4l States Research Articles

The excitation energies and hyperfine structures for 2l, 3l states in lithiumlike ions

Combining the multi-configuration Dirac–Hartree–Fock method and the model-quantum electrodynamics (QED) approach, the wave functions, transition energies and hyperfine structure constants for 2l, 3l states in Li-like Ne7+, Mg9+, Al10+, P12+, Ar15+ and Ca17+ ions are calculated. The effects of electron correlation, Breit interactions, nuclear recoil and QED effects are analyzed in detail. We find that the contribution of the non-diagonal elements of the self-energy is significant for the 2p1/2→2s1/2 and 2p3/2→2s1/2 transitions. However, for the 3l→2s1/2 transitions, the contribution of non-diagonal elements is small. The accuracy of the currently calculated hyperfine structure constants is expected to be within 1%.

Electron capture in slow collisions of O6+ions with atomic hydrogen

Aims. Electron capture in collisions of highly charged O6+ions with ground-state hydrogen atoms is a very important process in solar wind X-ray studies.Methods. In the present study, the full quantum-mechanical molecular-orbital close-coupling method is employed to study electron capture reactions in collisions of O6+ion with ground-state atomic hydrogen in the energy region from 10−4keV u−1to 5 keV u−1. The ab initio multi-reference single- and double-excitation configuration interaction (MRD-CI) method is used to calculate the potential and coupling data used in the QMOCC calculations.Results. Total and state-selective cross sections for the dominant and subdominant reaction channels are calculated and compared with the available experimental and theoretical data. The branching ratios for Lithium-like O5+excited ions are used to calculate the contribution of cascade radiative transitions fromn = 5 levels to the population of 4l states. From the calculated cross sections, reaction rate coefficients are obtained for temperatures between 1000 and 1 × 109K and compared with other calculations.

Energy levels, transition rates and lifetimes for Li-like ions with Z ≤ 10 in the 1s2s(3S)3ℓ states

SynopsisEnergy levels, transition rates and lifetimes for Li-like ions with Z ≤ 10 in the 1s2s(3S)3ℓ states were calculated using the Dirac-Fock approach.

Theoretical study for photoionization of Mg-like S4+ ion

Photoionization of the Mg-like S4+ ion has been studied for the ground 1S and excited 3,1P initial states. Using a noniterative eigenchannel R-matrix method, we have investigated the partial photoionization cross sections leading to the final photo-ionic 3l states. The autoionizing resonance structures arising from the ground and excited states are identified and characterized. Our calculational results, which show excellent agreement between length and velocity gauges, are compared with the available previous Opacity Project results, and some significant discrepancies are found.

Theoretical photoionization spectra for the Mg-like S4+ Ion in the energy range between the S5+ 4s and 4f thresholds

The partial and the total photoionization cross sections of the Mg-like S4+ ion, leaving the residual S5+ 3l and 4l states from the ground 3s21Se and the excited 3s3p3,1Po initial states, have been calculated for photon energies ranging from the S5+ 4s to the S5+ 4f threshold. The complex features appearing in the cross sections represent the tangled autoionizing Rydberg resonances converging to the different S5+ 4l thresholds. The present results are compared with the available previous National Institute of Standards and Technology(NIST) and Opacity Project(OP) results.

Photoionization of Be-like N3 + and Ne6 + ions: features of Be isoelectronic sequences of Z ⩽ 10

Using a noniterative eigenchannel R-matrix method, we have studied the photoionization for ground 1S and excited 3, 1P initial states of the Be-like N3 + and Ne6 + ions, up to the energy range of the final photo-ionic 3d state. The autoionizing resonance structures arising from the ground and excited states are identified and characterized. Our calculated photoionization cross sections with excellent agreement between length and velocity gauges are compared with the available experimental and previous theoretical results, and good agreement is shown. For the isoelectronic sequences of Z ⩽ 10, the Z-dependent spectral structures and developments of the cross sections are discussed based on the present results of N3 + and Ne6 + ions and the previous results of other ions obtained by the same noniterative eigenchannel R-matrix method. The intermixing among the resonances converging to the final photo-ionic 2p and the various 3l states is increased as Z, resulting in a much more complex pattern of resonances for the photoionization.

