Showing papers on "Quadrupole published in 1987"

Transition probability, B(E2)up-arrow, from the ground to the first-excited 2/sup +/ state of even-even nuclides

Abstract: Adopted values for the reduced electric quadrupole transition probability, B(E2)up-arrow, from the ground state to the first-excited 2/sup +/ state of even-even nuclides are given in Table I. Values of tau, the mean life of the 2/sup +/ state, E, the energy, and ..beta../sub 2/, the quadrupole deformation parameter, are also listed there. The ratio of ..beta../sub 2/ to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q/sub O/, is deduced from the B(E2)up-arrow value. The product E x B(E2)up-arrow is expressed as a precentage of the energy-weighted total and isoscalar E2 sum-rule strengths.

Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals

Abstract: We present a macroscopic theory for anisotropic second- and third-harmonic generation obtained in reflection from the surface and bulk of cubic centrosymmetric single crystals. The theory is based on possible electric dipole, electric quadrupole, and magnetic dipole sources. Completely general expressions for the harmonic fields are obtained for (100), (111), and (110) faces independent of the details of the surface response but consistent with crystal symmetry. The results obtained agree with all existing experimental data obtained by various groups during the past few years. The possibility of separating out surface and bulk responses is considered using symmetry, polarization, or geometry arguments and it is concluded that for second-harmonic generation this cannot be done in general without additional information. Third-harmonic generation, barring any strong resonantly enhanced surface electric dipole effects, is essentially a bulk probe.

Improving the validity of hyperfine field distributions from magnetic alloys: Part I: Unpolarized source☆

Abstract: The evaluation of magnetic hyperfine field distributions from 57Fe Mossbauer spectra in systems with both magnetic dipole and electric quadrupole interactions is considered. This problem is treated in higher order perturbation theory, and the case of general magnetic texture and isotropic electric quadrupole texture is treated in full. Simple expressions are given enabling the calculation of all spectrum line positions, intensities and widths. It is shown that in cases where first order perturbation treatments yield low-field artifacts in the magnetic hyperfine distribution, this procedure yields much more reliable results. It is also shown that the calculated magnetic spin texture is much more reliable. The asymmetry effects from the electric quadrupole interaction and from a correlation between this and a dipole magnetic field are considered.

Deuterium NMR study of methyl group dynamics in L‐alanine

Abstract: Deuterium quadrupole echo spectroscopy is used to study the dynamics of the CD3 group in polycrystalline L‐alanine‐d3. Temperature‐dependent quadrupole echo line shapes, their spectral intensities and τ dependence, and the anisotropy of the 2H spin‐lattice relaxation were employed to determine the rate and mechanism of the –CD3 group motion. The rigid lattice Pake pattern observed at low temperature (T −70 °C). The quadrupole echo line shapes and their τ dependence, which are especially sensitive to the rate and mechanism of the motion, can be simulated quantitatively with the threefold jump model. We find Ea=20.0 kJ/mol for this process which is higher than is observed for most methyl groups, probably because of steric crowding in the L‐Ala molecule. Finally, we observe a line shape due to the prese...

Mössbauer spectroscopy of R2Fe14B

Abstract: The authors present results obtained by 57Fe Mossbauer spectroscopy on R2Fe14B, where R represents any of the rare earth elements except Pm, Eu and Yb. Additional measurements have been performed on oriented powder for R=Y, Pr and Ho. For the case of Y the measurements at 4.2 K were performed in applied magnetic fields up to 4 T. From these measurements it is deduced that the only compounds with an easy c axis at room temperature which show a spin reorientation of the iron sublattice at a lower temperature are the Nd and Ho alloys. Iron hyperfine fields are anisotropic and the anisotropy has different signs on different sites. An analysis of the non-4f contribution to the electric field gradient at the 161Dy or 166Er nuclei in Dy2Fe14B and Er2Fe14B is consistent with published results on 155Gd in Gd2Fe14B. In order to explain that a spin rotation is found only for R=Nd, Ho the authors invoke the relative small quadrupole moment of the 4f shell for these two ions and crystal field terms of higher than second order.

