Nuclear Electric Quadrupole Interaction Research Articles

Bloch-Type Equations for Acoustic Nuclear-Magnetic Resonance

Acoustic nuclear-magnetic resonance differs from the conventional NMR in that an acoustic signal of frequency ω at or near the nuclear Larmor frequency ωo = (gnβnHo)ħ−1 or its first harmonic is applied to the sample instead of the customary electromagnetic signal. In the acoustic case nuclear Zeeman transitions are induced by virtue of a modulated nuclear-electric quadrupole interaction in contrast with the conventional situation where the nuclear-magnetic dipole interaction is operative. In spite of these differences, it is possible to write phenomenological equations of the Bloch form, familiar in the theory of conventional NMR, for the case of acoustic NMR, providing an appropriate choice is made for the amplitude and direction of the effective magnetic field. This macroscopic description of acoustic NMR is applicable for negligible saturation.

Hyperfine Structure ofGe73in theP13andP23Atomic States and the Nuclear Magnetic Dipole Moment ofGe71

The hyperfine-structure constants of ${\mathrm{Ge}}^{73}$ in the $^{3}P_{1}$ and $^{3}P_{2}$ atomic states of the $3{p}^{2}$ electronic configuration have been measured with the atomic-beam magnetic-resonance method. The values of the magnetic dipole hyperfine-interaction constant $a$ are 15.5480(18) Mc/sec and -64.4270(7) Mc/sec, respectively, for the $^{3}P_{1}$ and $^{3}P_{2}$ states. The nuclear electric quadrupole interaction constants $b$ are -54.566(9) Mc/sec and +111.825(13) Mc/sec, respectively, for these two states. On the basis of these measurements of $a$, the known spin and nuclear magnetic dipole moment of ${\mathrm{Ge}}^{73}$ and the measured spin and $a$ factors of ${\mathrm{Ge}}^{71}$, the nuclear magnetic dipole moment of ${\mathrm{Ge}}^{71}$ can be calculated. It is $\ensuremath{\mu}=0.546(5)$ nm.

Quadrupolar Relaxation ofXe131in Xenon Gas

A theoretical study is made of the spin-lattice relaxation of ${\mathrm{Xe}}^{131}$ ($I=\frac{3}{2}$) nuclei in pure xenon gas due to collision-induced nuclear electric quadrupole interactions. The calculation treats a pair of colliding Xe atoms as a rotating diatomic molecule, whose nuclear electric quadrupole interaction couples the nuclear spin and rotational angular momenta. This interaction permits the nuclei to relax by exchanging energy with the rotational motion of the colliding atoms. The quadrupole interaction in such a diatomic molecule is computed by considering the effects of exchange and Van der Waals interactions in deforming the spherical electronic charge clouds of the free atoms. It is found that the exchange interaction makes the dominant contribution to the quadrupole interaction. Averaging the single-collision transition probabilities over all types of collisions gives the following result for the spin-lattice relaxation time ${T}_{1}:\frac{1}{{T}_{1}}=0.046\ensuremath{\rho}$ ${\mathrm{sec}}^{\ensuremath{-}1}$, where $\ensuremath{\rho}$ is the density in amagats. This is in good agreement with the observed result: $\frac{1}{{T}_{1}}=0.039\ensuremath{\rho}$ ${\mathrm{sec}}^{\ensuremath{-}1}$.

The temperature dependence of the nuclear magnetic resonance of vanadium

Measurements have been made of the line width, intensity and shift of the 51V magnetic resonance from vanadium metal over the range 25-330 °K. The absence of any detectable anomalies in these properties shows that the transition at around 250 °K cannot be associated with the occurrence of antiferromagnetism unless the fluctuation frequency of the internal magnetic fields exceeds 2 × 1012 c/s. From consideration of nuclear electric quadrupole interactions, it is estimated that any deviation from cubic crystal symmetry at or below the transition point is less than 2 parts in 103. The Knight shift increases from 0.571% at 25 °K to 0.580% at 330 °K with an accuracy to ±0.001%. From a comparison of the temperature dependence of Knight shift and magnetic susceptibility, the hyperfine field at a vanadium nucleus due to one d-electron spin was estimated to be -112 ± 17 kilogauss.