Laboratory experiments on soft x-ray emissions from the solar wind

We have observed emission spectra in collisions of hydrogen-like oxygen and nitrogen ions with a helium target gas in the soft x-ray region using a window-less Si(Li) detector at collision energies of about 100 keV. The dominant soft x-ray emission is the 1s2–1s2p transition of helium-like ions produced by a single-electron capture reaction. We indicate that the cascades from the upper states give a large population of the 2p state, even though direct capture into the 2p state is much smaller than the 3ℓ and 4ℓ states. The intensity ratios of the 1s–2p and 1s–3p transitions are discussed, along with a comparison with the theoretical calculation.

Polarization degrees of 3p 2P3/2–3s 2S1/2 transition in O5+(1s 23p) produced in collisions of O6+ with He and H2

Electron capture processes in collisions of O6+ with ground state He and H2 are investigated using the two-centre atomic orbital close-coupling method. Total and state-selective one-electron capture cross sections are obtained for collision energies between 0.5 and 300 keV/u. The comparison with the available experimental state-selective capture data in the overlapping energy range (0.5–100 keV/u for O6++He and 0.5–8 keV/u for O6++H2) shows a good overall agreement. The polarization degrees of 3p 2P3/2–3s 2S1/2 radiation from O5+(3p 2P3/2) produced in O6++He and O6++H2 collisions are calculated from the magnetic substate-selective cross sections with inclusion of cascade contributions from higher n = 4 and n = 5 states. Good agreement is obtained with the experimental data available in the energy range 3–8 keV/u. Below ∼10 keV/u, the polarization degrees of O5+(3p 2P3/2) in both collision systems exhibit an oscillatory structure and above this energy they steadily increase with the increase of collision energy, reaching the values of about 0.37 at 300 keV/u. The energy behaviour of the polarization degree of O5+(3p 2P3/2) in the O6++He collision system is determined almost exclusively by the direct electron capture to 3p0 and 3p1 states of O5+, while in the case of the O6++H2 collision system in the energy region below ∼40 keV/u it is strongly affected by the cascade contributions from the 4l states, which are the dominant capture states in this system.

Photoionization of the ground state of the Be-like C2+ ion leading to C3+ 2l and 3l states

Total and partial photoionization cross sections of the Be-like C2+ ion leading to the C3+ 2l and 3l(l = 0, 1) states from the 1S ground state have been calculated. The lower members of all autoionizing Rydberg series converging to the C3+ 2p, 3s, 3p, and 3d thresholds are identified and their energies and widths are determined. Except for the resonances converging to the C3+ 2p threshold, all of the resonance series are perturbed by overlapping series converging to other thresholds. In addition, the 4s4p 1P resonance is found to lie just below the C3+ 3d threshold. The calculations show excellent agreement between length and velocity gauges. Comparison with experiment for the photoionization of a mixture of the 1S ground state and 3P metastable states of C2+ in the photon energy range 40.8–56.9 eV shows good agreement with the present theoretical results; for the comparison, a calculation of photoionization of the metastable state was also performed. The present calculations are also compared with other previous theoretical and experimental results.

