Nonspherical Charge Research Articles

Investigation on the electromagnetic properties of the D(∗)Σc(∗) molecules

We systematically explore their electromagnetic characteristics to improve our understanding of the quark-gluon dynamics underlying the complex and controversial nature of multiquark systems. In this study, the magnetic dipole moments of DΣc, DΣc∗ and D∗Σc doubly-charmed pentaquarks are extracted, which are directly related to the inner organization of the relevant states. The magnetic dipole moments of these pentaquarks are evaluated employing the QCD light-cone sum rules technique with isospin spin-parity I(JP)=12(12-), I(JP)=12(32-) and I(JP)=12(32-), for DΣc, DΣc∗ and D∗Σc doubly-charmed pentaquarks, respectively. Our predictions for the magnetic dipole moment μDΣc=2.98-0.54+0.76μN for the DΣc pentaquark, μDΣc∗=1.65-0.34+0.45μN for the DΣc∗ pentaquark, and μD∗Σc=-3.63-0.60+0.79μN for the D∗Σc pentaquark. Furthermore, we have also extracted the electric quadrupole and the magnetic octupole moments of the DΣc∗ and D∗Σc doubly-charmed pentaquarks. These values show a non-spherical charge distribution. As a by-product, the magnetic dipole moments of the isospin-32 partners associated with these doubly-charmed pentaquarks have also been determined. The magnetic dipole moments are calculated as follows: μDΣc=3.78-0.70+0.94μN, μDΣc∗=2.08-0.43+0.57μN, μD∗Σc=-4.59-0.76+0.99μN for the isospin-32 partners DΣc, DΣc∗ and D∗Σc doubly-charmed pentaquarks, respectively. We hope that our predictions of the magnetic dipole moments of the doubly-charmed pentaquarks, in conjunction with the results of other theoretical investigations of the spectroscopic parameters and decay widths of these intriguing pentaquarks, will prove valuable in the search for these states in future experiments and in elucidating the internal structure of these pentaquarks.

A connection between the Darwin term and a nonspherical charge distribution

A derivation of the Darwin term is given based on assuming a nonspherical charge distribution. The total translational energy of the system is obtained for a static electric field, and the corresponding quantum equation is found to contain the Darwin term under certain conditions.

Electromagnetic properties of the Σc(2800)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{c}(2800)^+$$\\end{document} and Λc(2940)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _c(2940)^+$$\\end{document} states via light-cone QCD

The Σc(2800)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{c}(2800)^+$$\\end{document} and Λc(2940)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _c(2940)^+$$\\end{document} states are among the most interesting and intriguing particles whose internal structures have not yet been elucidated. Inspired by this, the magnetic dipole moments of the Σc(2800)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{c}(2800)^+$$\\end{document} and Λc(2940)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _c(2940)^+$$\\end{document} states with quantum numbers JP=12-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^P = \\frac{1}{2}^-$$\\end{document} and JP=32-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^P = \\frac{3}{2}^-$$\\end{document}, respectively, are analyzed in the framework of QCD light-cone sum rules, assuming that they have a molecule composed of a nucleon and a D(∗)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D^{(*)}$$\\end{document} meson. The magnetic dipole moments are obtained as μΣc+=0.26±0.05μN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _{\\Sigma _c^{+}}=0.26 \\pm 0.05~\\mu _N$$\\end{document} and μΛc+=-0.31±0.04μN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _{\\Lambda _c^{+}}=-0.31 \\pm 0.04~\\mu _N$$\\end{document}. The magnetic dipole moment is the leading-order response of a bound system to a weak external magnetic field. It therefore offers an excellent platform to explore the inner organization of hadrons governed by the quark-gluon dynamics of QCD. Comparison of the findings of this analysis with future experimental results on the magnetic dipole moments of the Σc(2800)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{c}(2800)^+$$\\end{document} and Λc(2940)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _c(2940)^+$$\\end{document} states may shed light on the nature and internal organization of these states. The electric quadrupole and magnetic octupole moments of the Λc(2940)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _c(2940)^+$$\\end{document} states have also been calculated, and these values are determined to be QΛc+=(0.65±0.25)×10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {Q}}_{\\Lambda _c^+} = (0.65 \\pm 0.25) \ imes 10^{-3}$$\\end{document} fm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^2$$\\end{document} and OΛc+=-(0.38±0.10)×10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal {O}}_{\\Lambda _c^+} = -(0.38 \\pm 0.10) \ imes 10^{-3}$$\\end{document} fm3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}, respectively. The values of the electric quadrupole and magnetic octupole moments show a non-spherical charge distribution. We hope that our estimates of the electromagnetic properties of the Σc(2800)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{c}(2800)^+$$\\end{document} and Λc(2940)+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _c(2940)^+$$\\end{document} states, together with the results of other theoretical studies of the spectroscopic parameters of these states, will be useful for their search in future experiments and will help us to define the exact internal structures of these states.

