2p Wave Research Articles

Structural and transport properties of Ni- and Ti-doped lithium manganese spinels

Rietveld refinements were performed on synchrotron X-ray powder diffraction patterns of Li1.05Mn2O4−δ, Ni- and Ti- doped Li1.05Mn2O4−δ to investigate the structural changes in conjunction with the non-adiabatic small polaron-hopping behavior. Samples with and without substitution were confirmed to belong to the Fd3¯m space group of the cubic system. The lattice parameters a and the oxygen positional parameters u decreased with increasing Ni content, and increased with increasing Ti content. In Ni-doped samples, M−O bond lengths (M: transition metal at the 16d site) were shorter and O-M-O angles were larger than those of Li1.05Mn2O4−δ. The local distortion in MO6 octahedra decreased as a result of Ni substitution. The less distorted MO6 octahedra enhanced the overlap of the Mn 3d and O 2p wave functions. This may explain why the polaron-hopping energies WH of Li1.05Mn2−xNixO4−δ (x ​= ​0.2 and 0.3) are smaller than that of Li1.05Mn2O4−δ. Ti substitution kept the increase of M−O bond length small. The O-M-O angle decreased slightly compared to that of Li1.05Mn2O4−δ, but barely changed with increasing Ti content. Structural changes in MO6 octahedra by Ti substitution were too small to affect the overlap of the Mn 3d and O 2p wave functions. This explains why the hopping energies WH of Li1.05Mn2−xTixO4−δ remained unchanged. Ni and Ti have different ionic radii from Mn. Thus, substitution of Ni and Ti modify the lattice distortion, and consequently induced a gradual increase in the self-trapped polaron’s energy, i.e., the activation energy of thermopower ES.

Bc excitations at LHC experiments

The 2S [Formula: see text] states observed by ATLAS, CMS and LHCb Collaborations are discussed. The observation perspectives of [Formula: see text], 2P wave, 3P wave and D wave states of [Formula: see text] at LHC experiments are estimated.

Bc excitations at LHC: first observations and further research prospects

Status of the Bc meson excitatons search is presented in our work. We discuss the 2S Bc states first discovered by ATLAS and newly confirmed by CMS and LHCb collaborations. We review the observation prospects for the rest predicted states (B∗c, 2P wave, 3P wave and D wave) at LHC experiments. Cascade decays to the ground state as well as direct decays to the lepton pair are regarded for these states.

PrBa 2Cu 3O 7 investigated by 141Pr Mössbauer spectroscopy

The 141Pr Mössbauer isomer shift and hyperfine field of PrBa 2Cu 3O 7 and some other praseodymium oxides were measured. When we put the isomer shift of these oxides on a linear scale, we find for PrBa 2Cu 3O 7 the mean valency 3.4(1). This value corresponds to the number of holes which goes into the Pr-2(Cu(2)-O 2) layers. The spectra below T N ≈ 17 K are broadened, but no well resolved hyperfine field split pattern is observed. We surmise that these spectra are due to relaxation. In the discussion we ascribe the different results on the valency of Pr in PrBa 2Cu 3O 7 reported in the literature to a different use of the term valency. A model is furthermore proposed in which we suggest that the correlation of the Pr4f shell introduced into the O 2p wave functions is responsible for the anomalous properties of PrBa 2Cu 3O 7

L-subshell ionization studies in Au and Bi by 4.8-8.8 MeV boron ion bombardment

L-subshell ionization of Au and Bi induced by boron impact has been investigated for impact energies ranging from 4.8 to 8.8 MeV. The results for all the three subshell ionization cross-sections show plateau like structure for the energy dependence which we feel can be attributed to plausible Stark mixing of target atomic 2s and 2p wave functions. Comparison of the data with the ECPSSR (perturbed stationary states (PSS) with projectile energy loss (E), Coulomb deflection (C) and relativistic (R) correction for target electron motion) and semiclassical approximation (SCA) calculations shows significant deviations for L 1- and L 2-subshell ionization cross-sections. The experimental X-ray production cross-sections and their ratios with respect to L α also show significant deviations from theory. Fresh calculations with more realistic target atomic wave functions and improved binding energy corrections are necessary for bringing better agreement with the experimental data.

