Hexadecapole Interaction Research Articles

Hyperfine spectrum of RbBr

The molecular beam electric resonance technique has been used to conduct a high precision examination of the hyperfine spectrum of 85Rb79Br and 85Rb81Br. Coupling constants for the nuclear electric quadrupole interactions, the spin–rotation interactions, the tensor and scalar spin–spin interactions, and their dependence on vibrational and rotational state have been determined. A slightly improved value of the electric dipole moment is also obtained, and the inclusion of an electric hexadecapole interaction for the rubidium nucleus is found to somewhat improve the fit.

Investigation of the multiplicities of nuclear quadrupole resonance spectrums isotopes 113,115In in crystals InSe grown from the melt

For researchers, the problem of interpreting the origin nature of NQR spectra multiplicity is always one of the main experimental tasks. For the purpose of interpreting the nature of the occurrence of NQR spectra multiplicity in the layered crystal InSe, the spectra of NQR 113,115 In for four spin transitions, the average values of which are only approximately satisfied the ratio ν1: ν2: ν3: ν4 =1: 2:3:4 were studied. In the studied NQR spectra, two multiplet groups, confirming the presence of polytypic structure in crystals are clearly observed. The feature of multiplet groups is the presence of fine structure with the splitting constant, which is clearly observed for the three higher transitions and constitutes10 ± 0,5 kHz. The quantitative similarity of the spectra 113,115 In in InSe reflects that the corresponding splitting occurs almost entirely due to the interaction of nuclei In. It is established that for higher transitions deviation is observed. It is shown that, in multiplet groups for higher-order transitions, multiplet groups of lines are observed that, in our opinion, is connected with the presence hexadecapole interaction with the electric field gradient of crystal. This interaction is caused not only by p-, but also d-, f- electrons in layered crystal with highly distorted configuration of the charge distribution in the vicinity of indium nuclei. In addition, as a result of exciting the electrons d- or f- of the indium atom shell by coordinating interactions, the additional contribution of hexadepole moment in the form of additional lines in the multiplet spectra of NQR may occur.

About existence of hexadecapole interaction in spectrums NQR 115In in InSe

Researchers assumed the existence of nuclear hexadecapole interaction of nuclei with a significant quadrupole moment long ago, but, unfortunately, there is no definiteness in the results. The scientific literature presents the direct experimental evidence only in some cases for the nuclei with large mass number, such as 127 I, 121 Sb, 123 Sb or 175 Lu . The problem of detection of this effect is that it is vanishingly small and, according to the researches, it is on the border of detectability of measuring equipment. Moreover, the situation is aggravated by the fact that this effect exists along with the high value of the quadrupole moment of the nuclei, which masks the occurrence of the hexadecapole interaction of small value. The purpose of the article is to prove the occurrence of the hexadecapole interaction in layered crystals with the strong anisotropy of the chemical bond, such as InSe. The presence of two-dimensional electronic structure of these crystals leads to the unusual physical properties, and the hexagonal crystal structure with axial symmetry makes these compounds perfect for studying the electronic distribution by the NQR method. The spectra NQR 115 In in InSe crystals, grown from the melt, and recorded by continuous method for four resonance transitions of 115 In with spin 9/2, were suggested. The multiplicity of spectra NQR with additional lines, which meet the forbidden transitions, was detected. It is believed, that this anomaly is caused by the presence of the hexadecapole interaction of nuclei 115 In with the electric field gradient in InSe

Electron penetration into the nucleus and its effect on the quadrupole interaction

A series expansion of the interaction between a nucleus and its surrounding electron distribution provides terms that are well-known in the study of hyperfine interactions: the familiar quadrupole interaction and the less familiar hexadecapole interaction. If the penetration of electrons into the nucleus is taken into account, various corrections to these multipole interactions appear. The best known correction is a scalar term related to the isotope shift and the isomer shift. This paper discusses a related tensor correction, which modifies the quadrupole interaction if electrons penetrate the nucleus: the quadrupole shift. We describe the mathematical formalism and provide first-principles calculations of the quadrupole shift for a large set of solids. Fully relativistic calculations that explicitly take a finite nucleus into account turn out to be mandatory. Our analysis shows that the quadrupole shift becomes appreciably large for heavy elements. Implications for experimental high-precision studies of quadrupole interactions and quadrupole moment ratios are discussed. A literature review of other small quadrupole-like effects is presented as well (pseudoquadrupole effect, isotopologue anomaly, etc.).

