Kβ X-ray emission from He-like ions

Relativistic calculations on the energies and electric dipole rates of K_β X-rays from 1s3p(¹P₁,³P₁)-1s² (¹S₀) transitions for He-like ions in the range Z=14–54 are carried out using multi-configuration Dirac–Fock (MCDF) wave functions in the active space interaction approach. The contributions from Breit interaction and quantum electrodynamics have also been included in the calculation. An attempt has been made to find a scaling expression for Breit energy in terms of Zα .The scaled Breit energies are in good agreement with the earlier accurate relativistic results and this ensures the reliability of our scaling procedure. The behavior of MCDF wavefunctions for a given J in the non-relativistic limit has also been studied. The calculated K_β X-ray energies and rates agree well with other available experimental and theoretical values.     

Transition rates of electrons in superheavy elements

Transition rates for electrons in the superheavy elementsZ=114, 126, 134, 145, 164 and 173 are calculated.K, L andM-shells are considered as final states. The 2s-1s transition of multipolarityM 1 is dominant for Z = 173 with a transition time of 10^?18 s. The radical expectation values 〈r〉 and 〈r²〉^1/2 are given.     

2p3/2−13x−1–3x−13d3/2−1 x‐ray satellites in the Lα2 region

The energies and intensities of the various transitions corresponding to the transition scheme 2p_3/2^?13x^?1–3x^?13d_3/2^?1 (i.e. L₃M_x–M_xM₄) were used to compute theoretical Lα₂ satellite spectra in 13 elements in the atomic number range of 62 ≤ Z ≤ 90. The energies were calculated using available HFS data on K–LM and L–MM transition energies. The intensities of all the possible transitions were estimated by considering cross‐sections for the Auger transitions simultaneous to a hole creation and then distributing statistically the total cross‐sections for initial two‐hole states 2p_3/2^?13x^?1 (L₃M_x) amongst various allowed transitions from these initial states to 3x^?13d_3/2^?1 (M_xM₄) final states. Each transition was assumed to give rise to a Gaussian line and the overall spectrum was computed as the sum of these Gaussian curves. The calculated spectra were compared with the available measured Lα satellite spectra. The peaks in the theoretical satellite spectra were identified as the experimentally reported satellites Lα_s, La₁₃, La₁₄ and La₁₇, which lie on the high‐energy side of the Lα₂ dipole line. Copyright © 2005 John Wiley & Sons, Ltd.     

Probabilities for radiative vacancy transfer from Li (i=1, 2, 3) sub-shells to the M, N and higher shells for elements with 77≤Z≤92

The probabilities for transfer of the L_i (i=1, 2, 3) subshell vacancy to the M, N and higher shells through radiative decay, ηLiJ(R), have been deduced for the elements with 77≤Z≤92 using the measured L X-ray production cross-sections at (i) the 59.54 keV γ-rays such that BL₁<Einc<BK and (ii) the K X-rays of a suitable secondary target chosen such that BL₃<EKα<BL₂ and BL₁/L₂<EKβ<BK; where BK/Li is the K shell/L_i subshell ionisation threshold of the target element. The deduced probabilities are compared with those calculated using the radiative and nonradiative transition rates based on the Dirac-Fock (DF) and the relativistic Dirac-Hartree-Slater (RDHS) calculations, respectively.     

New atomic data for Kr XXXV useful in fusion plasma

Energy levels and emission line wavelengths of high-Z materials are useful for impurity diagnostics due to their potential application in the next generation fusion devices.For this purpose,we have calculated the fine structural energies of the 67 levels belonging to the 1s 2,1s2l,1s3l,1s4l,1s5l,and 1s6l configurations of Kr XXXV using GRASP(general purpose relativistic atomic structure package) code.Additionally,we have reported the transition probabilities,oscillator strengths,line strengths,and transition wavelengths for some electric dipole(E1) transitions among these levels.We predict new energy levels and radiative rates,which have not been reported experimentally or theoretically,forming the basis for future experimental work.     