51123 Surface residual stress analysis of metals and alloys

Abstract : The critically refracted longitudinal wave (CRLW) technique was used to establish how feasible it is to measure stress changes at the surface and interior of a material, in particular naval airframe metals such as Ti-6AI-4V, 6061-T651 Aluminum, and 4340 steel. The CRLW propagation characteristics were found to be potentially practical if use of the 2P wave is implementable to have it as a reference wave. The CRLW technique was effective in detecting stress gradients in bent plates by measuring the acoustoelastic effect on the longitudinal wave velocity. The CRLW technique was applied in the range of 1.0 to 10 MHz and the expected longitudinal wave velocity changes followed the expected trends in the A16061-T651 and 4340 steel plates (0.50 inch thick). The longitudinal wave velocity changes measured in the Ti-6Al-4V plate did not follow the expected trends probably due to its thickness (0.25 inch).

An Ab Initio Molecular Orbital Approach to Electronic Structures of the F Center in NaCl. Effects of Basis Set and Cluster Size

Abstract NaCl clusters with a Cl− ion vacancy, Na66+, Na6Cl126−, Na14Cl122+, and Na14Cl184−, are calculated by ab initio molecular orbital calculations to investigate electronic states of F centers in alkali halides. The model clusters are embedded in a point charge field. Description of “1s” ground and “2s” and “2p” excited states of an electron trapped by the vacancy is discussed concerning to basis set and cluster size. The 1s and 2p wave functions of the F-center electron are efficiently described by one s Gaussian-type function placed on the vacancy center and one p Gaussian-type functions placed on the nearest neighbor Na ions when Na 3s is of double ζ quality. The 1s–2p excitation energy is in good agreement with the experimental data. As regards the electron binding energies and the orbital size the 1s wave function almost converges in the cluster Na6Cl126− but the 2p wave function does not converge even in the largest cluster Na14Cl184−.

Hartree-Fock calculation of transition rates for atoms with multiple open shells of the same symmetry and the same occupation number.

X-ray and Auger transition rates and fluorescence yields have been calculated for the [2p,3p] vacancy states of Ar. The standard Hartree-Fock procedure leads to radial 2p wave functions with a node in the tail region. The calculated transition rates agree well with experiment. A calculation in which special techniques are employed to obtain nodeless 2p wave functions leads to rather poor estimates of the lifetimes, similar to results of earlier Hartree-Fock-Slater calculations. The frozen-core approximation, widely used to calculate Auger rates, yields erroneous results. Reasons for these difficulties are discussed.

Transfer reactions induced by 12C ON 18O and 26Mg AT 46 MeV

Angular distributions of levels observed in the 18O(12C, 10Be)20Ne, 26Mg(12C, 11B)27Al, 26Mg(12C, 10Be)28Si and 26Mg(12C, 9Be)29Si reactions have been measured at 46 MeV incident energy; some of them show a strong oscillating pattern. Spectroscopic factors extracted from a DWBA analysis of the (12C, 11B) 1p transfer with the LOLA code, are consistent with those derived from (3He, d). The influence of recoil effects on both the shapes of the angular distributions and the absolute magnitudes of cross sections have been studied for (12C, 11B) and (16O, 15N). The 2p transfer reactions leading to 20Ne and 28Si have been analyzed using realistic microscopic wave functions. Effects of configuration mixings on both the relative and the absolute cross sections are presented. The validity of approximating the 2p wave function by a 0s cluster component is discussed and some nuclear structure information is derived. The 26Mg(12C, 9Be)29Si reaction populates preferentially the same levels as the 28Si(d, p)29Si reaction. A DWBA analysis using a 3He cluster form factor gives relative spectroscopic strengths close to those derived from (d, p) stripping.

Evaluation of Two-Center Exchange Integrals

The evaluation of two-center exchange integrals for any homonuclear molecules using Slater-type wave functions is reduced to the solution of Poisson's equation. An expression is obtained for the exchange integrals in terms of integrals which can be evaluated analytically. In particular, all cases which arise from 2s and 2p wave functions are discussed in detail and the auxiliary integrals evaluated. The pertinent results are collected in tables, and the final result for a particular exchange integral is given explicitly.

