Zeeman Splitting Of Nuclear Quadrupole Resonance Lines

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EPR and Mössbauer Spectroscopies

Interaction between the nuclear spin I and the electron spin S is described by the hyperfine coupling tensor A and results in splitting into (2I + 1) lines. Two main contributions: (1) Fermi contact term (requires spin density at the nucleus; caused by spin polarization); the Fermi contact term is isotropic.

University of Delaware

Strong Field Zeeman Splitting of Chloride Nuclear Quadrupole Resonance in Paradichlorobenzene KAMACK, HARRY J. Mathematics Solutions of Integral Equations Arising in Particle Size Analysis Mechanical Engineering KEEN, ARNOLD RALPH Production of Industrial Inert Gas from Stack Gas Chemistry KELLY, WILLIAM HENDERSON

14.2 Electron paramagnetic resonance (EPR) spectroscopy

Note: In the absence of nuclear hyperfine interaction the nuclei involved have no nuclear spin, and therefore, there will be no nuclear Zeeman term or nuclear electric quadrupole term. Thus the relation is rigorously correct for S = systems. g-matrix When the paramagnetic species exhibits an anisotropy, the spatial dependency of the g-

Diamond-nitrogen-vacancy electronic and nuclear spin-state

resulting in further state mixing and an electron-nuclear spin flip anticrossing. Solving for the eigenstates of H gs indicates that transverse magnetic fields induce state mixing in the low axial magnetic field regime by bringing the nuclear spin states into resonance via the electronic Zeeman term [μ Bg

Solid-State Deuterium NMR Spectroscopy of Membranes P

(a) Energy levels and resonance lines in 2H NMR spectroscopy. The Zeeman Hamiltonian Hˆ Z is perturbed by the quadrupolar Hamiltonian Hˆ Q giving an unequal spacing of the nuclear spin energy levels, indicated by m where m = 0, ±1. The quadrupolar splitting ν Q is the difference in the frequencies (ν± Q

NMR and EPR spectroscopies with Quantum-Espresso

Principles of magnetic resonance Zeeman splitting Gyromagnetic ratio A spin in a magnetic field will align parallel or antiparallel to the field. The Zeeman splitting is proportional to the total magnetic field. The energy splitting can be probed by an electromagnetic wave of frequency ω:

Mossbauer Spectroscopy: Zeeman splitting and Resonant Line Width

Zeeman Splitting I=3/2-1/2 1/2 3/2 1/2-1/2 I=1/2 3/2 mj Fe57 is simple example of pure nuclear Zeeman effect. Cubic symmetry of iron lattice means no quadrupole shifts in nuclear energy levels.

Quadrupole Coupling Tensor for 11B in Datolite

fig. l(c) for the case when the quadrupole interaction is sufficientl7 large that second order perturbation terms are required for a complete description of the energy levels. The result of this additional inter­ action is that the 2I+l nuclear Zeeman levels are shifted by unequal amounts so that they are no longer equidistant.

I Nuclear Quadrupole Resonance in 4,4 -Diiodobiphenyl

Zeeman analysis using a single crystal. Experimental The spectrometer used for the detection of the 127I reso-nance lines was a super-regenerative parallel transmission line oscillator with a frequency modulation (similar to the one described by Kojima et al.8))The Zeeman effect was ex-amined at room temperature using the zero-splitting cone

About the possibility of identification of hydrocarbon

unique resonance absorption spectra of substances are the Zeeman effect and the so-called chemical shift. The Zeeman effect (Pieter Zeeman was a Dutch physi-cist who received the Nobel prize for his discovery in 1902) is the split of lines of atomic spectra in a magnetic field (Fig. 1). The resulting absorption spectrum of a substance is


Y is the unperturbed nuclear resonance frequency. Since we are particularly concerned with the case where the quadrupole splitting is small compared with the Zeeman splitting, the Boltzmann factors relating the equilibrium populations 3 2 I -5 t. t aP Y Figure 1. Spin-lattice and spin-spin transitions affecting energy level populations


where the first term in the sum is the electron Zeeman splitting, followed by per-turbational correction terms of increasing order for the hyperfine splitting. To ob-tain the resonance line positions, the above expressions are inserted into resonance condition 11E(,) ( ,)+ 22mE m hvIImw−−= , which is then solved for B0.

anCl Zeeman quadrupole spectra in CoHgCI44HaO to the

Abstract. A new ~CI nuclear quadrupole resonance was reported at room tempe- rature for the first time in CoHgCI4.4H:O at 20.583 MHz. The results of the Zeeman effect revealed that the principal Z-direction is parallel to b axis and the value of the asymmetry parameter r/ is 0.042.

