Core Polarization Effects Research Articles

Atomic data of intermediate autoionzing Rydberg series nf[K]J (n = 4, 5), nd[K]J (n = 5, 6), np[K]J (n = 6, 7) and ns[K]J (n = 7, 8) of neutral argon atom in the multiconfiguration Dirac-Hartree-Fock framework

We report the results of an accurate computation of the energy levels, oscillator strengths \(f_{ij}\), the radiative transition rates \(A_{ij}\), the Lande g-factor, the magnetic dipole and the electric quadrupole hyperfine constants of the intermediate Rydberg series \(n{\rm f}[K]_{J}\) \( (n = 4, 5)\), \( n{\rm d}[K]_{J}\) \( (n = 5, 6)\), \(n{\rm p}[K]_{J}\) \((n = 6, 7)\) and \(n{\rm s}[K]_{J}\) \((n = 7, 8)\) relative to the ground state 3p6 1S0 for neutral argon atom spectra based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) approach. In this approach, the quantum electrodynamics (QED) effects with transverse photon Breit interaction and vacuum photon polarization self-energy corrections are included. Moreover, the perturbation due to the core-polarization and electron correlation effects are taken into account. We also reported the oscillator strengths and transition rates in Coulomb and Babushkin gauges for the 3p5(2P)3d-3p5(2P)4f, 3p5(2P)3d-3p5(2P)5f, 3p5(2P)4d-3p5(2P)4f, 3p5(2P)4d-3p5(2P)5f, 3p5(2P)5d-3p5(2P)4f, 3p5(2P)5d-3p5(2P)5f, 3p5(2P)6d-3p5(2P)4f and 3p5(2P)6d-3p5(2P)5f transition arrays as well as the 3p5(2P)5d-3p5(2P)6p, 3p5(2P)7s-3p5(2P)6p, 3p5(2P)7s-3p5(2P)7p and 3p5(2P)8s-3p5(2P)7p transition arrays. Insofar as experimental or theoretical values by other authors exist, comparison is made with those values; it turns out that, for most of the levels, a rather satisfying agreement with these experimental and theoretical results is obtained, thus confirming the reliability of our data.

Magnetic moments and g-factors in odd-A Ho isotopes**Supported by Scientific and Technological Research Council of Turkey (TUBITAK) (115F564)

The ground-state magnetic moment, gK factor and quenching spin gyromagnetic ratio have been calculated using the microscopic method based on the Quasiparticle Phonon Nuclear Model (QPNM) for 155−169Ho nuclei for the first time. It is shown that the residual spin-spin interactions are responsible for the core polarization, and because of the core polarization the spin gyromagnetic factors are quenched. By considering the core polarization effects, a satisfactory agreement is obtained for the computed ground state gK factor, which gives an intrinsic contribution to the magnetic moments. In order to assess the collective contribution to the magnetic moments, the rotational gyromagnetic factors gR have been also calculated within the cranking approximation using the single particle wave function of the axially symmetric Woods-Saxon potential. For the ground-state magnetic moments of odd-proton 155−165Ho nuclei, a good description of the experimental data is obtained with an accuracy of 0.01–0.1 μN. From systematic trends, the quenching spin gyromagnetic factor, gK factor and magnetic moment have also been theoretically predicted for 167,169Ho where there is no existing experimental data.

Stark broadening of several Bi iv spectral lines of astrophysical interest

The presence of spectral lines of bismuth in stellar atmospheres has been reported in different stars. The anomalous values of the spectral intensities of Bi II and Bi III, compared to the theoretical Local Termodinamic Equilibrium (LTE) standards of Bi I/Bi II/Bi III, have been reported in the spectra obtained with the High Resolution Spectrograph of the Hubble/Goddard Space Telescope in the chemically peculiar stars HgMn stars χ Lupi and HR 7775. Spectral lines of 1436.8, 1902.3, 2630.9 and 2936.7 A of Bi II and 1423.4 A of Bi III were reported and their relative intensities were measured in these studies Litzen & Wahlgren 2002. These lines are overlapped with spectral lines of 1437.65, 2630.1 and 2937.1 A of Bi IV. A study of the Stark broadening parameters of Bi IV spectral lines can help to study these overlaps. In this paper, using the Griem semi-empirical approach, we report calculated values of the Stark parameters for 64 spectral lines of Bi IV. The matrix elements used in these calculations have been determined from 17 configurations of Bi IV. They were calculated using the COWAN code including core polarization effects. Data are displayed for an electron density of 10¹⁷ cmˉ³ and temperatures T=10 000–160 000 K. Also calculated radiative lifetimes for 12 levels with experimental lifetime are presented, in order to test the goodness of our calculations. Theoretical trends of the Stark width and shift parameters versus the temperature for spectral lines of astrophysical interest are displayed.