Patterns of term structure in simple spectra.

view Abstract Citations (3) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Patterns of term structure in simple spectra. Layzer, David Abstract Theoretically, a pure configuration of electrons outside closed subshells has a definite, calculable pattern of term structure. For example, the two intervals between the three terms of (closed sub- shells) (p1) have the theoretical ratio 1.5. The observed patterns, however, often vary widely from atom to atom. For example, the above-mentioned ratio for (Is ) ( p1) is about -5 in Bei and 8 in BIl. Discrepancies of this kind are generally, and in my opinion correctly, ascribed to the mixing of configurations. Two obstacles have stood in the way of a successful quantitative theoretical description of configuration mixing: the lack of reliable criteria for recognizing the important components in a configuration mixture; and the lack of workable mathematical machinery for calculating the degree of mixing of given configurations. In this paper I try to overcome both these obstacles. My first point is that the data can be grouped so as to exhibit useful regularities in the structure of configuration-sequences. A configuration-sequence is defined as a set of identical configurations in an iso-electronic sequence, e.g., (Is2) ( p2) in Bei, BIl, CIII If 1(Z) is the interval between two terms of a configuration in such a sequence, Z denoting the atomic number, then the interval-difference I (Z I) - 1(Z) becomes sensibly constant for moderately large Z. The set of all independent interval-differences for a given sequence characterizes the sequence as a whole. A simple theoretical argument now shows that the structure of this set is influenced only by a very special kind of configuration mixing, which I call stable mixing. Only a small number of configurations can participate in a stable mixture, and these may be readily enumerated in every instance. I have found a method of predicting the structure of the set of interval-differences characterizing a configuration-sequence, and have successfully applied it to the sequence (is ) ( p2). This method, moreover, may be used to predict patterns of term structure in individual atoms. The crux of the method lies in the construction of analytic one-electron wave functions of a very general form. The 15, 25, and 2p wave functions are as accurate as the corresponding numerical wave functions of Hartree and Fock. The variational wave functions are used as the basis for a perturbation treatment, which can be carried out to any desired degree of accuracy. The Observatory, University of Michigan, Ann Arbor, Mich. Publication: The Astronomical Journal Pub Date: April 1951 DOI: 10.1086/106496 Bibcode: 1951AJ.....56...43L full text sources ADS |

On the Theory of the Structure of CH4 and Related Molecules. Part I1

The primary purpose of the present series of papers is to give more explicit mathematical form to the theory of Mulliken and Hund, and in some instances to the alternative theories of Pauling and Slater and of Heitler and Rumer, for valence in carbon compounds. A critical comparison is given of the Slater-Pauling and Hund-Mulliken concepts of CH4, which are based respectively on localized bonds (``electron pairs'') with the Heitler-London method, and on one-electron wave functions (Mulliken's ``orbitals'') for a self-consistent field with tetrahedral symmetry. The H-M procedure avoids hybridization of the carbon 2s and 2p wave functions, but allows two (though never three or more) electrons to accumulate on one H atom, as well as up to eight on a C atom. Inadequate cognizance is thus taken of the tendency of inter-electronic Coulomb forces to keep two electrons apart. The S-P procedure avoids this excessive accumulation, but at the expense of not letting an individual wave function be of a symmetry type (irreducible group representation) appropriate to a tetrahedral field. In particular, its s-p hybridization ``undiagonalizes'' the internal energy of the C atom. These points are illustrated by explicit exhibition of the secular determinant, which is the main new feature. Because inter-electronic repulsions make the dynamical problem more complicated than a one-electron one, the tetrahedral symmetry need only be preserved in the properties of the total wave function of the entire system rather than that of one electron, but the departures from individual tetrahedral symmetry should be less than in the Slater-Pauling theory if the Hartree self-consistent field is really a good approximation. Thus both the H-M and S-P methods, though qualitatively exceedingly illuminating, have their own characteristic drawbacks from a quantitative standpoint unless refined by inclusion of higher approximations which ultimately merge the two methods but which practically are very difficult to make.