Hyperfine spectra of KBr and KI

The molecular beam electric resonance technique has been used to conduct a high precision examination of the hyperfine spectra of 39K 79Br, 39K 81Br and 39K 127I. Coupling constants for the nuclear electric quadrupole interactions, the spin–rotation interactions, the tensor and scalar spin–spin interactions, as well as the electric dipole moment of KI, and their dependence on vibrational and rotational state have been determined. A few transitions observed for 41K 127I show a small shift in the iodine nuclear electric quadrupole interaction, and the fit improves somewhat with the inclusion of an iodine nuclear electric hexadecapole interaction term.

An anomaly in the isotopomer shift of the hyperfine spectrum of LiI

A high-precision examination of the hyperfine spectrum of 6LiI in comparison with 7LiI shows a shift in the iodine nuclear electric quadrupole moment that cannot be accounted for by a model in which the electric field gradient at the iodine site is assumed to depend only upon the internuclear distance between Li and I. The other hyperfine interactions are consistent between the two isotopomers, including the previously reported electric hexadecapole interaction of the iodine nucleus.

Evidence for a nuclear hexadecapole interaction in the hyperfine spectrum of LiI

The molecular beam electric resonance technique has been used to examine the hyperfine spectrum of LiI7 to determine the nuclear hexadecapole interaction of the iodine nucleus. The nuclear magnetic octupole interaction was also considered but found to be marginally significant. A total of 172 transitions in vibrational states 0-3 and rotational states 1-6 have been included in a fit to determine the iodine nuclear quadrupole, spin-rotation, and hexadecapole interactions, the lithium quadrupole and spin-rotation interactions, and the tensor and scalar parts of the spin-spin interaction. Vibration and rotation dependencies of these constants have been determined. The results include: eHh=−0.0151(30), eQIqI=−194351.212(17)−8279.521(46)(v+1/2)+100.616(34)(v+1/2)2−0.3949(73)(v+1/2)3−6.41977(50)J(J+1)+0.10593(33)(v+1/2)J(J+1),eQLiqLi=172.613(52)−3.26(14)(v+1/2)+0.00145(87)J(J+1),cI=6.80260(32)+0.00303(49)(v+1/2)−0.000118(13)J(J+1), cLi=0.75872(72)−0.0088(11)(v+1/2), c3=0.62834(68)−0.0050(11)(v+1/2), c4=0.06223(36)+0.00041(26)(v+1/2), and eΩIωI′=0.000112(73), all in kHz with one standard deviation uncertainties for the last 2 digits in ( ).

Hexadecapole interaction and the ΔI = 4 staggering effect in rotational bands

A role of the multipole interaction in the description of the ΔI = 4 staggering phenomenon is investigated in a model consisting of a single-j shell filled by identical nucleons. Exact diagonalization of the quadrupole-plus-hexadecapole Hamiltonian shows that the hexadecapole-hexadecapole interaction can produce a ΔI = 4 periodicity in the yrast sequence.