Quadrupole echo distortion as a tool for dynamic NMR: Application to molecular reorientation in solid trimethylamine

Abstract: Deuterium NMR quadrupole echo spectra of trimethylamine‐d9 (TMA‐d9) were recorded in the solid phase from about −150 °C to the melting point (−117 °C). The spectra exhibit pronounced line shape variation with temperature which is interpreted in terms of two independent dynamic processes, (i) threefold methyl group reorientation about the respective C3 axes, and (ii) threefold whole molecule reorientation about the molecular C’3 axis. To derive quantitative kinetic parameters for these processes the experimental spectra are compared with simulated traces, placing particular emphasis on the effect of line shape distortion due to the delay time τ between the π/2 pulses in the quadrupole echo experiment. This approach improves the sensitivity of the fitting method and allows accurate determination of the kinetic parameters for both the C3 and C3 reorientation processes. The results are k(−150 °C)=3.0×104 s−1, k’(−150 °C)=0.1×104 s−1, ΔE=3.0±0.6 kcal/mol, and ΔE’=8.0±1.6 kcal/mol, respectively. In Appendix A a...

The prediction of nuclear quadrupole moments from abinitio quantum chemical studies on small molecules. I. The electric field gradients at the 14N and 2H nuclei in N2, NO, NO+, CN, CN−, HCN, HNC, and NH3

Abstract: Electric field gradients (efg’s) at the nitrogen nuclei in N2, NO+, NO, CN, and CN− and at the nitrogen and hydrogen nuclei in HCN, HNC, and NH3, calculated using ab initio quantum chemical methods, are reported. Employing extensive Gaussian basis sets, the efg’s were computed at the self‐consistent field (SCF), singles and doubles configuration interaction [CI(SD)], and coupled pair functional (CPF) levels of theory as the expectation values of the efg operator and also as the energy derivatives of the appropriate perturbed Hamiltonian using the finite field method. Corrections due to zero point vibrational motions were also calculated. The effect of basis set incompleteness on the calculated efg’s, together with the experimental nuclear quadrupole coupling constants, are used to estimate the 14N and 2H nuclear quadrupole moments, and to test the quality of the correlated wave functions generated by the CI(SD) and CPF methods. The recommended values, on the basis of the present calculations, are 2.05±0.0...

Improving the validity of hyperfine field distributions from magnetic alloys: Part II: Polarized source and spin texture

Abstract: It has been shown in Part I of this work that 57 Fe Mossbauer spectra for the case of mixed electric and magnetic interactions can be calculated with much higher accuracy by using higher order perturbation theory. This is extended for the case of polarized radiation in order to treat cases of magnetic texture in more detail. It is shown that, in this case, the line intensities can be expressed as functions of the magnetic texture including the perturbation of the electric quadrupole interaction. As in Part I, the case of an isotropic electric quadrupole texture is considered.

The Quadrupole Gravitational Lens

Abstract: An asymmetric lens made of a spherically symmetric galaxy and a quadrupole tidal part allows a very simple pictorial examination of the multiplicity and positions of the images, for any mass density profile. The lens equations can be reduced to one equation in one variable. In the special case of a singular isothermal sphere with a tide (SIST), the lens properties are described by five parameters. Two parameters determine the angular scale and orientation, while three determine the configuration of the images. A comprehensive investigation of the SIST lens is performed, including the variation of the configurations with the parameter values, the critical surfaces in the parameter space, and the extremal solutions. Analytic expressions are derived for the SIST parameters, and additional image positions, in the case when the intensity ratio and positions relative to the galaxy for two of the images are given as input. Quadrupole lenses with a point mass and a pseudoisothermal sphere as the main part are also described in terms of direction diagrams. A direct relation between deflection profile and rotational velocity is derived.

Secondary ion mass spectrometry profiling of shallow, implanted layers using quadrupole and magnetic sector instruments

Abstract: The analysis of shallow, steeply varying profiles, using secondary ion mass spectrometry with quadrupole and magnetic sector instruments, is described. The problems in generating a reliable profile, free of transient effects, and ion beam induced displacements and broadening effects, in both types of instruments are discussed. The most important conclusion is that one should be capable of varying the primary beam energy, primary mass, the angle of incidence, and the polarity of the secondary ions independently of each other. We also report the use of special experimental conditions which circumvent some of the problems posed in magnetic sector instruments; low‐energy Cs beams (down to 1 keV) are used in combination with sensitive detection of positive secondary ions. Finally, it is shown that for a 5‐kV As+ implanted Si specimen all the projected ranges and decay lengths of the profiles, measured with different primary masses, angles of incidence, and primary energies, can be correlated in a universal cur...

Laser probing of the rotational alignment of N+2 drifted in helium

Abstract: Results are presented on laser‐induced fluorescence studies of the rotational alignment of N+2 drifted in helium. The alignment which is caused by collisions of the ions with the helium buffer gas is observed in the uniform electric field of a drift tube. The angular momentum vectors of the ions are preferentially aligned perpendicular to the electric field vector. At a drift field of 14 Td, corresponding to a collision energy of 52 meV (c.m.), a quadrupole moment A(2)0=−0.11±0.03 is determined for the N=10 rotational state. This yields an approximate population ratio of 2:3 for finding molecules with rotational angular momentum vectors parallel and perpendicular to the electric field vector, respectively. In addition to the alignment studies, a detailed characterization of the drift tube using laser‐induced fluorescence detection of N+2 is presented. Theoretical results for the determination of alignment parameters using saturated laser‐induced fluorescence are presented.