High-field ENDOR and the sign of the hyperfine coupling

Two different approaches for assigning electron nuclear double resonance (ENDOR) signals to their respectiveM _s manifolds by a controlled generation of asymmetric ENDOR spectra, are described and applied to a number of systems. This assignment then allows a straightforward determination of the sign of the hyperfine coupling. Both approaches rely on a high thermal polarization that is easily achieved at high fields and low temperatures. For high-spin systems, such asS = 5/2 the assignment is afforded by the selective inversion of the | ?3/2〉 → | ?1/2〉 electron paramagnetic resonance (EPR) transition which is highly populated as compared to its symmetric counterpart, the |1/2〉 → |3/2〉 EPR transition, and therefore is easily identified. ForS = 1/2 the determination of the sign of the hyperfine coupling becomes possible when the cross- and nuclear-spin relaxation rates are much slower than the electron-spin relaxation rate and variable mixing time pulse ENDOR is used to measure the spectrum. Under these conditions the signals of theM _s = 1/2 (α) manifold become negative when the mixing time is on order of the electron-spin relaxation time, whereas those of theM _s =?1/2 (β) manifold remain positive. Under partial saturation of the nuclear transitions and short mixing time the opposite behavior is observed. Pulse W-band¹H ENDOR experiments demonstrating these approaches were applied and the signs of the hyperfine couplings of the water ligands in Mn(H₂O) ₆ ²⁺ , the H_α and H_β histidine protons in the Cu(histidine)₂ complex, the imidazole protons in Cu(imidazole) ₄ ²⁺ and the cysteine β-protons in nitrous oxide reductase were determined.     

High-resolution X-ray emission Lα1 and Lβ2 Spectra of Hf, Ta, W, Re, and Os

The shape and relative intensities S _α=I(α_1s )/I(α_1s ), S _β=I(β_1s )/I(β₂) of the short-wavelength X-ray Lα₁ and Lβ₂ satellites arising from the radiative decay of the states corresponding to L ₃ M _4,5 configurations were investigated experimentally for Hf, Ta, W, Re, and Os. It was established that, in the case of W, the values S _α=2.5%, S _β=4.2% are five to seven times larger than those for Hf and Ta, and by (30–60)% smaller than those for Re and Os. On the basis of the obtained values of S _α,S _β, as well as the observed two-component structure of the Lα₁ and Lβ₂ satellites, it is concluded that the Coster-Kronig L ₁-L ₃ M ₅ transitions (CK) are allowed by the energy conservation law even for tungsten, and, starting with this element, they represent a major channel of generation of the states of LL ₃ M ₅ configuration. Possible features of such a process for the W atom are discussed in comparison with those for Re and Os.     

Theory of molecular-orbital and compound-nucleus x-ray emission in heavy-ion-atom collisions with nuclear sticking

Calculations are made of x-ray emission in head-on 200-MeV (lab) Ni+Ni and 860-MeV (lab) Yb+Yb collisions for various values of the compound nucleus lifetimeτ. TheK x-ray emission probability is obtained by coherently summing the amplitude for a molecular-orbital x-ray transition from the 2pσ, 2pπ, 3pσ, or 3pπ to the 1sσ molecular orbital with the amplitude for a compound-nucleus x-ray transition from the united-atom 2p or 3p levels to the 1s level while the projectile and target nuclei stick. If ω _Kα τ \(<< \) 1, where ω _Kα τ is the united-atom transition frequency, only molecular orbital x-rays are observed. If ω _Kα τ \( > > \) 1, compound nucleus x-rays are observed. Independent of the projectile velocity, the atomic number of the combined system, and the mechanism for the creation of the 1sσ vacancy, the compound-nucleus x-rays become sufficiently sharp at ω _Kα τ ≈ 20 to permit the measurement of the united-atomKα andKβ x-ray energies to an accuracy of <±5%. The lifetime of the compound nucleus may be sufficiently long to observeK x-rays of 100?Z _u?140 in fusion-fission nuclear reactions.     

Theoretical study on the 1s22s-1s2 np transitions for Ni25+ ion

The transition energies, wavelengths and oscillator strengths for the 1s²2s-1s² np (n ? 9) transitions of Ni²⁵⁺ ion are calculated. In calculation of the energies, we not only take account of the firstorder corrections from relativistic and mass-polarization effects, but also estimate the higher-order relativistic contribution and QED correction by introducing the effective nuclear charge. The results agree with experimental data available in literature satisfactorily. Grotrian diagram showing these transitions is given.     