Semi-empirical calculations of radiative decay rates in Mo II. A comparison between oscillator strength parametrization and core-polarization-corrected relativistic Hartree-Fock approaches

We present a semi-empirical determination of Mo II radiative parameters in a wide wavelength range 1716–8789Å. Our fitting procedure to experimental oscillator strengths available in the literature permits us to provide reliable values for a large number of Mo II lines, predicting previously unmeasured oscillator strengths of lines involving 4d45p and 4d35s5p odd-parity configurations. The extracted transition radial integral values are compared with ab-initio calculations: on average they are 0.88 times the values obtained with the basic pseudo-relativistic Hartree Fock method and they agree well when core polarization effects are included. When making a survey of our present and previous studies and including also those given in the literature we observe as general trends a decreasing of transition radial integral values with filling nd shells of the same principal quantum numbers for ndk(n + 1)s→ndk(n + 1)p transitions.

Inelastic Longitudinal C2 Form Factors with Core-Polarization Effects for 10B Nucleus

An effective two-body density operator for point nucleon system folded with the full two-body correlations (which include the tensor correlations and short-range correlations), which take account of the effect of the strong tensor force and the strong short-range repulsion in the nucleon–nucleon forces, is produced and used to derive an explicit form for ground-state two-body charge density distributions. The inelastic longitudinal form factors C2 are calculated using this transition charge density with excitation of the levels in 10B (J π , T):(1+, 0) at E x = 0.718 MeV, (1+, 0) at E x = 2.154 MeV, (2+, 0) at E x = 3.587 MeV, (3+, 0) at E x = 4.774 MeV, (2+, 0) at E x = 5.920 MeV, and (4+, 0) at E x = 6.025 MeV. In this work, the core-polarization transition density is evaluated by adopting the shape of Tassie model together with the derived form of the ground-state two-body charge density distributions with the effect of higher occupation probabilities η. It is noticed that the core-polarization effects which represent the collective modes are essential in obtaining a remarkable agreement between the calculated inelastic longitudinal F(q)s and those of the experimental data.

Radiative data for highly excited 3d84d levels in Ni II from laboratory measurements and atomic calculations

This work reports new experimental radiative lifetimes and calculated oscillator strengths for transitions from 3d8 4d levels of astrophysical interest in singly ionized nickel. Radiative lifetimes of seven high-lying levels of even parity in Ni II (98400 -100600 cm-1) have been measured using the time-resolved laser-induced fluorescence method. Two-step photon excitation of ions produced by laser ablation has been utilized to populate the levels. Theoretical calculations of the radiative lifetimes of the measured levels and transition probabilities from these levels are reported. The calculations have been performed using a pseudo-relativistic Hartree-Fock method, taking into account core polarization effects. A new set of transition probabilities and oscillator strengths has been deduced for 477 Ni II transitions of astrophysical interest in the spectral range 194 - 520 nm depopulating even parity 3d8 4d levels. The new calculated gf-values are, on the average, about 20 % higher than a previous calculation by Kurucz (http://kurucz.harvard.edu) and yield lifetimes within 5 % of the experimental values.

Microscopic Large Scale psd Shell Model with M3Y Residual Interaction to Calculate Electron Scattering Form Factors

The longitudinal and the transverse electron scattering form factors for 6Li, 9Be, 11B and 12C nuclei have been studied with and without core polarization effects using shell model calculations. The psdmwk is used as effective interaction for psd-shells. The core-polarization effects are calculated in the first-order perturbation theory including excitations up to 4ħω using the Michigan three-range Yakawa M3Y as a realistic interaction. The wave functions of radial single particle matrix elements have been calculated with harmonic oscillator potential. For all nuclei under studying, Comparison between experimental and theoretical calculations show that the form factors with core-polarization effect calculations give good consistency with experiment data. So we concluded that the large scale model space enhanced the results to become closed to the experimental data.

