Increase In Nuclear Charge Research Articles

Influence of relativistic effects on photoionization process of hydrogen-like ions in plasma environment

In this study, the photoionization cross sections of C<sup>5+</sup>, Al<sup>12+</sup>, and W<sup>73+</sup> ions in a Debye plasma environment are calculated in the dipole approximation. The main emphasis is placed on investigating the influence of relativistic effects on shape resonances, Cooper minima, and virtual state effects. The relativistic effects lead to fine-structure splittings, allowing the appearance of double-shape resonance peaks in the total cross-section. Because the width and energy position of resonance peak are affected by the near critical screening length, the increase of nuclear charge Z leads to the significant differences in the size, width, and position of the double-shape resonance peak. The energy position of Cooper minimum in the photoelectrons is related to the critical screening length corresponding to the final continuum state. Unlike the deeper minima observed in the total photoionization cross-sections for C<sup>5+</sup> and Al<sup>12+</sup> ions, for the higher nuclear charge of W<sup>73+</sup> ions, the significant fine-structure splitting arising from relativistic effects results in substantial differences in the positions of the Cooper minima in the partial cross-sections. Therefore, when superimposed on the total cross section, these minima appear shallower. The W<sup>73+</sup> ion has a higher nuclear charge, and the screening length related to the virtual state effect is completely different from that of C<sup>5+</sup> ion and Al<sup>12+</sup> ion. Moreover, for the same screening length, there is a significant difference in the virtual state enhancement amplitude between C<sup>5+</sup> ion and Al<sup>12+</sup> ion in the low energy region .

Plasma screening effect on electron-electron interactions

In the calculation of atomic structures within the plasma environment, the plasma screening effect on nuclei - electron interactions is generally considered, but the plasma screening effect on electron - electron interactions is less considered. In this work, the MCDHF method combined with the screening potential is used to study plasma screening effect on the atomic structure parameters versus the electron density, electron temperature, nuclear charge and the number of bound electrons. For the ground states and the first excited states of helium-like ions, the energy shifts, transition energy shifts and transition probability shifts caused by the plasma screening effect on electron-electron interactions increase with the increase of electron densities and decrease with increasing the electron temperatures, respectively. With the increase of nuclear charge, the energy shifts increase gradually and tends to a stable value, while the transition energy shifts and transition probability shifts decrease gradually and tend to 0. The energy shifts increase with the increase of the number of bound electrons. The electron density, electron temperature, nuclear charge and number of bound electrons corresponding to the percentages of transition energy shifts and transition probability shifts caused by plasma screening on electron-electron interactions greater than or equal to 10%, are called as the critical electron density, critical electron temperature, critical nuclear charge and critical number of bound electrons, respectively. When one of the following four conditions is satisfied, the percentages of transition energy shifts and transition probability shifts caused by plasma screening on electron-electron interactions will be greater than or equal to 10%, and the plasma screening effect on electron - electron interactions can not be ignored. 1) The electron density is greater than or equal to the critical electron density, when the electron temperature is a fixed value. 2) The electron temperature is less than or equal to the critical electron temperature, when the electron density is a fixed value. 3) The nuclear charge is less than or equal to the critical nuclear charge, when the electron density and temperature are both fixed. 4) The number of bound electrons is greater than or equal to the critical number of bound electrons, when the electron density and temperature are both fixed.

A problem with explaining the electron configuration of scandium

The statements and arguments based on experimental evidence used to support the claim that the 3d sub-level is below the 4s sub-level in scandium are examined. The flaw in all the arguments is that they assume the order in which the 3d and 4s sub-levels arrange remains the same in both the neutral atom and in its ions. Analysis of the ground and excited states of atomic spectra shows that as the number of electrons relative to the nuclear charge increases, the 3d level moves higher in energy relative to the 4s level. It is perfectly possible that in a neutral scandium atom the 3d sub-level is above the 4s sub-level and that when it ionizes the energy levels simultaneously rearrange during the process.