Magnetic and quadrupole moments of the , , and states in the diquark-antidiquark picture

The magnetic and quadrupole moments of the , , and states are calculated within the QCD light-cone sum rules. The compact diquark-antidiquark interpolating currents and the distribution amplitudes of the on-shell photon are used to extract the magnetic and quadrupole moments of these states. The magnetic moments are acquired as , , and for the , , and states, respectively. The magnetic moments evaluated for the , , and states are sufficiently large to be experimentally measurable. The magnetic moment is an excellent platform for studying the internal structure of hadrons governed by the quark-gluon dynamics of QCD because it is the leading-order response of a bound system to a weak external magnetic field. The quadrupole moment results are , , and for the , , and states, respectively. We obtain a non-zero, but small, value for the quadrupole moments of the states, which indicates a non-spherical charge distribution. The nature and internal structure of these states can be elucidated by comparing future experimental data on the magnetic and quadrupole moments of the , , and states with the results of the present study.

The Bosons of the Conventional Superconductors

For the conventional superconductors it will be shown that not only the superconducting energy gap, Egap(T=0), and the critical field, Bc(T=0), but also the London penetration depth, λL(T=0), scale in a reasonable approximation with the superconducting transition temperature, TSC, as ~TSC, ~TSC2 and ~T-1/2, respectively. From these scaling relations the conclusion obtained earlier, using a completely different method, is confirmed that the London penetration depth corresponds to the diameter of the Cooper-pairs. As a consequence, only one layer of Cooper pairs is sufficient to shield an external magnetic field completely. The large diamagnetism of the superconductors is caused by the large orbital area of the Cooper-pairs. From the fact that, in the zero-field ground state, the temperature dependence of the superconducting heat capacity is given above and below TSC by power functions of absolute temperature it follows that the only critical point is T=0. The superconducting transitions of the element superconductors, therefore, are all within the critical range at T=0. As a consequence, above and below TSC there is short-range order only. As we know from Renormalization Group (RG) theory, in the critical range the dynamics is the dynamics of a boson field, exclusively. Evidently, the Cooper-pairs have to be considered as the short-range ordered units created by this boson field. It is reasonable to assume that the relevant bosons in the superconducting state are identical with the bosons giving rise to the universal linear-in-T electronic heat capacity above TSC. Plausibility arguments will be given that these bosons must be electric quadrupole radiation generated by the non-spherical charge distributions in the soft zones between the metal atoms. The radiation field emitted by an electric quadrupole can be assumed to be essentially curled or circular. In the ordered state below TSC, the bosons are condensed in resonating spherical modes which encapsulate the two Cooper-pair electrons and shield their charge perfectly.