Core polarization and modern realistic shell-model Hamiltonians

The understanding of the convergence properties of the shell-model effective Hamiltonian, within the framework of the many-body perturbation theory, is a long-standing problem. The infinite summation of a certain class of diagrams, the so-called “bubble diagrams,” may be provided calculating the Kirson–Babu–Brown induced interaction, and provides a valid instrument to study whether or not the finite summation of the perturbative series is well-grounded. Here, we perform an application of the calculation of the Kirson–Babu–Brown induced interaction to derive the shell-model effective Hamiltonian for [Formula: see text]-shell nuclei starting from a modern nucleon–nucleon potential, obtained by way of the chiral perturbation theory. The outcome of our calculation is compared with a standard calculation of the shell-model Hamiltonian, where the core-polarization effects are calculated only up to third-order in perturbation theory. The results of the two calculations are very close to each other, evidencing that the perturbative approach to the derivation of the shell-model Hamiltonian is still a valid tool for nuclear structure studies.

Core-Polarization Effects on the Isoscalar and Isovector Transitions in 24Mg Using Extended Shell Model

Core-Polarization Effects on the Isoscalar and Isovector Transitions in ²⁴Mg Using Extended Shell Model

Determination of magic wavelengths for the7s S1/22−7p P3/2,1/22transitions in Fr

Magic wavelengthsfor the $7S_{1/2}-7P_{1/2,3/2}$ transitions in Fr were reported by Dammalapati \textit{et al.} in [Phys. Rev. A 93, 043407 (2016)]. These $\lambda_{\rm{magic}}$ were determined by plotting dynamic polarizabilities ($\alpha$) of the involved states with the above transitions against a desired range of wavelength. Electric dipole (E1) matrix elements listed in [J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the $7P_{1/2,3/2}$ states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $\alpha$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P-7S$, $7P-8S$ and $7P-6D$ transitions to $\alpha$ of the $7P$ states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $\alpha$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $\alpha$ are found to be in excellent agreement with the other available theoretical results; whereas substituting the E1 matrix elements used by Dammalapati \textit{et al.} give very small $\alpha$ values for the $7P$ states. Owing to this, we find disagreement in $\lambda_{\rm{magic}}$ reported by Dammalapati \textit{et al.} for linearly polarized light; especially at wavelengths close to the D-lines and in the infrared region. As a consequence, a $\lambda_{\rm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $\alpha$ will be very useful for guiding experiments to carry out their measurements.

Experimental radiative lifetimes for highly excited states and calculated oscillator strengths for lines of astrophysical interest in singly ionized cobalt (Co ii)

This work reports new experimental radiative lifetimes and calculated oscillator strengths for transitions of astrophysical interest in singly ionized cobalt. More precisely, nineteen radiative lifetimes in Co+ have been measured with the time-resolved laser-induced fluorescence technique using one- and two-step excitations. Out of these, seven belonging to the high lying 3d$^7$($^4$F)4d configuration in the energy range 90697 - 93738 cm$^{-1}$ are new, and the other twelve from th3d$^7$($^4$F)F)4p configuration with energies between 45972 and 49328 cm$^{-1}$1 are compared with previous measurements. In addition, a relativistic Hartree-Fock model including core-polarization effects has been employed to compute transition rates. Supported by the good agreement between theory and experiment for the lifetimes, new reliable transition probabilities and oscillator strengths have been deduced for 5080 Co II transitions in the spectral range 114 - 8744 nm.