Hyperfine Structure in the ^3P_1 Level of the Twenty-Four-Hour Isomer of Mercury 197†

The hyperfine structure of Hg197* was measured with greater accuracy than had been obtained in conventional spectroscopic work. The nuclear magnetic dipole and electric quadrupole interaction constants, A and B, were calculated: A=−2328.8±1.7 Mc/sec; B=−901±13 Mc/sec. The isotope shift is 2240±130 Mc/sec relative to Hg198. An electronic g value of 1.4861±0.00036 was found for the 3P1 level.The data were gathered with the use of level-crossing, double-resonance, and magnetic scanning techniques. The relatively new level-crossing experiment was applied to Hg199 and Hg197.The measurements reported here are useful in two ways: They lead to values of the nuclear moments and estimates of the nuclear charge distribution, and they pave the way for more accurate experiments that will yield data on the distribution of the nuclear magnetization.

Temperature Dependence of the Nuclear Quadrupole Spectrum ofNb93in Ferroelectric KNbO3

The nuclear electric quadrupole interaction of ${\mathrm{Nb}}^{93}$ in ferroelectric KNb${\mathrm{O}}_{3}$ has been measured as a function of temperature in the tetragonal, orthorhombic and rhombohedral phases. The values of $(\frac{1}{\ensuremath{\nu}})(\frac{d\ensuremath{\nu}}{\mathrm{dT}})$ for these three phases are approximately -${10}^{\ensuremath{-}3}$, -${10}^{\ensuremath{-}3}$, and -${10}^{\ensuremath{-}4}$ per degree centigrade, respectively. In the tetragonal phase at 220\ifmmode^\circ\else\textdegree\fi{}C, $\frac{{e}^{2}\mathrm{qQ}}{h}$ has been measured as 24 Mc/sec and the asymmetry parameter $\ensuremath{\eta}$ is zero. An ionic calculation of field gradients in the tetragonal phase has been made including point charge and induced dipole contributions. The results of this calculation give the Sternheimer antishielding factor ($1\ensuremath{-}{\ensuremath{\gamma}}_{\ensuremath{\infty}}$) as 15 in good agreement with its estimated value of +16. The temperature dependence of the electric field gradient at the ${\mathrm{Nb}}^{93}$ site as calculated from this ionic model is in agreement with the measured temperature dependence in the tetragonal phase.

Atomic-Beam Measurement of the Hyperfine Structure and Nuclear Moments of Iodine-131

The nuclear magnetic dipole and nuclear electric quadrupole interaction constants a and b were measured in 8-day I/sup 131/ by an atomic beam magnetic resonance experiment. The results were a = 575.903 plus or minus 0.007 Mc/sec, b = 578.866 plus or minus 0.075 Mc/sec. The zero-field hyperfine splittings computed from these values of a and b were DELTA nu (5,4) = 3292.99 plus or minus 0.09 Mc/sec, DELTA nu (4,3) = 2138.22 plus or minus 0.05 Mc/sec, DELTA nu (3,2) = 1314.24 plus or minus 0.07 Mc/sec. The nuclear magnetic dipole moment and nuclear electric quadrupole moment were calculated as mu /sub 131/ = 2.738 plus or minus 0.001 nm, Q/sub 131/ = --0.41 plus or minus 0.01 x 10/sup -24/ cm/sup 2/. The value of mu /s ub 131/ obtained differed slightly from that obtained by other workers, whereas the value of Q confirmed an earlier measurement made by a different method. (auth)

Hyperfine Structure and Nuclear Moments of 17-Hr Bromine-76

The nuclear spin, the nuclear magnetic-dipole interaction constant $a$, and the nuclear electric-quadrupole interaction constant $b$, have been determined for 17-hr bromine-76 by an atomic-beam experiment. The results are: $I=1$, $|a|=345.422\ifmmode\pm\else\textpm\fi{}0.014$ Mc/sec, $|b|=314.329\ifmmode\pm\else\textpm\fi{}0.022$ Mc/sec, $\frac{b}{a}=0.9100\ifmmode\pm\else\textpm\fi{}0.0001$. The nuclear magnetic-dipole and electric-quadrupole moments are calculated to be, respectively, $\ensuremath{\mu}=\ifmmode\pm\else\textpm\fi{}0.5479\ifmmode\pm\else\textpm\fi{}0.0001$ nuclear magneton, and $Q=\ensuremath{\mp}0.27\ifmmode\pm\else\textpm\fi{}0.01$ barn. The sign of $\ensuremath{\mu}$, though not determined, is probably negative. The hyperfine structure separations are $\ensuremath{\Delta}\ensuremath{\nu}(\frac{5}{2}, \frac{3}{2})=1256.47\ifmmode\pm\else\textpm\fi{}0.05$ Mc/sec, and $\ensuremath{\Delta}\ensuremath{\nu}(\frac{1}{2}, \frac{3}{2})=189.11\ifmmode\pm\else\textpm\fi{}0.05$ Mc/sec. The hyperfine structure is of particular interest because the $F=\frac{1}{2} \mathrm{and} \frac{3}{2}$ levels are inverted and not in normal order. This inversion is the first case of its kind established in an atomic-beam experiment.