Electromagnetic form factors of the Bc-like tetraquarks: Molecular and diquark-antidiquark pictures

In this study, we use the molecular and diquark-antidiquark tetraquark pictures to investigate magnetic and quadrupole moments of the Bc-like ground state tetraquarks with the QCD light-cone sum rules with quantum numbers JP=1+. In the numerical analysis, to obtain the magnetic and quadrupole moments of Bc-like tetraquark states molecular and diquark-antidiquark forms of interpolating currents, and photon distribution amplitudes have been used. The magnetic moments are acquired as μZucu¯b¯Mol=1.18−0.40+0.52μN, μZucu¯b¯Di=3.05−0.95+1.19μN, μZdcd¯b¯Mol=0.32−0.10+0.18μN, and μZdcd¯b¯Di=2.38−0.75+0.95μN. The hadrons' magnetic and quadrupole moments are another fundamental observable as their mass, which provides information on the underlying quark structure and dynamics. The results obtained in both pictures are quite different from each other. Any experimental measurement of the magnetic moments can provide an understanding of the internal structure of these states. We get nonzero but small values for the quadrupole moments of Bc-like tetraquark states showing non-spherical charge distributions. Hopefully, the examinations given in this study will be helpful to an experimental search of them, which will be an interesting research subject.

Evaluating the shape and orientation effect of non-spherical charge on the pressure distribution of underwater explosion: Finite element analysis

Limited studies available are presented to investigate the shape and orientation effect of pressure distribution and peak pressure of non-spherical charge in near-field underwater explosion (UNDEX). A detailed 3-D finite element model based on arbitrary Lagrange-Euler (ALE) algorithm is used to study the near-field pressure distribution of UNDEX within infinite water field. The numerical results of the model are verified against the empirical results. The influence of the shape and orientation effect on the pressure distribution was also analyzed based on the numerical data. It is found that the model is suitable for the reproduction of the near-field shock waves for the non-spherical explosives within infinite water field. The shape and orientation effect have significant impact on the pressure distribution of near-field UNDEX. The deviation of the incipient pressure of the non-spherical charges from the constant-mass spherical charge (C0) increases with the length-to-diameter ratio increasing. Compared with the cylindrical charge (C1), the peak pressure of spherical charge continue to reduce with lower attenuation speed in the same propagation time from 0.02 ms to 0.22 ms. However, the peak pressure of cuboid charge is not monotone changing with the same propagation time. The pressure distribution and peak pressure of UNDEX have direct relation with the detonation modes, especially in the near-field region. A reference formula for the peak pressure of the non-spherical charge is also obtained to provide a reference for engineering design.

Electromagnetic properties of doubly heavy pentaquark states

Motivated by the latest discovery of doubly charmed tetraquark \(T^+_{cc}\) by LHCb collaboration, we have studied the magnetic moments of the possible doubly heavy pentaquark states with quantum numbers \(J^P = 1/2^-\) and \(J^P = 3/2^-\) within the light-cone sum rules method. In the analysis, these possible pentaquark states are considered in diquark–diquark–antiquark structure. The magnetic moments of hadrons encode helpful details about the distributions of the charge and magnetization inside the hadrons, which help us to figure out their geometric configurations. As a by-product, the electric quadrupole and magnetic octupole moments of the spin − 3/2 doubly heavy pentaquark states are also extracted. These values show a non-spherical charge distribution. It will be interesting and useful to examine the magnetic moments of these possible doubly heavy pentaquark states with different theoretical approaches.

Electromagnetic properties of the $$ D \bar{D}^* K$$ molecular hexaquark state

We systematically study the electromagnetic properties of multiquark states. In this study, inspired by the recent series of studies that showed the likely existence of a $$ D \bar{D}^* K$$ state, we examine the magnetic moment of $$ D \bar{D}^* K$$ hexaquark state in three-meson molecular structure, as well as having isospin and spin-parity quantum numbers $$I(J^P) =3/2(1^-)$$ via light-cone sum rules. The magnetic moment obtained for the $$ D \bar{D}^* K$$ molecular hexaquark state is quite large due to the double electric charge, and its magnitude indicates that it is accessible in future experiments. As a byproduct, the quadrupole moment of the $$ D \bar{D}^* K$$ molecular hexaquark state is also extracted. This value indicates a non-spherical charge distribution. The magnetic moments of hadrons contains valuable knowledge on the distributions of charge and magnetization their inside, which can be used to better understand their geometric shape and quark-gluon organizations. The results given in this study constitute an estimate of the magnetic moment of this $$D \bar{D}^* K$$ state and should serve as an inspiration to conduct experimental examinations of this state.