Erratum: Three-cluster dynamics within anab initioframework [Phys. Rev. C88, 034320 (2013)

In this study, we introduce a fully antisymmetrized treatment of three-cluster dynamics within the ab initio framework of the no-core shell model/resonating-group method. Energy-independent nonlocal interactions among the three nuclear fragments are obtained from realistic nucleon-nucleon interactions and consistent ab initio many-body wave functions of the clusters. The three-cluster Schrodinger equation is solved with bound-state boundary conditions by means of the hyperspherical-harmonic method on a Lagrange mesh. We discuss the formalism in detail and give algebraic expressions for systems of two single nucleons plus a nucleus. Using a soft similarity-renormalization-group evolved chiral nucleon-nucleon potential, we apply the method to a 4He+n+n description of 6He and compare the results to experiment and to a six-body diagonalization of the Hamiltonian performed within the harmonic-oscillator expansions of the no-core shell model. Differences between the two calculations provide a measure of core (4He) polarization effects.

Oscillator strengths for high-excitation Ti ii from laboratory measurements and calculations

This work reports new experimental radiative lifetimes of six 3d2(3F)5s levels in singly ionized titanium, with an energy around 63 000 cm-1 and four 3d2(3F)4p odd parity levels where we confirm previous investigations. Combining the new 5s lifetimes with branching fractions measured previously by Pickering et al., we report 57 experimental log gf values for transitions from the 5s levels. The lifetime measurements are performed using time-resolved laser-induced fluorescence on ions produced by laser ablation. One- and two-step photon excitation is employed to reach the 4p and 5s levels, respectively. Theoretical calculations of the radiative lifetimes of the measured levels as well as of oscillator strengths for 3336 transitions from these levels are reported. The calculations are carried out by a pseudorelativistic Hartree-Fock method taking into account core-polarization effects. The theoretical results are in a good agreement with the experiments and are needed for accurate abundance determinations in astronomical objects. (Less)

Enhanced spin-dependent parity-nonconservation effect in the7sS1/22→6dD5/22transition in Fr: A possibility for unambiguous detection of the nuclear anapole moment

Employing the relativistic coupled-cluster method, comparative studies of the parity non-conserving electric dipole amplitudes for the $7s \ ^2S_{1/2} \rightarrow 6d \ ^2D_{5/2}$ transitions in $^{210}$Fr and $^{211}$Fr isotopes have been carried out. It is found that these transition amplitudes, sensitive only to the nuclear spin dependent effects, are enhanced by more than 3 orders compared to the low-lying $S-D_{5/2}$ transitions in Ba$^+$ and Ra$^+$ owing to the very large contributions from the electron core-polarization effects in Fr. This translates to a relatively large and, in principle, measurable induced light shift, which would be a signature of nuclear spin dependent parity nonconservation that is dominated by the nuclear anapole moment in a heavy atom like Fr. A plausible scheme to measure this quantity using the Cyclotron and Radioisotope Center (CYRIC) facility at Tohoku University has been outlined.

The Nuclear Structure for Exotic Neutron-Rich of 42, 43, 45,47K Nuclei

In this paper the proton, neutron and matter density distributions and the corresponding root mean square (rms) radii of the ground states and the elastic magnetic electron scattering form factors and the magnetic dipole moments have been calculated for exotic nucleus of potassium isotopes K (A= 42, 43, 45, 47) based on the shell model using effective W0 interaction. The single-particle wave functions of harmonic-oscillator (HO) potential are used with the oscillator parameters b. According to this interaction, the valence nucleons are asummed to move in the d3f7 model space. The elastic magnetic electron scattering of the exotic nuclei 42K (J?T= 2- 2), 43K(J?T=3/2+ 5/2), 45K (J?T= 3/2+ 7/2) and 47K (J?T= 1/2+ 9/2) investigated through Plane Wave Born Approximation (PWBA). The inclusion of core polarization effect through the effective g-factors is adequate to obtain a good agreement between the predicted and the measured magnetic dipole moments.

Many-electron correlations in computations of sodium atom photoabsorption

The role of many-electron correlations in photoabsorption processes has been investigated. The results of numerical computations of photoionization cross sections of sodium atom are presented. The many-body effects such as interchannel correlations resulting in autoionization resonance peaks, as well as effects of atomic core polarization were taken into account in the computations in terms of RPAE. Polarization corrections were accounted for using both static and dynamic polarization potentials. The influence of correlations on the position and the form of resonance peaks was studied. The obtained results demonstrate necessity of taking into account polarization effects, especially for clarification of autoionization resonance peaks position and the cross-section magnitudes in the low energy range. The best agreement with experimental data was reached with the model of dynamic polarization potential based on Dyson equation.