Nuclear Quadrupole Interactions in Two Tutton's Salts

This paper reports results of nuclear induction experiments on two isomorphic single crystals of Tutton's salts, ${\mathrm{Rb}}_{2}$Mg${(\mathrm{S}{\mathrm{O}}_{4})}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O and ${\mathrm{Cs}}_{2}$Mg${(\mathrm{S}{\mathrm{O}}_{4})}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}6${\mathrm{H}}_{2}$O, belonging to crystal class $\frac{P{2}_{1}}{a}$. The splittings, due to nuclear electric quadrupole interactions, of the nuclear magnetic resonance spectra of ${\mathrm{Rb}}^{87}$ and ${\mathrm{Cs}}^{133}$ observed in these experiments are analyzed by using perturbation theory. Analysis of the data yields a quadrupole coupling constant for ${\mathrm{Rb}}^{87}$ of $|\frac{\mathrm{eQq}}{h}|=3141\ifmmode\pm\else\textpm\fi{}35$ kc/sec, and the asymmetry of the field gradient at the nuclear site is $\ensuremath{\eta}=\frac{({\ensuremath{\varphi}}_{\mathrm{xx}}\ensuremath{-}{\ensuremath{\varphi}}_{\mathrm{yy}})}{{\ensuremath{\varphi}}_{\mathrm{zz}}}=0.47\ifmmode\pm\else\textpm\fi{}0.01$. The principal axis of the field gradient is directed toward the nearest sulfate ion but no correlation of asymmetry and near neighbor locations is observed.Comparison of the magnitudes of the field gradient at the nuclear sites of Rb and Cs were obtained by comparing the observed line patterns for the symmetry axis rotations, using the known moments of Cs and Rb. The complexity of the Cs spectra precluded a more complete comparison of the electric field symmetry.

Paramagnetic resonance in diluted copper salts II. Salts with trigonal symmetry

An interesting transition in the paramagnetic resonance spectrum has been observed for a number of cupric salts with trigonal symmetry. At room temperature only a single nearly isotropic line is observed, with a small hyperfine structure. Below a certain temperature, which depends on the salt, the spectrum is that of three kinds of copper ion each with nearly axial symmetry about one of three mutually perpendicular directions. The behaviour of this spectrum is similar to that of the copper Tutton salts in the anisotropy of the (/-tensor and magnetic hyperfine structure, and in the presence of a nuclear electric quadrupole interaction. A careful analysis of the spectrum is made for (Cu, Mg) 3 La 2 (NO 3 ) 12 .24D 2 O.

Double-Bond Character of Conjugated Carbon-Chlorine Bonds

The π electron loss of a chlorine atom conjugated with a resonating system can be obtained at least approximately from experimental measurements of the asymmetry of the chlorine nuclear electric quadrupole interaction. Using molecular orbital theory the π electron loss ρ can be simply expressed in terms of the chlorine Coulomb integral, the carbon-chlorine resonance integral, and the energies and wave functions of the system with which the chlorine atom is conjugated. Comparison of theoretical and experimental values of ρ show that the carbon-chlorine resonance integral is about one-third of the carbon-carbon resonance integral. The basic conclusion is that chlorine atoms in general resonate only weakly with attached aromatic systems. Most of the effects previously ascribed to double bond character can alternatively be explained by an increased electronegativity of the carbon sp2 orbital.