A DFT study on the complex formation between desferrithiocin and metal ions (Mg2+, Al3+, Ca2+, Mn2+, Fe3+, Co2+, Ni2+, Cu2+, Zn2+)

In recent years, Metal-chelating compounds, namely siderphores have been considered very much because of their crucial role in various fields of the environmental researches. Their importance lies in the fact that they are able to be bonded to a variety of metals in addition to iron. A theoretical study on the structures of desferrithiocin siderphore coordinated to Mg2+, Al3+, Ca2+, Mn2+, Fe3+, Co2+, Ni2+, Cu2+ and Zn2+ metal ions was carried out, using the CAM-B3LYP/6-31G(d) level of the theory in the water. In order to understand the factors which control the stability, reactivity and the strength of toxic metals excretion as well as microbial uptake of the metal-siderphore complexes, we examined the stability and binding energies of the desferrithiocin and various metal ions with different spin states. The binding affinity of desferrithiocin to Fe3+ (log β2=23.88) showed that the desferrithiocin can scavenge the excess iron(III) from the labile sources. Also, the binding energy values were well described by addition of the dispersion-corrected D3 functional. Because of the importance of the charge transfer in the complex formation, donor-acceptor interaction energies were evaluated. Based on this analysis, an increase in the effective nuclear charge increases E(2) values. Vibrational analysis showed that the critical bonds (CO stretching and CH bending) are in the range of 1300–1800cm−1. Finally, some probable correlations between the complexation behavior and quantum chemistry descriptors have been analyzed.

The role of postcollisional effects in multiple ionization of diatomic molecules by multiply-charged ion impact

An analysis of the influence of postcollisional effects in multiple ionization of diatomic molecules for impact of He2+ and C6+ beams is made. A comparison between the present theoretical results with the ones previously obtained for impact of proton beams shows that contribution of Auger-type processes becomes less important compared to direct ionization ones as the value of the projectile nuclear charge increases.

A study of quasidegeneracy effects in the be-isoelectronic series

Coupled-pair (CPMET), doubly-excited configuration interaction (D-CI) and linear coupled-pair (LCPMET) calculations on several members (Li−, Be, B+, C2+, Ne6+, Ar14+, Zn26+) of the Be-isoelectronic series are reported and compared with other methods such as perturbation theory. Special attention is given to the reliability of coupled-pair methods for both positive and negative ions in the presence of quasidegeneracy. The impact of disconnected quadruply excited configurations is significant for Li− and decreases considerably for the positive ions as the nuclear charge increases. The present single-reference state results indicate that coupled-pair methods are considerably more accurate than perturbation theory in the quasidegenerate systems considered. It is also emphasized that the description of quasidegeneracy effects should take into account both the energies of the configurations involved and the relative magnitudes of these configurations in the wave function.

Can correlation bring electrons closer together?

We discuss the exact Coulomb hole for the ground state of the helium atom and helium-like ions. We find that the correlated wavefunction yields a smaller probability of finding the electrons at large separations than does the Hartree–Fock wavefunction, leading to the counterintuitive conclusion that correlation brings distant electrons closer together. This effect becomes less pronounced as the nuclear charge increases.

Correlation energies for the He isoelectronic sequence with Z = 1–120 from the third-order Douglas–Kroll Hamiltonian

Recently it has been found that the correlation energies (CEs) for He-like ions derived from the four component relativistic Hylleraas configuration interaction decrease rapidly as the nuclear charge increases. This is in contrast to nonrelativistic results, for which the values are almost constant irrespective of the nuclear charge Z. Here, it is shown that the CEs of He-like ions from the third-order Douglas–Kroll Hamiltonian with a large Gaussian type set 33s28p28d28f show a similar trend to the four component relativistic CEs, although the absolute values of the calculated CEs are considerably greater than those of the four component ones.

Fully relativistic coupled-cluster static dipole polarizabilities of the positively charged alkali ions from Li+ to 119+

The static dipole polarizabilities of the positively charged alkali atoms from Li+ to 119+ (eka-Fr) were obtained from relativistic coupled-cluster theory using a scalar relativistic Douglas–Kroll Hamiltonian. Spin–orbit coupling effects were obtained from a fully relativistic four-component Dirac–Hartree–Fock scheme followed by a second-order many-body perturbation treatment to account for electron correlation. Electron correlation effects are found to be small for all ions, but become more sizable as the nuclear charge increases. Scalar relativistic effects dominate over electron correlation for Cs+, Fr+, and 119+. Spin–orbit coupling is non-negligible for the heaviest elements Fr+ and 119+, where they dominate over both electron correlation and scalar relativistic effects. Breit interactions obtained for Cs+ and Fr+ can safely be neglected. A relationship between dipole polarizabilities and second ionization potentials is established. The use of a basis set limit one-electron description and a high level treatment of electron correlation and relativistic effects makes our results the most accurate available for the stable dipole polarizabilities (1.00±0.04 a.u. for Na+, 5.52±0.04 a.u. for K+, 9.11±0.04 a.u. for Rb+, 15.8±0.1 a.u. for Cs+, 20.4±0.2 a.u. for Fr+, and 32±1 a.u. for 119+).