Bulk and Nanocrystalline Cesium Lead-Halide Perovskites as

) to produce the Zeeman splitting of nuclear-spin energy levels mI In the case of quadrupolar nuclei (I > 1/2) such as halides, the Zeeman energy states are perturbed by the interaction of the electric-field gradient (EFG) with the quadrupole moment of the nuclear spin the so-called quadrupole interaction.

53Cr, 17O and 14N nuclear quadrupole resonance in ammonium

The nuclear quadrupole spectrum of ammonium dichromate has been published on two previous occasions [1, 2]. Both using cross relaxation as the detection mode [3]. This form of detection relies on matching the splitting of the proton levels to that of the quadrupole levels by magnetic field adjustments, so line(s) in the spectrum are subject to

Mossbauer Spectroscopy for the Determination of Quadrupole

Quadrupole Splitting Quadrupole moment comes from a non-spherical nuclear charge distribution Quadrupole splitting arises from an internal electric field gra-dient ∆E= e 3m2 I −I(I+1) 4I(2I−1) Q∂ 2V ∂z2, e is charge of electron, I is angular momentum, mI magnetic quantum number of nuclear state, Q quadrupole moment, V

MŁossbauer Spectroscopy Lab Guide

nuclear magnetic dipole and/or electric quadrupole mo-ments with internal or external fields in the absorber (Zeeman or electric quadrupole splittings). In a famous experiment that tested the red shift predicted by the gen-eral theory of relativity, the shift was caused by a ≈ 100 foot difference in height of the source and absorber!

Strong Quadrupole Interaction in ENDOR Spectroscopy

haviour as in the nuclear quadrupole resonance exper- then the theory of Zeeman splitting of pure quadrupole resonance spectra can be used in the ENDOR lines from nuclei with strong quadrupole

Nuclear Quadrupole Coupling of B-12 in a Single Be Crystal

5 NUCLEAR QUADRUPOLE COUPLING OF 12B IN A SINGLE 1437 under field reversal and variation of the angle 8 between crystal c axis and external magnetic field. The resonance lines are narrow and, with a sufficiently strong quadrupolar coupling, the crystal can always be oriented so that the quadru­ pole splitting falls within a convenient range.

Orientation dependence of the 23 Na nuclear quadrupole spin

Orientation dependence of the 23Na nuclear quadrupole spin-lattice relaxation in sodium nitrate D. G. HUGHES and K. REED Department of Physics, University of Alberta, Edmonton, Canada MS. received 4th June 1971 Abstract. The orientation dependence of W,/Wl has been measured for 23Na in sodium

Tc and Other Cuprate Properties in Relation to Planar Charges

quadrupole moment that interacts with the electric field gradient at the nuclear site. This quadrupole interaction typically perturbs the Zeeman splitting (if the external magnetic field is strong enough), and information about the local charge symmetry can be conveniently obtained from the NMR spectra for various external field directions.

Optically detected nuclear quadrupolar interaction of 14N in

to the strong dependence of the quadrupole coupling constant on the electronic environment [11,15 17]. Several techniques are used to measure nuclear quadrupolar interactions. For instance, nuclear magnetic resonance (NMR) spectroscopy is used to measure the quadrupolar coupling when it is a small perturbation to the much larger Zeeman


intensity of the Zeeman spectrum drops below noise level and when neigh-bouring resonance lines, if present, begin to overlap. Super-regenerative oscillators1' are used in order to get a high S/N ratio. The difficulty encoun-tered due to overlap between the unsuppressed side-band responses of self-0 a C Table 1.

M¨ossbauer Spectroscopy

nuclear magnetic dipole and/or electric quadrupole mo­ ments with internal or external fields in the absorber (Zeeman or electric quadrupole splittings). In a famous experiment that tested the red shift predicted by the gen­ eral theory of relativity, the shift was caused by a ≈ 100 foot difference in height of the source and absorber!


level shift due to quadrupole interaction is proportional to 3m2 K −K(K+1), where Kis the nuclear spin of the noble gas atom and mK is the magnetic quantum number of the spin K. Therefore, the quadrupole interaction causes a splitting of the nuclear magnetic resonance line. This quadrupolar splitting provides a clear signature of the

B-2 Mossbauer Spectroscopy

(2) nuclear Zeeman effect, and (3) quadrupole splitting are due to hyperfine interactions, while the (4) temperature shift is a relativistic effect. Recoil-free fraction The depth of the Mössbauer resonance is determined by the fraction of recoil-free emissions in the source and

Actual Problems of Computer Parametric Identification of the

Pulsed excitation of nuclear quadrupole resonance (NQR) and nuclear magnetic resonance (NMR) is wide-ly used in physics to study internal electric fields, as well as during the study of non-equilibrium states of nuclear spins (relaxation processes) [1, 2]. In particu-lar, the spin echo phenomenon provides the most con-

Bulk and nanocrystalline cesium lead halide perovskites as

and the coupling strength given by the quadrupole constant (C Q). It is produced by neighboring nuclei and electrons and reflects the chemical and electronic surrounding of a spin. In NMR spectroscopy, the Zeeman interaction (H ZE) induces the splitting of the nuclear spin states in a magnetic field.