Case study of theAr9+−Hecollision system at low velocity

The Ar{sup 9+}-He charge-exchange collision system is studied at low kinetic energy (E=2.25 keV/amu), using two complementary instrumental techniques: x-ray and vacuum ultraviolet photon spectroscopy and Auger-electron spectroscopy. It is shown that single capture populates mostly n=4 and 5 in Ne-like argon 1s{sup 2}2s{sup 2}2p{sup 5}nl. The analysis and identification of the lines show the cascade population of 1s{sup 2}2s2p{sup 6}3l states. These are not expected to be seen since in the entrance channel the projectile has the core 1s{sup 2}2s{sup 2}2p{sup 5} {sup 2}P{sub J}{sup o}. They are identified by photon emission. Double capture populates mostly Na-like core excited states corresponding to the configurations 1s{sup 2}2s{sup 2}2p{sup 5}3l5l{sup '}. They are identified and it is seen that the continuum 2p{sup 6} {sup 1}S{sub 0} to which they Auger decay is the only one available in this case.

Polarizabilities of helium in high-angular-momentumstates

The static dipole, quadrupole, and octupole polarizabilities ofhelium are calculated for the n 1L and n 3L states withn up to 10 and L up to 9, using variational wavefunctionsin Hylleraas coordinates.

RELATIVISTIC MANY-BODY CALCULATIONS OF ENERGIES OFn= 3 STATES FOR THE BORON ISOELECTRONIC SEQUENCE,Z= 6–30

Energies of the 2s2(1S)3l, 2s2p(1P)3l, 2s2p(3P)3l, 2p2(3P)3l, 2p2(1D)3l, and 2p2(1S)3l states, withl = s,p, andd, for B-like ions with nuclear chargesZin the range 6–30 are determined to second order in relativistic many-body perturbation theory starting from a frozen-core Dirac–Fock basis. These perturbation theory calculations include the first- and second-order diagram contributions from the Coulomb and Breit operators for diagonal and nondiagonal matrix elements. Corrections for the frequency dependence of the Breit interaction are taken into account in lowest order. The Lamb-shift correction to the energies is also included in lowest order. Contributions of the three-electron interaction are compared with contributions of the one- and two-electron interactions. Comparisons are made with other theoretical calculations and with experimental data. We obtain excellent agreement for term splitting, even for low-Zions.

Spectrum of plasma containing Ne- and Na-like ions: consistent account for Rydberg and autoionizing Rydberg series in balance equations

This is a theoretical study of argon plasma under conditions, where Ne- and Na-like ionization stages are dominant. Balance equations are generalized to treat 37 3l states of Ne-like ion and 37 adjacent series of Rydberg states of Na-like ion simultaneously. This allows us to include in the kinetics a diffusion-like motion of the state of the system "Ne-like ion plus one electron" through the multitude of excited levels spread over an energy region of 50 eV. The populations Ni - i (i = (1, ..., 37)) of the Ne-like ion states are introduced explicitly; those of adjacent 37 Rydberg series are accounted for through continuous functions Ni(ε). These functions describe the population distribution within each Rydberg series dependent on the Rydberg electron enegy ε. The elementary processes of the collisionalradiative model connecting all Ne- and Na-like states, as well as processes of redistribution of populations inside each Rydberg series, are accounted for. The rate coefficients for all processes within the Ne-like residue have been calculated previously, using a detailed many-body relativistic theory. The dielectric capture cross sections and autoionization probabilities are presented as analytical continuation of the collisional excitation cross sections. The excited-excited states transitions are included. The rest of the processes are treated in a simple semiclassical approximation. The Lotz formula is generalized by unambiguous analytical continuation to cover the case of bound-bound transitions between Rydberg states of Na-like ions. The radiation reabsorption in a long plasma cylinder is included through Biberman-Holstein coefficients for all transitions. The inclusion of Na-like states, accounting for diffusion-like processes, increases the population inversion for the "lasing candidates" by at least a factor of two for a wide range of plasma conditions. This is important for the ionization equilibrium too. Besides, the functions Ni(ε) bear diagnostic information. Detailed calculations have been done for the homogeneous steady-state Maxwellian plasma. The role of transient processes in the population inversion creation is under discussion.