类铍离子磁四极M2 2s2 1S0—2s2p3P2 (Z=10—103)禁戒跃迁

利用全相对论多组态Dirac-Fock方法系统地计算了高离化类铍离子的磁四极M2 2s²¹S₀—2s2p³P₂ (Z=10—103)自旋禁戒跃迁的能级间隔、跃迁概率和振子强度，计算中考虑了重要核的有限体积效应，Breit修正和QED修正，所得结果和最近的实验数据以及理论值进行了比较，结果表明：高原子序数的高电荷离子(Z≥70)磁四极M2自旋禁戒跃迁几乎可以和中性原子的光学允许跃迁相比拟，不仅在天体等离子体中，在ICF和MCF高温激光等离子体中，磁四极自旋禁戒跃迁和其他自旋禁戒跃迁（磁偶极、电四极）一样不容忽视，在双电子复合、不透明度、自由程等理论计算中应该考虑其影响. 关键词： 磁四极M2 能级间隔 跃迁概率 振子强度     

K-shell X-ray production for fluorine ions on target elements Ti to La

The production of target atomK-shell X-rays has been studied for 2 to 28 MeV fluorine ions incident on thin solid targets of 14 elements with atomic numbers Z₂=22 to 57. Total X-ray production cross sections, energy shifts ofK _α andK _β lines andK _α/K _β intensity ratios were measured with a Si(Li) detector. The results of cross section measurements are compared with theoretical predictions of inner shell ionization. In most cases, satisfactory agreement between measured cross sections and theoretical Coulomb ionization cross sections, corrected for the perturbation of the target atom by the projectile charge and for relativistic effects, was obtained.     

Oscillator strengths and transition probabilities of the Be(I) isoelectronic sequence for 2p2-2s2p and 2s2p-2s2 transitions

Oscillator strengths and transition probabilities are obtained from an intermediate coupling scheme. The initial basis of the eigenstates is formed inLS-coupling. To obtain the resulting energy matrix,Z^-1 perturbation theory is applied. The values of oscillator strengths and transition probabilities for 1s²2p²?1s²2s2p and 1s²2s2p?1s²2s² transitions are calculated and the comparison is made with some recent results. The nuclear charges (Z) involved varied fromZ=4(Be(I)) toZ=35(Br(XXXII)).     

CalciumK X-ray spectra produced by oxygen,alpha-particle,and proton bombardment

Kα andKβ X-rays of calcium were produced by bombarding a thick calcium wafer with oxygen, helium and hydrogen ions. These reactions produce a substantial amount of inner shell ionization. TheK X-ray spectra contain X-ray lines from calcium which emanate from initial states with a varying degree ofK orL shell vacancies. The initial configurations were assigned on the basis of Hartree-Fock-Slater calculated energies. Related intensity ratio of1s→2p (Kα) transitions and of1s→3p (Kβ) transitions of H plus Ca, He plus Ca and O plus Ca were obtained. In addition to observing many new transitions due to multipleK and/or multipleL shell vacancies, energy shifts relative to the H plus Ca spectrum were observed in the O plus Ca spectrum due toM shell vacancies.     

An experimental investigation of the onset of theL 2-L 3 M 4 andL 2-L 3 M 5 Coster-Kronig transitions forZ>90

L-M coincidence measurements were made on x rays from the radioactive decays of ₉₆ ²⁴⁴ Cm, ₉₄ ²³⁸ Pu, and ₉₂ ²³² U. The observation ofM x rays in coincidence with theL ₃ N _{4, 5} transition indicates that the onset of theL ₂-L ₃ M ₅ Coster-Kronig transition takes place atZ=91 or 92. The measured ratio of theM x-ray counting rates, coincident with theL ₃ N _{4, 5} andL ₂ M ₄ transitions, establishes that both theL ₂-L ₃ M ₄ and theL ₂-L ₃ M ₅ transitions are energetically possible forZ≧94, but the results do not rule out the possibility that these transitions begin as low asZ=92. The measurement ofL-M x-ray coincidences, together with relative Coster-Kronig electron intensities from theory or experiment, provides a new way to measure the totalL ₂-L ₃ Coster-Kronig transition probability,f ₂₃, at highZ for radioactive sources where the primary vacancies are created primarily in theL ₂ andL ₃ subshells. The present result atZ=94 indicates that the theoretical calculations of McGuire of the relative partial Coster-Kronig transition rates forL ₂-L ₃ M _4,5 are accurate to within 10 percent.     

Relativistic atomic level calculations with nuclei carrying additional fractional charges

One-electron energy levels and wavelengths have been calculated for Na-like ions whose nuclei carry quarks with additional charges ±e/3, ±2e/3. The calculations are based on relativistic self-consistent field procedures. The deviations from experimental values exhibit regularities which allow an extrapolation for the wavelengths of 3s-3p, 3s-4p, 3p-3d, and 3p-4s transitions for the nuclear chargeZ=11+1/3, ±2/3. A number of transitions are found in the region of visible light which could be used in an optical search for quark atoms.     