Interface charge transfer process in ZnO:Mn/ZnS nanocomposites

ZnO:Mn/ZnS nanocomposites were prepared by seed-mediated growth of ZnS QDs onto the preformed ZnO:Mn nanoparticles. The formation of the nanocomposite structure has been evidenced by XRD, HRTEM, and XPS. The architecture of the nanocomposite with outer ZnS QDs around ZnO:Mn cores is sustained by the sulfur and oxygen depth profiles resulted from XPS. When the two components are brought together, the band gap of ZnS component decreases while that of ZnO:Mn increases. It is the result of interface charge transfer from ZnO:Mn to ZnS QDs. Here ZnO:Mn valence states are extended through the interface into unoccupied gap states of ZnS. The energy band setup is modified from a type II into a type I band alignment. The process is accompanied by enhancement of composite UV emission of PL spectra as compared to its counterparts. The charge transfer from valence band also determines the increase of the core-polarization effect of s shell electrons at Mn2+ nucleus, thus determining the increase of the hyperfine field through the reduction of the covalency degree of Zn(Mn)–O bonds. The quantum confinement in ZnS QDs promotes the ferromagnetic coupling of singly occupied states due to Zn vacancies determining a superparamagnetic behavior of the ensemble. When the nanocomposites are formed, due to interface charge transfer effects, an increased number of filled cation vacancies in ZnS QDs develop, thus disrupting the pre-existing ferromagnetic coupling between spins resulting in a significant reduction of the overall saturation magnetization. The possibility to modulate nanocomposite properties by controlling the interface interactions may be foreseen in these types of materials.

Construction of the energy matrix for complex atoms

The continuation of series of papers concerning the construction of the energy matrix for complex atoms is presented. The second-order perturbation theory contributions originating from core polarization effects in the hyperfine structure are considered. Fifteen new formulae for angular coefficients of core polarization parameters are given. The complete set of corrections up to the second-order perturbation theory was taken into account and the accuracy of the wave functions in the intermediate coupling scheme, on the example of the lanthanum atom, was checked.

The Nuclear Structure for Exotic Neutron-Rich of 42, 43, 45,47K Nuclei

In this paper the proton, neutron and matter density distributions and the corresponding root mean square (rms) radii of the ground states and the elastic magnetic electron scattering form factors and the magnetic dipole moments have been calculated for exotic nucleus of potassium isotopes K (A= 42, 43, 45, 47) based on the shell model using effective W0 interaction. The single-particle wave functions of harmonic-oscillator (HO) potential are used with the oscillator parameters b. According to this interaction, the valence nucleons are asummed to move in the d3f7 model space. The elastic magnetic electron scattering of the exotic nuclei 42K (J?T= 2- 2), 43K(J?T=3/2+ 5/2), 45K (J?T= 3/2+ 7/2) and 47K (J?T= 1/2+ 9/2) investigated through Plane Wave Born Approximation (PWBA). The inclusion of core polarization effect through the effective g-factors is adequate to obtain a good agreement between the predicted and the measured magnetic dipole moments.

Numerical Calculation of the Wave-Vector Dependent Cole-Cole Diagram of Copper

The Cole-Cole diagram of Copper is calculated in the energy range of ⟨ 1 ; 0; 0⟩, ⟨ 1 ; 1 ; 0⟩ , ⟨ 1 ; 1 ; 1 ⟩ and ⟨ 1 ; 0; 0⟩ in the units of 2�a 1 . The modied augmented-plane- method with the Chodorow potential is utilized to calculate the energy spec- trum and Bloch wave functions. The Cole-Cole diagrams exhibit anti-clockwise rotation as the frequency increases for all q > 0. However, the rotation direction is reversed { becomes clockwise { in the spatial case q = 0. The static dielectric function deceases as q 2 , the area of the Cole-Cole diagram decreases as the wave-vector increases. The free electrons in Copper metal exhibits two plasmons for wave-vectors smaller than 0: 5 2 �a 1 . In order to show the effect of core polarization