Magnetic dipole moments of the hidden-charm pentaquark states: P_c(4440), P_c(4457) and P_{cs}(4459)

In this work, we employ the light-cone QCD sum rule to calculate the magnetic dipole moments of the P_c(4440), P_c(4457) and P_{cs}(4459) pentaquark states by considering them as the diquark–diquark–antiquark and molecular pictures with quantum numbers J^P = frac{3}{2}^-, J^P = frac{1}{2}^- and J^P = frac{1}{2}^-, respectively. In the analyses, we use the diquark–diquark–antiquark and molecular form of interpolating currents, and photon distribution amplitudes to obtain the magnetic dipole moment of pentaquark states. Theoretical examinations on magnetic dipole moments of the hidden-charm pentaquark states, are essential as their results can help us better figure out their substructure and the dynamics of the QCD as the theory of the strong interaction. As a by product, we extract the electric quadrupole and magnetic octupole moments of the P_c(4440) pentaquark. These values show a non-spherical charge distribution.

Calculation of electric field gradient in spherical quantum dots

ABSTRACTWe have calculated the ground and excited energy states of the quantum dot as a function of the depth of confining potential well and radius R. Based on the calculated energies and wave functions, the electric field gradient induced by the non-spherical charge at impurity is investigated as a function of dot radius and the confining potential. For Deuterium dot with spherical confining potential, the expectation value of the quadrupole moment operator is carried out. The calculations show that the dot radius, the confining potential and the impurity charge have a great influence on the electric field gradient and the quadrupole moment. It is found that as the confining potential increases, the peak position of the electric field gradient shifts toward smaller dot radii and its amplitude increases with the increase of confining potential.

Study the Shapes of Nuclei for Heavy Elements with Mass Number Equal to (226≤A≤252) through Determination of Deformation Parameters for Two Elements (U&Cf)

The current paper focuses on the studying the forms of (even-even) nuclei for the heavy elements with mass numbers in the range from (A=226 - 252) for isotopes. This work will consist of studying deformation parameters which is deduced from the "Reduced Electric Transition Probability" which is in its turn dependent on the first Excited State . The "Intrinsic Electric Quadrupole Moments" (non-spherical charge distribution) were also calculated. In addition to that the Roots Mean Square Radii (Isotope Shift) are accounted for in order to compare them with the theoretical results.
 The difference and variation in shapes of nuclei for the selected isotopes were detected using 3D-plots for them (with symmetric axes); a 2D-plot were also used for each isotope to discriminate between them by the values of semi-major is equal (a) axes and semi minor is equal (b) axes.

Nature of lattice distortions in the cubic double perovskite Ba2NaOsO6

We present detailed calculations of the electric field gradient (EFG) using a point charge approximation in ${\mathrm{Ba}}_{2}{\mathrm{NaOsO}}_{6}$, a Mott insulator with strong spin-orbit interaction. Recent $^{23}\mathrm{Na}$ nuclear magnetic resonance (NMR) measurements found that the onset of local point symmetry breaking, likely caused by the formation of quadrupolar order [Chen, Pereira, and Balents, Phys. Rev. B 82, 174440 (2010)], precedes the formation of long range magnetic order in this compound [Lu et al., Nat. Commun. 8, 14407 (2017); Liu et al., Physica B 536, 863 (2018)]. An extension of the static $^{23}\mathrm{Na}$ NMR measurements as a function of the orientation of a 15 T applied magnetic field at 8 K in the magnetically ordered phase is reported. Broken local cubic symmetry induces a nonspherical electronic charge distribution around the Na site and thus finite EFG, affecting the NMR spectral shape. We combine the spectral analysis as a function of the orientation of the magnetic field with calculations of the EFG to determine the exact microscopic nature of the lattice distortions present in low temperature phases of this material. We establish that orthorhombic distortions, constrained along the cubic axes of the perovskite reference unit cell, of oxygen octahedra surrounding Na nuclei are present in the magnetic phase. Other common types of distortions often observed in oxide structures are considered as well.

