Isotope shifts and electronic configurations of some of the energy levels of the neutral gadolinium atom

Isotope shift ΔT (156–160) have been evaluated for 52 odd and 90 even energy levels of the neutral gadolinium atom from the measurements carried out on 166 lines of the first spectrum in the region 4535–4975 Å on a photoelectric recording Fabry-Perot Spectrometer and enriched samples of ¹⁵⁶Gd and ¹⁶⁰Gd. Earlier studies provide data for just two lines in this region. Assignment of electronic configurations to some of the energy levels have been either confirmed or revised; some unassigned levels have been assigned probable configurations. The present study provides, for the first time, isotope shift of the two levels of 4f⁷6s²7 s configuration of Gd I.     

Isotope shifts in energy levels of the neutral neodymium atom

Isotope shift ΔT(142–144) have been evaluated for 281 odd and 110 even levels of the neutral neodymium atom from the isotope shift measurements made in the classified lines of Nd I spectra covering the region 3930–6510 Å. These investigations were carried out on a recording Fabry—Perot spectrometer using enriched isotopes excited in liquid-air cooled hollow cathodes. Electronic configurations of the energy levels have been discussed and probable configurations assigned to many odd and even levels. Most of the high even levels could be assigned to 4f³5d²6p configuration.     

Isotope shifts in odd and even energy levels of the neutral and singly ionised gadolinium atom

Isotope shift studies in the gadolinium spectra have been extended in the region 4140–4535 Å. Isotope shift Δσ(156–160) have been measured in 315 lines of the neutral and singly ionised galolinium atom using a recording Fabry—Perot Spectrometer and gadolinium samples enriched in ¹⁵⁶Gd and ¹⁶⁰Gd isotopes. Some of the Gd I lines studied involve transitions from newly identified high odd levels of 4f⁸6s 6p, 4f⁷5d 6s 7s and 4f⁷5d³ configurations to low even levels of 4f⁸6s² and 4f⁷6s²6p configurations. Electronic configurations of the energy levels have been discussed on the basis of observed isotope shifts. In some cases assigned configurations have been revised and probable configurations have been suggested.     

Isotope shifts in the energy levels of the singly ionized neodymium atom

Isotope shifts ΔT (142–144) have been evaluated for odd and even energy levels of the singly ionised neodymium atom from the measurements carried out in 168 spectral lines in the 3930–5820 Å region, employing a recording Fabry-Perot spectrometer and highly enriched isotopes excited in liquid-air cooled hollow cathodes. The electronic configurations 4f³5d6s, 4f³5d6p and 4f⁴6p could be assigned to some of the energy levels on the basis of the present study.     

Isotope shifts and electronic configurations of the odd parity energy levels of singly ionised samarium

Isotope shift ΔT (148–154) has been evaluated for twelve low-lying even and 89 odd parity levels of singly ionised samarium (Sm II) from the isotope shift (IS) studies in 182 spectral lines of Sm II in the 3890–4525 Å region. These studies were carried out on a recording Fabry-Perot spectrometer using eriched isotopes¹⁴⁸Sm (96%) and¹⁵⁴Sm (98%) excited in liquid nitrogen-cooled hollow-cathodes. Earlier data on isotope shifts are available for only eight lines in this region. It has been found that for a few spectral lines there are errors both in magnitudes and signs of isotope shifts, reported earlier. Most of the 89 odd parity levels of Sm II, for which ΔT values have been evaluated presently, have in literature either no electronic configuration assignments or only tentative assignments. We have suggested the leading configuration for most of these odd levels of Sm II on the basis of ΔT values evaluated in the present studies.     

A new energy level of the neutral tantalum atom

Investigating the hyperfine structure (hfs) of the not yet classified line λ=4160.99 Å we succeeded in the determination of the electronic angular momenta of the combining levels and in the identification of the lower level using the hfs constants of all known levels as a finger-print card-index. In this way the lower level turned out to be thea ² G _9/2 level, which has even parity. Using the energy of this level and the wavenumber of the transition it was possible to determine the energy of the (odd parity) upper level to 34716.23 ± 0.02 cm^?1. The total angular momentum quantum number amounts toJ=11/2. Additionally, it was possible to identify the line λ=3436.00 Å as a further combination with this new level.     

Reevaluation of term isotope shifts of low even levels of 4f86s2 configuration and high odd-parity levels of neutral gadolinium atoms

Isotope shift ΔT(¹⁵⁶Gd–¹⁶⁰Gd) of the even-parity energy levels of 4f⁸6s² and 4f⁷6s²6p configurations of neutral gadolinium atoms (Gd I) have been reevaluated using the level isotope shift (ΔT) of two odd-parity levels reported recently. Earlier the isotope shifts of these even-parity energy levels were evaluated using empirical relation. Our extensive isotope shift data has been used for the reevaluation of ΔT values of these low even-parity energy levels which have been utilised for revision of the ΔT values of high-lying odd-parity energy levels of Gd I.     

Lower bounds for the energy levels of the lithium atom

A recent modification of the intermediate hamiltonian method, intended to circumvent the problem associated with a low-lying continuum in the operator H⁰, has been applied to the lithium atom with a basis of discrete hydrogenic functions. The intended raising of the continuum occurs, but not to the extent that the beginning of the continuum is raised above the ground state of the atom; indications are that no basis of discrete hydrogenic eigenfunctions can accomplish this. Since these calculations were performed on the full lithium atom hamiltonian, they are not strictly comparable to those of Fox and Siglillito, in which a simplified hamiltonian was used.     