The nuclear hexadecapole interaction of iodine-127 in cadmium iodide measured using zero-field two dimensional nuclear magnetic resonance

Two dimensional nuclear quadrupole correlation spectroscopy has been used to measure simultaneously the two nuclear spin transition frequencies for the iodine resonance of cadmium iodide at zero magnetic field. Because of the layer structure and resultant polymorphism in this substance, conventional zero-field NMR spectra are inhomogeneously broadened by several hundred kHz. However, the 2D spectra obtained by our method are subject only to homogeneous linewidth, which for this compound is of the order of 5 kHz. This greatly increased precision allows more accurate evaluation of the nuclear hexadecapole coupling in cadmium iodide; which we measure as 0.216±0.514 kHz (i.e., indistinguishable from zero). This gives a maximum value of the nuclear hexadecapole moment several times lower than that recently reported for the same nucleus in potassium iodide.

Medium-energy hadron-nucleus scattering in the 1/Nexpansion formalism

The algebraic-eikonal approach to the medium-energy hadron-nucleus scattering is generalized to arbitrary interactions and boson types using the 1/N expansion technique for the interacting boson model. The results are used in a comparative study of proton scattering from deformed nuclei in the sd and sdg boson models. The two models give almost identical results for a pure quadrupole interaction but widely differ when a hexadecapole interaction is included.

Quadrupole echoes and the 127I nuclear hexadecapole interaction in KI

A quadrupole echo method for searching for the nuclear hexadecapole interaction (HDI) is described. A sequence of three radio frequency pulses applied at times 0, τ, and nτ (n>1) gives a simple pattern of nuclear spin (5)/(2) echoes when only the nuclear Zeeman and quadrupole interactions are present. Calculations for n=2.5, 3.0, 4.0, and 5.0 show that these patterns undergo an elaborate change when the HDI is also present and that these echo patterns are unique to the HDI. Three pulse echoes were used to search for the 127I HDI in a single crystal of KI but, for this sample, a two pulse sequence was found to be more effective. For KI, 2.8 kHz is the estimated magnitude of the 127I hexadecapole coupling constant, eHV(4)/h, where eH is the 127I electric hexadecapole moment and V(4) is a fourth derivative of the electrostatic potential at the nuclear site. This is the smallest HDI measured in a solid so far.

γ-unstable nuclei in the sdg boson model

Following the recent Pt(p, p′) experiments which indicated the need for g bosons to reproduce the E4 data, we have extended the O(6) limit of the sd boson model to include g bosons. It is shown that a γ-unstable hamiltonian in the sdg model consisting of a quadrupole interaction and a g boson energy leads to results that are very similar to the O(6) limit. Deviations from the empirical energy spectrum that stem from the γ-unstable nature of the hamiltonian can be improved by including a consistent hexadecapole interaction which induces triaxiality. The same hexadecapole operator can also account for the strong E4 transitions. Applications are made to the Xe and Pt isotopes.

Shapes and phase transitions in generalized boson models

Geometrical properties of the interacting boson model with arbitrary kinds of bosons (s, d, g, …) are investigated. A general expression for the energy surface is derived and the effects of various multipole interactions on the equilibrium shape are discussed. It is shown that a quadrupole interaction alone always leads to an axial shape and a hexadecapole interaction is needed in order to induce a triaxial shape. Another interesting feature that is not possible in the standard sd model is the emergence of prolate-oblate shape co-existence in the extended boson models which may be relevant in the study of high spin states.

Electric hexadecapole of 3d electron cloud of Ti3+ ion

The concept of electric hexadecapole is adopted to d electron clouds of transition metal. By analogous treatment of nuclear electric hexadecapole interaction with the surrounding electric field, the ligand field splittings of d orbitals is the electric hexadecapole splittings. The electric hexadecapole moment of 3d electron cloud of Ti3+ ion has been evaluated as 2.5 × 10-50 C·m4.

On nuclear electric hexadecapole interactions (NEHI) in solids

The importance of nuclear electric hexadecapole interaction in solids is stated. The recent measured results of antinomy isotopes in Sb 2S 3 and of niobium 93 in NbF 5 polycrystals are reported.