Field Enhanced Dielectronic Recombination of Lithiumlike Ti19+ and Ni25+ Ions

Within a series of systematic measurements of the dielectronic recombination (DR) of lithiumlike ions in the presence of external fields we have determined the absolute recombination rates of Ti19+ and Ni25+ ions. In both cases the electron energy range covers all DR resonances attached to 2s → 2p1/2 and 2s → 2p3/2 Δn = 0 core excitations. The experimental resolution permits the study of the field effects for the two 2pjnℓ series of Rydberg DR resonances separately. For both the Ti19+ and the Ni25+ ions the electric field induced enhancement is by factors of up to 1.8 stronger for the 2p3/2 series than for the 2p1/2 series. Moreover, we find that the magnitude of the field induced DR rate enhancement becomes smaller as the nuclear charge increases. The dependence of the DR rate coefficient on magnetic fields in an E × B field configuration, that was only recently established by theory and experiment, is also found for Ti19+, whereas for Ni25+ a change of the magnetic field over the range 42–80 mT did not significantly influence the DR rate enhancement induced by the electric field.

Relativistic X-ray Elastic Scattering Factors for He–Ar from Dirac–Hartree–Fock Wave Functions

X-ray and electron elastic scattering factors for He through Ar ground states have been computed from Dirac–Hartree–Fock (DHF) wave functions. Differing from earlier studies, the present DHF wave functions are not restricted to single configurations and will go into the nonrelativistic Hartree–Fock (HF) ground states when the speed of light c → \infty. The relativistic effects have been analyzed through the differences of scattering factors calculated at DHF and HF levels of theory. It has been found that the effects become stronger as the nuclear charge increases and anomalous behavior observed in the literature for C, N, O, Si, P and S is due to the use of either single- or average-energy multiconfiguration DHF wave functions to extract the relativistic effects for these systems preventing attainment of the correct nonrelativistic limit. Scattering factors of common ions of the first- and second-row elements and the valence state of C and Si are also given.

On the electron affinities of the Ca, Sc, Ti and Y atoms

For the Ca, Sc, Ti and Y atoms calculations are performed for the ground states of the neutrals and the ground and several low-lying excited states of the negative ions. Overall the computed electron affinities are in good accord with experiment. The calculations show the rapid stabilization of the 3d orbital relative to the 4p as the nuclear charge increases. The 3F° and 3D° terms are found to be close in energy in Sc − and in Y −. This confirms earlier speculation that some of the peaks in the photodetachment spectra of Y − originate from the bound excited 3F° term of Y −.

Effects of configuration mixing in M1 and E2 transitions between ground-state terms of sulfurlike ions.

Magnetic-dipole and electric-quadrupole transition rates for S-like ions between ground-state terms have been calculated using multiconfiguration Dirac-Fock wave functions. Sudden changes were found in these transition rates from one element to the next where there is a change of the dominant configuration. Also, ordering of the levels changes as the nuclear charge increases, but this is not necessarily reflected as a sudden change in transition rates. Our results demonstrate the necessity of using multiconfiguration calculations in the study of the systematics of transition rates along isoelectronic sequences.

The 4s2S–4p2P transition of the Al sequence

In the Hartree–Fock approximation the f-value trend for the 4s2S–4p2P transition of the Al sequence varies smoothly as the nuclear charge increases. The effect of the core is primarily a screening effect. However, when correlation with the core is included, 'accidental' degeneracies with other configurations at selected Z-values destroy the usually smooth trend and dips appear.The f-values for these transitions are presented and the various effects illustrated.

1s22s2S1/2-1s2s2p4P5/2and 1s22s21S0-1s22s2p3P2magnetic quadrupole transitions

A Z-expansion method is used to calculate the energies (including first-order relativistic corrections) and probabilities of 1s22s2S1/2-1s2s2p4P5/2 and 1s22s2 1S0-1s22s2p3P2 magnetic quadrupole transitions in the lithium and beryllium sequences respectively. It is found that, compared to spin-spin autoionization to the 1s2kf2F5/2 continuum level, the magnetic quadrupole decay of 1s2s2p4P5/2 to the ground state becomes increasingly significant as the nuclear charge increases. Probabilities for the 1S0-3P2 transition are found to be small.