Single-shot spatially-localized NQR using field-dependent

Zeeman splitting Laplace inversion Classification Authentication abstract Nuclear quadrupole resonance (NQR) is commonly used to characterize solid materials containing quadrupolar nuclei. For example, NQR is a promising technique for detecting plastic explosives and other forbidden substances as well as for authenticating pharmaceutical products.

F. Tran, A. Khoo, R. Laskowski, P. Blaha

I Isomer shift, quadrupole splitting, Zeeman splitting I The fraction of recoil-free events and lifetime of the excited state limit the number of isotopes that can be used successfully for Mossbauer¨ spectroscopy: 1 R. M¨ossbauer, 1961 Nobel Prize in physics


TAB L E ° CONTENTS. F PAGE 1 The Mossbauer Effect 1 2 Description of the Educational Mossbauer Analyzers 10 EXPERIMENT 1 Gamna-Ray Spectrum of the MOssbauer Source

Powder Zeeman Study of the Nuclear Quadrupole Resonance Lower

S. Ramaprabhu and K. V. S. Rama Rao Zeeman Study of the Nuclear Quadrupole Resonance 113 Here / is the nuclear spin, 6 and

Powder Zeeman Study of the Nuclear Quadrupole Resonance Lower

The Zeeman effect of the nuclear quadrupole resonance (NQR) lower transition (± 3/2 <- 1/2) spectrum for 7=5/2 in crystalline powder has been studied and the frequency splittings of the ±3/2 <- ± 1/2 transition line have been plotted as a function of the asymmetry parameter t] and

Nuclear Magnetic Resonance Study of Three Dimensional Dirac

resonance lines. This e ect is due to the quadrupole interaction. Because Na 3Bi has two sodium sites with di erent symmetries, a complete NMR spectrum may have two sets of three resonance lines from each of the sodium sites and one set of nine resonance lines from the bismuth atoms. The resonance lines can be further characterized with spin

Quadrupole Couplings of N12 and B12 Implanted in Metal Single

(Mg, Be, Zn), where the respective nuclear quad­ rupole moments interact withthe crystalline elec­ tric field gradient. The advantages of single crys­ tal over polycrystalline stopping materials have already been demonstrated in the case of the l;aB quadrupole coupling in Be. 1,3 The experimental technique employed in measuring the quadrupole

Measurement of the hyperfine splitting of Cs atoms in

of OROCHI method, especially observing Zeeman resonance and determining nuclear spins. The measurement of HFS splitting of atoms introduced into He II is indispensable to clarify the nuclear properties by deducing nuclear moments as well as the study of nuclear spins. For this purpose, we perform a precision measurement of HFS of 133Cs atoms

Nuclear quadrupole resonances in compact vapor cells: The

netic resonance NMR the NQR lines could be clearly resolved by using highlyspectra 1 , as well as in the pure nuclear quadrupole resonance asymmetric cells. They performed a detailed perturbation-NQR regime, where little or no Zeeman interaction was present 2 Solutions for the transition energies between nuclear spin sublevels were

NMR at Very Low Temperatures: Population Difference

The fine structure splitting for the NQR lines re-sulting from the Zeeman perturbation is illustrated Bulletin of Magnetic Resonance-(m+1) + m B = 0 B # 0 Figure lb: Energy level diagram for a nuclear elec-tric quadrupole interaction for a nucleus with spin / in the presence of a small magnetic field B. The quantum number m = I z.-(m+1) m +m

Diamond-nitrogen-vacancy electronic and nuclear spin-state

95 resulting in further state mixing and an electron-nuclear spin 96 flip anticrossing. Solving for the eigenstates of H gs indicates 97 that transverse magnetic fields induce state mixing in the 98 low axial magnetic field regime by bringing the nuclear 99 spin states into resonance via the electronic Zeeman term 100 [μ Bg

The nuclear quadrupole resonance magnetometer: A new method

Zeeman splitting of a nuclear quadrupole resonance line is presented. With a single crystal of potas' sium chlorate as the sensor, an nqr magnetometer with center frequency of 28 MHz and bandwidth of 10 MHz could cover a range of 10 nT to greater than 1 T. Precision at specific crystal ori entations