The molecular dynamics simulation of water clusters

Abstract: Water clusters containing 15, 27, and 64 molecules have been investigated by molecular dynamics at various temperatures. Profiles for atomic density, the polarization vector, local energy, and the pressure tensor have been obtained. A simple way to calculate the local electric potential as an average Coulomb potential at a sphere of radius r has been offered that resulted in more reliable data. The orientation of water molecules at the surface has been studied in detail. The most probable position of the molecular plane has been shown to be perpendicular and of the dipole vector parallel to the surface. Two models of water molecules with different values of the quadrupole component Qzz along the dipole axis have been considered. The theoretical prediction of the proportionality of the surface potential and Qzz has been confirmed.

Nuclear Quadrupole Interaction and Time‐Resolved Perturbed γ‐γ‐Angular Correlation Spectroscopy: Applications in Chemistry, Materials Science, and Biophysical Chemistry. New Analytical Methods (31)

Abstract: The study of nuclear quadrupole interactions, i.e. of the strength, symmetry, and orientation of the electric field gradient tensor, yields valuable information on charge density distributions on an atomic scale. Apart from the nowadays “conventional” methods of NMR and Mossbauer spectroscopy there is yet another technique: time-resolved perturbed γ-γ-angular correlation spectroscopy. This technique is very well suited for applications in chemistry (e.g. comparative studies of bond conditions of inorganic complexes in the solid and in solution or in the melt), in molecular biology (e.g. intramolecular dynamics in biomolecules), and in materials science (e.g. investigation of catalyst surfaces) because of, inter alia, the extremely small sample requirements and the temperature independence of the sensitivity. The variation of the electric field gradient tensor (strength, symmetry, possibly orientation) is observed as a function of external parameters or, in the case of reactions, as a function of the degree of reaction. The interpretation of results requires the assignment of observed signals to known species or configurations. In this progress report we review modern areas of application of perturbed angular correlation spectroscopy.

The prediction of nuclear quadrupole moments from ab initio quantum chemical studies on small molecules. II. The electric field gradients at the 17O, 35Cl, and 2H nuclei in CO, NO+, OH−, H2O, CH2O, HCl, LiCl, and FCl

Abstract: The electric field gradients (efg’s) at the oxygen and hydrogen nuclei in CO,NO+, OH−, H2O, and CH2O, and at the chlorine, lithium, and hydrogen nuclei in HCl, LiCl, and FCl, calculated using ab initio quantum chemical methods, are reported. Using extended Gaussian basis sets, the efg’s at the oxygen and chlorine nuclei were computed at the self‐consistent field (SCF), singles and doubles configuration interaction [CI(SD)], and coupled pair functional (CPF) levels of theory as the expectation values of the efg operator and also as the energy derivatives of the appropriate perturbed Hamiltonian using the finite field method. The efg’s at the hydrogen and lithium nuclei were computed as expectation values. Corrections due to zero point vibrational motions were also calculated. The effect of basis set incompleteness on the calculated efg’s is discussed and, where possible, corrected for. The calculated efg’s, together with the experimental nuclear quadrupole coupling constants, are used to estimate the 17O, ...

Collective oscillations of stored ions

Abstract: When ions of slightly di8'erent mass and the same charge are stored in a radio-frequency electric quadrupole trap, a collective oscillation is observed rather than the independent motions usually assumed. A high-temperature model of ion clouds, each characterized by ions of one mass, shows that the ions of each cloud move as a unit and exhibit a correlated motion with the other clouds when a strong coupling condition is satisfied. This phenomenon is expected to arise whenever more than one ion is trapped and might be observable in neutral atom traps as we11

The mössbauer spectrum of almandine

Abstract: Mossbauer spectra of a synthetic, pure almandine (Alm100) and a natural almandine-rich garnet (Alm86) were taken at temperatures between 295 and 4.2 K. Different widths and depths of the lines observed in the paramagnetic state require the spectra to be fitted with at least two components of slightly different quadrupole splittings and isomer shifts. Alm100 shows a gradual onset of magnetic order between 10.4 and 9.0 K, with about 50 percent of the sample magnetically ordered at 9.6 K. At 4.2 K both samples have complex spectra that can be fitted by two eight-line magnetic hyperfine patterns of equal intensities. These result from the existence of two different polar angles between the z-axis of the electric field gradient and the direction of the magnetic hyperfine field, or from two distinctly different electric field gradients. The former interpretation, in which the two angles are attributed to a modulated, non-collinear spin arrangement, is considered more likely. Both magnetic components have practically identical quadrupole splittings, 1/2eQV zz (1+η2/3)1/2, that average −3.70 mm·s−1, and a small asymmetry parameter of η=0.07. Alm100 has a magnetic hyperfine field of 25.7 T at 4.2 K, whereas Alm86 has a hyperfine field of only 23.3 T; the other features of the spectra of both samples are similar.