FINITE CHAINS WITH QUANTUM AFFINE SYMMETRIES

We consider an extension of the t-U Hubbard model taking into account new interactions between the numbers of up and down electrons. We confine ourselves to a one-dimensional open chain with L sites (4L states) and derive the effective Hamiltonian in the strong repulsion (large U) regime. This Hamiltonian acts on 3L states. We show that the spectrum of the latter Hamiltonian (not the degeneracies) coincides with the spectrum of the anisotropic Heisenberg chain (XX Z model) in the presence of a Z field (2L states). The wave functions of the 3L-state system are obtained explicitly from those of the 2L-state system, and the degeneracies can be understood in terms of irreducible representations of [Formula: see text].

He2+-H collisions: experimental charge exchange cross sections and their relevance for alpha particle diagnostics at JET

We have determined absolute cross sections for electron capture into the quasi-degenerate 4l states of He+ produced in collisions of He2+ on atomic hydrogen. The cross sections have been deduced by deconvoluting spatial HeII(n = 4 → n = 3) emission profiles. The measurements have been performed in the impact energy range of 2 –130 keV/amu. The results are compared with theory. In addition we discuss the relevance of these cross sections to α-particle diagnostics in fusion plasmas. At the JET tokamak the HeII(n = 4 → n = 3) emission can be used to determine related quantities like ion temperature, plasma rotation and local α-particle densities.

The multichannel eikonal theory of electron-hydrogen collisions. I. Excitation of H (1s)

The integral and differential cross sections for the electronic excitation of the 2l and 3l states of hydrogen obtained by the multichannel eikonal theory in a 10-channel basis are reported. The lambda , R and I parameters for the 2p state of hydrogen at 54.40 and 350 eV are also provided. Good agreement with the experimental data of Mahan et al. (1976) for the integral cross sections sigma 1s to 3l is achieved by the updated and extended multichannel eikonal theory. Two general conclusions follow from the results reported in the paper: (a) the first Born results underestimates experiment in s to d transitions and (b) indirect coupling mechanisms for the excitation of the 3d state of hydrogen are important and cannot be neglected. These conclusions indicate that the pseudostate basis used in a number of optical potential model calculations needs further refinement in the intermediate energy region.

TWO-BODY CORRELATION FOR THE EXCITED STATES OF THE ATOMS

The variational approach to two-body correlations in atoms proposed by Wilets et al, and developed by bresent authors is applied to treat the correlations of excited states of the atoms. The (ls)(nl)1,3L excited states of helium iseelectronic sequence, the (1s)2(2s)(nl)3L states of beryllium isoelectronic sequence and the (1s)2(2s)2(nl)2L states of boron have been calculated.The results show that these correlation wave functions have simple structure and are feasible in caloulation application. The accuracy of our method is very close to those of more complicated CI and 1/Z perturbation expansion methods.

Spectroscopy of Mg-like Ar produced in low-energy charge exchange collisions

After the single-electron capture collision Ar7++He to Ar6++He+ a measurement of Ar VII transition intensities in the region 100< lambda <1000 AA shows that the projectile captures the electron into the n=4 level of the Ar VII ion. A configuration interaction calculation of Ar VII energy levels is used to interpret and identify observed transitions. It is underlined that population of (Ar6+)3L states rather than (Ar6+)1L states is favoured.

Photon Emission from Core-Excited Be I and Be II States

Optical-emission spectra of core-excited Be I 5L and core-excited Be II 2L and 4L states have been studied by means of the beam-foil-excitation method. Multiconfigurational Hartree-Fock calculations have been performed for the optical transitions between the lower-lying Be I 5L states and between 1s2pnl (n = 2-4, l = 0-3) 2P0, 2Pe, 2D0, 2De, and 2Fe states in core-excited Be II 2L to facilitate the identifications. Some previously assigned core-excited Be II 4L transitions are shown to belong to either the core-excited Be I 5L or the core-excited Be II 2L spectrum. Additional identifications of core-excited Be II 2L transitions explain the main features of this spectrum. The identifications of Be II 1s2p4l 4L states are discussed.