Calculation of X-ray and Auger transition rates, lifetimes, X-ray wavelengths, and fluorescence yields of variously ionized silicon atoms

X-ray and Auger transition rates, X-ray wavelengths, and fluorescence yields are calculated for variously ionized silicon atoms with configurations 1s2s^m2pⁿ, m=0-2, n=1-6. The calculation has been performed using the Hartree-Fock atomic model. Intermediate coupling and configuration interaction have been taken into account. The energies and widths are found to be strongly affected by configuration mixing. The results from the present calculation have been compared with those available in the literature. The theoretical K_α hypersatellite and satellite spectra fall into several well-separated regions, corresponding to each of the possible number of spectator electrons in the 2s and 2p shells. The dependence of radiative rates and fluorescence yields on the number of spectator electrons is also investigated.     

Relativistic radiative transition rates and energies for the Li-like isoelectronic sequence: Electric and magnetic dipole and quadropole radiation

For Li-like ions in the isoelectronic sequence between the nuclear charges Z = 26 and 94, energies, oscillator strengths and probabilities of electric and magnetic dipole and quadropole transitions between the first 22 atomic levels were calculated by means of the multiconfigurational Dirac-Fock model. The effects of nonlocal Breit interaction, electron self-energy and vacuum polarization were included in calculating energy levels and radiative rates. The trends of transition energies and rates along the isoelectronic sequence, in particular, the enhancement of the forbidden transitions with increasing atomic number Z, are discussed.     

TheE1 transitions in kaonic atoms

The electric dipole transition rates in kaonic atoms are calculated by using distorted relativistic wave functions. The kaon-nucleus strong interaction which is responsible for the distortion of atomic states is considered to be proportional to the nuclear density and the effective isospin-averaged kaon-nucleon scattering length. Six atoms have been studied for which the last observed X-rays correspond to 3d-2p, 4f-3d, 5g-4f, 6h-5g, 7i-6h and 8j-7i transitions. It is found that the electric dipole transition rate is enhanced by an amount (0.3–7.6)×10¹³s^?1     

Spin polarization and angular distribution of Auger electrons formed as a result of decay of the 3<Emphasis Type="Italic">d</Emphasis><Superscript>−1</Superscript>5<Emphasis Type="Italic">p</Emphasis> state in the Kr atom

The results of numerical calculations of the energies of Auger transitions, as well as the angular distribution (α₂) and spin polarization (β₂) anisotropy parameters, are presented for transitions in a photoexcited Kr* atom with two open shells. Matrix elements are calculated by the multiconfigurational Fock-Dirac relativistic method using an intermediate type of coupling. The wavefunctions of the initial and final states of the Auger transition are calculated with allowance for relaxation effects. The one-electron wavefunction of the continuous spectrum for an Auger electron is obtained using the single-configuration Fock-Dirac method. The results are compared with experiment and a new experiment is proposed for identifying the Auger state not only from the energy, but also from the total angular momentum of the Auger state.     

Relativistic many-body calculations of E1, E2, M1, and M2 transitions rates for the 1 s 2 l′ 2 l′ ′ – 1 s 2 2 l lines in Li-like ions

Reduced matrix elements, oscillator strengths, and transition rates are calculated for all allowed and forbidden 1s2l′ 2l′ ′ – 1s ²2l electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions in lithiumlike ions with nuclear charges ranging from Z?=?6 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded E1, M1, E2, and M2 matrix elements. The calculations start with a Dirac potential and include all possible 1s2l′ 2l′ ′ configurations, leading to seven odd-parity and nine even-parity states. First-order perturbation theory is used to obtain intermediate coupling coefficients. Second-order RMBPT is used to determine the matrix elements, which are evaluated for the 22, 20, 16, and 18 possible E1, M1, E2, and M2 transitions, respectively. A detailed discussion of the various contributions to the energy levels and E1, M1, E2, and M2 matrix elements is given for lithiumlike iron, Z?=?26. The transition energies used in the calculation of oscillator strengths and transition rates are evaluated using second-order RMBPT. Trends of E1, M1, E2, and M2 transition rates as functions of nuclear charge Z are shown graphically for 1s2l′ 2l′ ′ – 1s ²2l transitions.