NQR and NMR of 139La in Antiferromagnetic La2CuO4-δ

Abstract: Rather complex Nuclear Quadrupole Resonance (NQR) spectrum of 139 La in La 2 CuO 4-δ , observed at low temperatures is successfully interpreted as a signal from a single La site which suffers a combined effect of a quadrupole coupling (coupling constant ν Q =6.38±0.02 MHz with asymmetry parameter η=0.01±0.01) and a small Zeeman term where the internal field ( H N =0.997±0.010 kOe) is nearly perpendicular to the direction of the maximum field gradient. The spin structure of Cu at low temperatures is suggested to be a simple antiferromagnet with sublattice moments parallel to the a -axis. The temperature dependences of ν Q and H N have been measured in detail. The fractional decrease of H N which is proportional to the Cu sublattice moments is found to be in general accord with the prediction of spin fluctuations theory for weak itinerant antiferromagnets.

Calibration of isomer shift and quadrupole coupling for 119Sn, 127I and 129I as derived from self-consistent charge Xα calculations and Mossbauer measurements

Abstract: The self-consistent charge (SCC) X alpha method has been applied to investigate the electronic structure of molecules which contain heavy, Mossbauer-active elements (Sn and I). For a series of halogen-containing compounds, with various oxidation states of the heavy elements, the authors have calculated orbital energies and dipole moments, which compare well with corresponding experimental data. In the case of hypervalent ions the inclusion of d besides s and p orbitals is sensitive with respective to dipole moments only and leaves orbital energies practically unaffected. For tin- and iodine-containing molecules they have calculated electron charge densities rho (0) and electric field gradients (EFG) at the nuclear site of the Mossbauer atom. Comparing these results with corresponding isomer shifts and quadrupole splittings (coupling constants), which were partly measured by one of them, they derive as calibration factors the fractional change of the nuclear radius Delta R/R and the quadrupole moment Q for 119Sn, 127I and 129I: Delta R/R(119Sn)=1.61*10-4, Delta R/R(127I)=-0.345 Delta R/R(129I), Delta R/R(129I)=4.18*10-4; Q(119Sn)=-0.061 b, Q(127I)=-0.60+or-0.03 b, Q(129I)=0.701Q(127I).

A relativistic approach to the elastic scattering of electrons by argon

Abstract: Phase shifts and total and differential cross sections are calculated for the elastic scattering of unpolarised electrons by argon atoms in the impact energy range of 0.1 to 40 eV. The target atom is represented by a frozen core in a continuum relativistic Hartree-Fock calculation with dipole and quadrupole polarisation corrections. Exchange is calculated exactly and the parameters of the model polarisation potential are fixed by independent calculations. The results are in good agreement with experiment and with some of the non-relativistic coupled Hartree-Fock calculations; they demonstrate the importance of core polarisation effects as well as of relativistic effects at low incident energies.

Aberrations of single magnetic quadrupole lenses

Abstract: A number of analytical instruments make use of strong focusing magnetic quadrupole lenses. Such lenses suffer from aberrations which may degrade the performance of the instruments. This paper presents a modification of the grid shadow method which may be used to measure the aberrations of magnetic quadrupole lenses. The method is applied to a system which consists of a single quadrupole and a single octupole and the third order effect of the octupole is shown to be in good agreement with theory. The method is also applied to measure the second and third order parasitic aberrations of the single quadrupole lens components of the Melbourne Proton Microprobe.

On the accuracy of source localisation in cardiac measurements (magnetocardiography)

Abstract: Describes a localisation study of the sources of bioelectrical activity in the human heart. In particular, the atrial activation (P wave) and the activation of an extra pre-excitation area in the Wolff-Parkinson-White syndrome are investigated. Different models based on the current multipole expansion are used to calculate the inverse solution. A comparison between calculated results, invasive electrophysiological studies and known physiological data is performed. The best results were obtained by the current multipole model with dipole and quadrupole terms. Non-invasive localisation of cardiac electric sources can be useful in studies of arrhythmia patients in the future.