The relationship between energies and spontaneous fission periods

This present study is an attempt to establish the relationship between energies and spontaneous fission periods of even—even nuclei. Spontaneous fission is a tunnel effect, and thus from general considerations one might expect that spontaneous fission periods, in analogy toα-decay [1, 2], would show a tendency to increase with increase in nuclear charge Z and with decrease in spontaneous fission energy E∼f,† and would also depend on mass number A. In fact, for other conditions equal increase in Z leads to an increase in barrier expansion, while increase in E∼f leads to a decrease in its permeability. Growth in A on the one hand increases the corrected fragment mass, thus hindering its passage through the barrier, while on the other hand it leads to increase in fragment dimensions, which reduces barrier height. By considering the influence of shell and subshell effects on E∼f we may, to a certain degree, consider the influence of these effects on spontaneous fission period. For calculation of E∼f the combined method was employed. Accurate experimental values of nuclear mass and transition energy [3] were used; in their absence formulas for nuclear transition energy base on the detailed experimental data of [4] were employed.

Alpha- and proton-induced x-ray deexcitation of titanium

Measurements of Kα and Kβ x rays induced by proton and α-particle beams from an electrostatic accelerator show a divergence from the normal x-ray spectra as the nuclear charge increases. These measurements are consistent with the explanation that the ion excitation produces multiple inner-shell electron vacancies, which in turn cause electronic-shell energy shifts. The intensity of these shifted lines is a measure of the amount of multiple inner-shell ionization.

Perturbation Corrections to the Uncoupled Hartree–Fock Method. Dipole Polarizabilities of the Neon Isoelectronic Sequence

The polarizability, α = α0 + α1, for the 10-electron atomic systems Ne, Na+, Mg2+, Al3+, and Si4+ has been calculated by the uncoupled Hartree–Fock method with the perturbation correction of Tuan and co-workers (PUCHF Method). The correction is rather significant, with the percentage ratio α1 / α% being around 20%. The contributions to α from individual orbitals were also investigated. It is shown that the outermost orbitals and the orbitals along the direction of external electric field give the largest contribution to α: The contribution from the two 2p0 orbitals is around 31.1%–42.2%. The α obtained by the PUCHF method differs from the coupled Hartree–Fock (CHF) method by 3.6% to 4.8% except for the neutral atom Ne which differs by 7.8%. The agreement of α between the PUCHF and CHF methods improves with increase of nuclear charge, as has been observed previously for the dipole and quadrupole polarizabilities of He, Li, and Be isoelectronic sequences by Epstein and Johnson. It is concluded that (1) the PUCHF method offers a simple and tractable way to study the contribution of individual orbitals to physical properties, and (2) for polarizabilities of positive ions the PUCHF method gives results with accuracy comparable to those obtained from the CHF method.

The variations in the thermal stabilities of the trichlorides, tribromides, and tri-iodides of the metals of the first transition series at 25°c

The problem of the variations in the feasibilities of the following decompositions at 25° MX3(s)→ MX2(s)+½X2(usual form) in going across the transition series from M = Sc to M = Zn, for X = Cl, Br, and I, is examined by stating it precisely, restating it precisely in a form that is more susceptible to theoretical study, and then studying it theoretically. It is found, by use of current theories, that the overall increases in feasibility across the series may be attributed to the increase in nuclear charge, that the discontinuities Cr Fe < Co may be attributed to the reversion of the gain in “exchange” energy in going from M3+ to M2+ to zero after the d shell has become half full, and that the fluctuations in the ligand-field stabilisation energies of the halides have only a mitigating effect.

Thick Target Fast Neutron Yield from 15-Mev Deuteron and 30-Mev Alpha-Bombardment

The total yield and angular distribution of fast neutrons from bombardment of thick targets of pure Be, Al, Ti, Cr, Mn, Co, Cb, Mo, Ag, Cd, Ta, Au, Pb, and Bi by 15-Mev deuterons and 30-Mev alpha-particles was measured. These studies were made using the reaction ${\mathrm{S}}^{32}(n,p){\mathrm{P}}^{32}$ as a threshold detector and also with fission ionization chambers. The total neutron yield per second per \ensuremath{\mu}amp of the cyclotron beam, $N$, was observed to decrease with increase in nuclear charge, $Z$, of the target according to the approximate empirical equations, $logN=10.18\ensuremath{-}0.0234Z$ for deuteron bombardment and $logN=9.68\ensuremath{-}0.0234Z$ for alpha. In all cases studied, the angular distribution of fast neutrons from target bombarded by deuterons showed a pronounced peak in the yield in the forward direction.