Shifted large-N expansion for the energy levels of neutral atoms

Energy levels of neutral atoms have been re-examined by applying the method of shifted large-N expansion (whereN is the number of spatial dimensions) to the model Yukawa potential with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number Z up to 84 and compare very well with those obtained within the framework of hypervirial-Padé scheme. It is observed that the large-N technique which is hitherto used in different contexts may also be applied to other areas of atomic physics.     

Effect of electron correlation on the Pa atom energy levels and electron coupling

The lower energy levels of the protactinium (Pa) atom are unusually difficult to treat theoretically. Pa is located where the 6d and 5f energies cross; simple calculations consistently put the electron configurations $5f^16d^27s^2$ and $5f^26d^17s^2$ in the incorrect order. We have used multireference spin?Corbit configuration interaction to compute the energies of these states to determine which additional interactions need to be included. We also discuss the less common J ₁ j coupling scheme suggested for these atomic states with applications also to the $5f^16d^2$ and $5f^26d^1$ states of $\hbox{Pa}^{2+}$ .     

The regularities of the Rydberg energy levels of many-valence electron atom Al

Within the scheme of the weakest bound electron potential model theory, the concept of spectral-level-like series is presented by reasonably classifying the Rydberg energy level of atom Al. Based on this concept, the regularities of the Rydberg energy levels are systematically studied. The deviations of the calculated values from the experimental values are generally about several percent of 1 cm, which is of high accuracy.     

Computer simulation of neutral atom traps

In this paper an efficient technique to compute properties of magnetic traps with axially symmetric configurations is presented. The corresponding computer code is available. By way of example we discuss quadrupole and octupole traps of comparable trapping volume and field strength. First the quality of the multipole expansion used to represent the field is tested and then Monte Carlo calculations for the efficiency of the traps are performed. They show the octupole configuration to be slightly more efficient than the quadrupole one.     

Isotope shift studies and electronic configuration assignments to the energy levels of neutral erbium

Isotope shifts ΔT (170-166) have been evaluated for 54 even and 94 odd energy levels covering almost all the known configurations of the neutral erbium. These ΔT values have been derived from the isotope shift measurements carried out in 159 lines in the region 3900–4605 A using a Fabry-Perot spectrometer and liquid-air-cooled hollow cathode source with highly enriched ¹⁷⁰Er and ¹⁶⁶Er isotopic samples. Electronic configurations assigned to energy levels of Er I by earlier workers have been mostly confirmed and in few cases revisions have been suggested on the basis of observed ΔT values. Probable configurations have been also suggested for unassigned levels of Er I, and a large number of even levels could be assigned to 4f¹¹ 5d 6s 6p configuration.     

Sigmatropic shifts and cycloadditions on neutral, cationic, and anionic pentadienyl+butadiene potential energy surfaces

Quantum chemical calculations were used to characterize [4,5] sigmatropic shifts in systems containing butadiene and pentadienyl substructures. Cationic, anionic, and radical systems with various tethers connecting these substructures were examined. In many cases, concerted [4,5] sigmatropic shifts with asynchronous bond making and breaking events were observed. The fundamental connections between [4,5] sigmatropic shifts and (5+4) cycloadditions are highlighted.     

Rational enhancement of the energy barrier of bis(tetrapyrrole) dysprosium SMMs via replacing atom of porphyrin core

With the coordination geometry of Dy^III being relatively fixed, oxygen and sulfur atoms were used to replace one porphyrin pyrrole nitrogen atom of sandwich complex [(Bu)₄N][Dy^III(Pc)(TBPP)] [Pc = dianion of phthalocyanine, TBPP = 5,10,15,20-tetrakis[(4-tert-butyl)phenyl]porphyrin]. The energy barrier of the compounds was enhanced three times, with the order of Dy^III(Pc)(STBPP) > Dy^III(Pc)(OTBPP) > [(Bu)₄N][Dy^III(Pc)(TBPP)] [STBPP = monoanion of 5,10,15,20-(4-tert-butyl)phenyl-21-thiaporphyrin, OTBPP = monoanion of 5,10,15,20-(4-tert-butyl)phenyl-21-oxaporphyrin]. Theoretical calculations offer reasonable explanations of such a significant enhancement. The energy barrier of 194 K for Dy^III(Pc)(STBPP) represents the highest one among all the bis(tetrapyrrole) dysprosium SMMs, providing a strategy to rationally enhance the anisotropy and energy barrier via atom replacement.     

Term isotope shift of high lying odd and even energy levels of Nd II

The isotope shifts of the odd and even parity energy levels of singly-ionised neodymium (Nd II) have been evaluated using the measurements carried out in more than 300 spectral lines of Nd II in the region 3290–5820 Å. Term shift, ΔT (¹⁴⁴Nd-¹⁵⁰Nd), is being reported for 23 low even and 15 high lying even parity levels of Nd II. ΔT for a level of 4f ³6s6p configuration and 8 even levels between 36892 and 43212 cm^-1 are being reported for the first time. ΔT values of 151 high lying odd parity levels are being reported and compared with some of the available earlier reported values. ΔT values of 47 odd parity levels are being reported for the first time, most of which are based on our isotope shift studies in UV region. The electronic configuration assignments to energy levels of Nd II by earlier workers are discussed on the basis of present ΔT values. Electronic configurations to some of the unclassified high lying odd levels have been suggested; the levels with ΔT (144–150) between 300mK and 380mK are assigned to 4f ³5d6s configuration whereas a level with ΔT value of 60mK to 4f46p configuration.