The paramagnetic resonance spectra of gadolinium and neodymium ethyl sulphates

Accurate measurements of the paramagnetic resonance spectra of gadolinium and neodymium ethyl sulphates have been made both in strong magnetic fields at a wave-length of 3 cm, and in weak fields at wave-lengths between 6 and 22 cm. (i) The Gd 3+ ion is in an 8 S state, whose levels are split by the action of the crystalline electric field, which is assumed to have C 3 h symmetry. The results are consistent with this supposition, except for some discrepancies in the position of the zero field lines, whose origin is not certain. The main parameters in the spin Hamiltonian are evaluated, and the spectroscopic splitting factor is found to be isotropic at 1.990±0.002. (ii) The Nd 3+ ion is in a 4 I 2/3 state, which is split by the crystal field leaving a Kramers doublet as the ground state. The hyperfine structure due to the two odd isotopes 143, 145 has been measured and gives the ratio of the nuclear magnetic moments (143/145) as 1.6083±0.0012. Some small discrepancies in the positions of the hyperfine lines in zero field are found, which prevent the determination of accurate values of the nuclear electric quadrupole interaction. The theory of Elliott & Stevens (1953 b ) leads to values of 1.0 and 0.62 nuclear magnetons for the moments of isotopes 143 and 145 respectively, with an uncertainty of about ±25% arising from lack of a precise value for r –3 ¯¯¯ , where r is the electron-nuclear distance.

The Electric Quadrupole Splitting of the Nuclear Magnetic Resonance Lines of Sodium in a Single Crystal of Na2S2O3·5H2O

Splitting of the nuclear magnetic resonance lines of sodium due to the nuclear electric quadrupole interaction was measured in a single crystal of sodium thiosulphate pentahydrate. Since each molecule contains two sodium nuclei which have different electric quadrupole interactions, and there are two groups of molecules with different orientations in a unit cell, twelve lines were observed in general. The experimental results were compared with the theoretical calculation of Bersohn and the values of e 2 q Q , η and the directions of the principal axes of the field gradient tensor were determined for each nucleus. The values of e 2 q Q and η are 2.26 Mc/sec and 0.334, and 0.830 Me/sec and 0.41 respectively for two nuclei in the molecule.

The Hyperfine Structure and Nuclear Moments ofPr141

The hyperfine structure of the ground state of ${\mathrm{Pr}}^{141}$ has been studied by the atomic beam magnetic resonance method. It has been established that the electronic ground state of Pr is $4{f}^{3}6{s}^{2}$, $^{4}I_{\frac{9}{2}}$. Of the five hyperfine intervals arising from this electronic state and a nuclear spin of $\frac{5}{2}$, the lowest two have been observed. They are $W(F=4)\ensuremath{-}W(F=3)=3708.05$ Mc/sec and $W(F=3)\ensuremath{-}W(F=2)=2782.25$ Mc/sec. If the hfs is assumed to be entirely due to an interaction between the $^{4}I_{\frac{9}{2}}$ state and the nucleus, the observed intervals may be expressed in terms of a magnetic dipole interaction constant $A$ and a nuclear electric quadrupole interaction constant $B$. It is found that $A=926.03\ifmmode\pm\else\textpm\fi{}0.1$ Mc/sec and $B=\ensuremath{-}13.9\ifmmode\pm\else\textpm\fi{}1.0$ Mc/sec. From these constants, the nuclear moments have been evaluated by means of approximate methods. The values obtained are $\ensuremath{\mu}=+3.8 \mathrm{nm}, Q=\ensuremath{-}0.054\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24} {\mathrm{cm}}^{2}.$

Nuclear Electric Quadrupole Spectra in Solids

Recent experiments have demonstrated the feasibility of observing nuclear electric quadrupole interactions of widely varying magnitudes in solids. While these effects can often be observed in powdered samples, the most complete information is obtainable from the Zeeman pattern of a single crystal. To facilitate interpretation of these experiments, the nuclear spin energy levels are derived for different relative magnitudes of quadrupole interaction and external magnetic field. Besides the knowledge of the gradient of the electric field tensor, in principle, low frequency molecular rotation should be detectable by means of the quadrupole spectra.

Nuclear Electric Quadrupole Interaction in Crystals with Nonaxially Symmetric Fields

Nuclear Electric Quadrupole Interaction in Crystals with Nonaxially Symmetric Fields

On the Ratio of the Nuclear Magnetic and Electric Quadrupole Interactions for AtomicCl35andCl37

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