The electromagnetic multipole moments of the charged open-flavor states

The electromagnetic multipole moments of the open-flavor states are investigated by assuming a diquark–antidiquark picture for their internal structure and quantum numbers for their spin-parity. In particular, their magnetic and quadrupole moments are extracted in the framework of light-cone QCD sum rule by the help of the photon distribution amplitudes. The electromagnetic multipole moments of the open-flavor states are important dynamical observables, which encode valuable information on their underlying structure. The results obtained for the magnetic moments of different structures are considerably large and can be measured in future experiments. We obtain very small values for the quadrupole moments of states indicating a nonspherical charge distribution.

Magnetic and quadrupole moments of the Zc(3900)

The electromagnetic properties of the tetraquark state $Z_c(3900)$ are investigated in the diquark-antidiquark picture and its magnetic and quadrupole moments are extracted. To this end, the light-cone QCD sum rule in electromagnetic background field is used. The magnetic and quadrupole moments encode the spatial distributions of the charge and magnetization in the particle. The result obtained for the magnetic moment is quite large and can be measured in future experiments. We obtain a nonzero but small value for the quadrupole moment of $Zc(3900)$ indicating a nonspherical charge distribution.

Transition sol-gel in nanodiamond hydrosols

We submit results of the study of hydrosols of the single crystalline diamond nanoparticles ranging of 4–5 nm, obtained by detonation synthesis. The stable hydrosols with negative and positive zeta potentials were obtained from industrial powder after additional purification and subsequent annealing in air or in hydrogen. Unusual behavior of the hydrosols was revealed with increasing concentration of diamond nanoparticles. The state is characterized by giant viscosity value and is reversible unlike SiO2 hydrogel. Formation of the state has been explained in the frame of model that assumes the polyhedral shape of diamond nanoparticles and consequently non-spherical surface charge distribution. Stability of hydrosol was determined in accordance to the Derjaguin - Landau - Vervey - Overbeek (DLVO) theory, although as it is clear from the DLVO theory, that the double electrical layer in hydrosol is not spherical in that case. This non-sphericity results in gel formation at a smaller threshold concentration than that of DLVO theory prediction. The suggested model is supported by experimental data on particle size distribution, obtained by dynamic light scattering, by small angle neutron scattering and by theoretical estimation of the threshold concentrations.

Scattering of electromagnetic waves by a cluster of charged spherical nanoparticles

The interaction of light with a cluster of charged spherical particles is studied. The electromagnetic field is expanded in terms of the vector multipole fields, and the expansion of the scattered field is related to that of the incident field. The dimer and the chainlike and disordered arrangements of ten particles are studied. Features of the absorption and scattering signals can be used to measure the charge. This paves the way for the optical measurement of a nonspherical dust particle charge in a plasma since a cluster of spherical particles may approximate a nonspherical one.

Photoelectron wave function in photoionization: plane wave or Coulomb wave?

The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.

Characterization of organic iodides with iodine-127 nuclear magnetic resonance spectroscopy

The spectra of the Iodine-127 nucleus could not be readily obtained since it has a spin number, I, of 5/2 and a nonspherical charge distribution. When we applied 127I NMR to organic iodides, the I− and IO4− signals of organic molecules provided a clear singlet in solutions of (CD3)2S(O) or (CD3)2NC(O)D. The spectra of 127I NMR revealed the oxidation state of iodine atoms in the organic molecule, which would not have been evident in the 1H and 13C NMR spectra. Here, we report the practical examples of the characterization of organic iodides via solution-127I NMR spectroscopy.

Chemical and Crystallographic Characterization of the Tip Apex in Scanning Probe Microscopy

The apex atom of a W scanning probe tip reveals a nonspherical charge distribution as probed by a CO molecule bonded to a Cu(111) surface [Welker et al., Science 336, 444 (2012). Three high-symmetry images were observed and related to three low-index crystallographic directions of the W bcc crystal. Open questions remained, such as the detectability of a contamination of W tips by sample material (here Cu), and the applicability of the method to distinguish other atomic species. In this work, we investigate bulk Cu and Fe tips. In both cases, we can associate our data with the fcc (Cu) and bcc (Fe) crystal structures using a simple electrostatic model that is based on the partial filling of d orbitals.