Nuclear electric hexadecapole coupling in the caesium cation

Abstract Caesium N.M.R. spectra of the caesium ion have been measured in a nematic lyotropic liquid-crystalline solution prepared from caesium decylsulphate/decanol/water. The contributions of an asymmetry parameter, a second order quadrupole coupling and a hexadecapole coupling to the spectra have been discussed. The N.M.R. spectra was shown to be consistent with the occurrence of a hexadecapole interaction in the quadrupole split spectrum. The ratio = 1:0.0000034 was obtained.

On the role of hexadecapole forces in describing γ-band states in the rare-earth region

Calculations are made for the isoscalar transition rates B(IS2, GS to 2+2 gamma ) and B(IS4, GS to 4+2 gamma ) in the RPA with a common system of equations for lambda mu =22 and 42 and for the inelastic form factors in the folding model. The analysing powers and cross sections in the (p,p') reaction with Ep=65 MeV for the levels 2+2 gamma and 4+2 gamma in 168Er are calculated within the coupled-channels method by using the microscopic form factors. It is shown that extremely large values of B(IS4, GS to 4+2 gamma )exp obtained in the (p,p') and ( alpha , alpha ') reactions are mostly due to the contribution of indirect excitation channels but not to a strong hexadecapole interaction lambda mu =42. A moderate value of the hexadecapole interaction constant kappa 0(42)=0.012 fm2 MeV-1 provides a satisfactory description of the available experimental data.

Search for hexadecapole interaction in KTaO3 by 181Ta-NMR

A single-crystal 181Ta-NMR experiment was performed in KTaO3 in an unsuccessful attempt to observe the splitting pattern characteristic of electric hexadecapole coupling. A linewidth of about 12 kHz was observed, and assigned to residual first-order quadrupole couplings arising from imperfections in this nominally cubic crystal. Experimental difficulties prevented the removal of the electric quadrupole (and magnetic dipole–dipole) couplings by multiple-pulse linenarrowing methods.

Nuclear electric hexadecapole interactions in solids

The detection and verification of the existence of nuclear hexadecapole interactions is interesting and important for understanding the structure of the nucleus and its neighboring electric field pattern corresponding to a nuclear position in the lattice of a crystal. The detailed arrangement of apparatus and the method of frequency measurement of an earlier experiment, which have not been reported before, are described. Progress of this research in the past 30 years is reviewed in the light of techniques of measurement. Major problems for further investigations are pointed out. Utilization of the nuclear hexadecapole interaction for detecting deep-lying physical phenomena (static and dynamic) such as various lattice defects, phase changes, and lattice dynamics in crystals is suggested.

Detection of a hexadecapole interaction in the atomic ground state3 H 6 of167Er

Using the atomic beam magnetic resonance method, precision measurements of the hyperfine structure and Zeeman interactions have been performed in the ground state 4f 126s 2 3 H 6 of167Er. The experimental data were analyzed using an effective operator parametrized in the space of states of the ground state multiplet. It yielded eight effective hyperfine structure and Zeeman interaction constants which served to calculate the seven hyperfine separations of the ground state. The results are: $$\begin{gathered} 2F 2F' v_{FF'} (MHz) \hfill \\ 5 7 - 354.371 9409 (27) \hfill \\ 7 9 - 2{\text{78}}{\text{.231}} {\text{8263(14)}} \hfill \\ {\text{9}} 11 - 69.050 7785 (4) \hfill \\ 11 13 + 302.735 3731(12) \hfill \\ 13 15 + 866.691 3871(10) \hfill \\ 15 17 + 1,652.383 5154 (6) \hfill \\ 17 19 + 2,689.380 8050(10) \hfill \\ \end{gathered}$$ From the effective Zeeman interaction constants it was possible to determine an improvedg I -value, uncorrected for atomic diamagnetism: $$ g_I = + 0.086 775 (19) \cdot 10^{ - 3}$$ Furthermore a hexadecapole interaction corresponding to a diagonal hexadecapole interaction constant $$A_4 = - 16 (10) Hz$$ could be established which is of the order of magnitude expected from Coulomb excitation experiments as well as theoretical calculations.