron D-state and spin-orbit distortion show that polarization transfer in such deuteron polarizations can be explored as a method of producing fast polarized neutrons with known polarization.     

<Emphasis Type="Italic">g</Emphasis> factor of Li-like ions with a nonzero nuclear spin

A relativistic theory of the g factor of Li-like ions with a nonzero nuclear spin is considered for the 1s ² 2s state. A correction to the atomic g factor for the magnetic-dipole hyperfine interaction is calculated including the one-electron contribution, as well as the contribution of interelectronic-interaction effects of the order of 1/Z. Along with corrections for the interelectronic interaction, quantum electrodynamic effects, nuclear recoil, and finite nuclear size, this correction allows high-precision theoretical values for the g factor of Li-like ions with a nonzero nuclear spin to be obtained. The results can be used for refining the nuclear magnetic moments from comparison with experimentally determined values of the g factor.     

Identification of local magnetic contributions in a Co2FeBO5 single crystal by XMCD spectroscopy

The temperature dependences of the X-ray absorption spectra (XAS) and of the spectra of X-ray magnetic circular dichroism (XMCD) are measured near the L _3,2 absorption edges of Co and Fe in ludwigite Co₂FeBO₅ single crystals. The antiparallel orientation of the magnetic moments of cobalt and iron is demonstrated. The coercive fields related to cobalt and iron ions are determined. The orbital (m _l ) and (m _s ) spin contributions to the total magnetic moments of cobalt and iron ions are identified. The ratios and relative directions of m _l and m _s are found.     

Calculation of the magnetic dipole constant of the hyperfine structure of the 6 S 5/2(3d 54s 2) term in the atomic spectrum of manganese

The contributions of spin polarization, valence correlations, and relativistic effects to the magnetic dipole constant of the hyperfine structure of the ⁶ S _5/2 (3d ⁵4s ²) term in the atomic spectrum of manganese are calculated and analyzed by the configuration interaction method and in the framework of the perturbation theory.     

Relativistic multireference configuration interaction calculations of lifetime of 2s22p 2P3/2 level along boron isoelectronic sequence

Lifetime of 2s²2p ²P_3/2 level along with fine structure separations for the lowest ²P doublet of boron-like ions, from Z=14 to Z=30 have been calculated using multireference relativistic configuration interaction (MR RCI) method based on the no-pair Dirac-Coulomb-Breit (DCB) Hamiltonian. Analytic basis sets of Gaussian-type functions are employed to expand the upper and lower components of the Dirac four-spinors in the matrix Dirac-Fock self-consistent field (DF SCF) and relativistic MR CI procedures. Error with respect to variation of basis set parameters was estimated. QED corrections were estimated by evaluation of electron self-energy and vacuum polarisation.     

Determination of the S and P° Rydberg energy levels of rubidium-like ions by the method of interpolation of relativistic quantum defects

The method of interpolation of relativistic quantum defects is used for determining the energies of Rydberg levels of rubidium-like ions. For this purpose, the values of relativistic quantum defects calculated by the Dirac-Fock method at three points, two of which correspond to discrete levels and the third, to the ionization threshold, are approximated by a second-degree polynomial. By using the continuous function μ(E) thus obtained, one can readily determine the energy value for any discrete level. A formula for calculating the threshold value of the quantum defect μ(0) (the phase shift δ(0)) is given. The approximation coefficients corresponding to the nS _1/2, nP°_1/2, and nP°_3/2 levels are presented. For better agreement with the experimental results, an empirical correction to the quantum defect is introduced, which weakly depends on energy. The calculations were performed for 17 members of the rubidium isoelectronic sequence (from Rb to Fr⁵⁰⁺).