Amplitude correlations in nuclear resonance spectroscopy

Both magnitudes and relative signs of inelastic decay amplitudes have been measured for proton resonances in the compound nuclei ⁴⁵Su, ⁴⁷V, ⁴⁹V, ⁵¹Mn, ⁵⁵Co, and ⁵⁷Co. Resonances with orbital angular momenta 1,2 and 3 and five different values of J^π were studied. For l = 1 and l = 2 resonances, sample sizes are sufficient to perform statistical analyses: distributions of the reduced widths, distributions of the products of reduced width amplitudes, and both amplitude and widt correlations have been determined over energy ranges of ～ 1 MeV. The distributions are compared with the predictions of random matrix theory, and good overall agreement is obtained. These result have provided new tests of the statistical theory of resonances and of the theory of isobaric analogue states. In addition, these data give the first experimental confirmation of the channel coupling required by direct reaction theory. The linear correlation coefficients are often surprisingly large (for these data sets, the average value is >0.5 ), so large in fact that the traditional DWBA treatment of direct reactions must fail in some cases. This failure is discussed with the aid of a simplified model. Tests of the Gaussian nature of reduced width amplitudes are also examined.     

Photon-echo detected nuclear quadrupole resonance spectroscopy

Rare-earth-ion-doped crystals (REICs) have played an important role in quantum information processing due to their excellent coherent properties. In order to obtain the information regarding the hyperfine structures of the rare-earth ions in REICs, optically detected nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) techniques based on RF resonance and various optical detection methods are widely employed in previous works. Here we demonstrate a new method of NQR spectroscopy based on the photon-echo detection. The hyperfine spectra of the ground state (⁷F₀) and the optically-excited state (⁵D₀) of ¹⁵¹Eu³⁺ in Y₂SiO₅ at zero field are obtained. This method can determine the hyperfine splittings within the ground state and the optically-excited state and is shown to be robust against electrical noise. Our results provide an alternative way for optical detection of NMR and NQR with high signal-to-noise ratio.     

Double-resonance circuit for nuclear magnetic resonance spectroscopy

A new double-resonance probe circuit design is described. The circuit contains no quarter-wavelength elements or equivalents, yet nonetheless achieves adequate isolation between the two input channels. It contains relatively few components, and so is both compact and efficient. It has been incorporated in two solid-state nuclear magnetic resonance (NMR) probes, with excellent results.     

New developments in nuclear magnetic resonance using noise spectroscopy

In the 30 years since Ernst and Kaiser introduced the idea of incoherent radiation fields and their application to NMR spectroscopy, relatively few researchers have exploited the advantages of noise spectroscopy. Some recent applications of one-dimensional noise spectroscopy in NMR are presented which display a versatility which commonly is not appreciated. Excitation schemes are discussed which demonstrate both broadband and narrowband features, and demonstrate both theoretically and experimentally how noise spectroscopy allows for the observation of distortion-free broadline spectra in solids whichmay not be amenable to techniques more traditionally used in pulsed NMR experiments. It is argued that these applications of noise spectroscopy deserve a more common place in the experimentalists arsenal.     

White noise nonlinear system analysis in nuclear magnetic resonance spectroscopy

Nonlinear noise excitation in nuclear magnetic resonance is a form of nonlinear spectroscopy which exploits the nonlinear susceptibilities in a very direct way. The nonlinear susceptibilities are defined by perturbation theory in the frequency domain. In nonlinear system analysis, on the other hand, the system response is described by a Volterra series in the time domain. The kernels of the Volterra functionals carry the information about the system and are to be determined by experiment.The series expansion of a molecular, atomic or nuclear system response is derived in quantum mechanics by time dependent perturbation theory, leading to a Volterra series with time ordered, triangular kernels. The kernels are multi-dimensional products of decaying exponentials, which describe coherence decays of particular density matrix elements. The Fourier transforms of the triangular Volterra kernels are the susceptibilies, which are formally identical in NMR spectroscopy and nonlinear optical spectroscopy. The nonlinear susceptibilities are multi-dimensional spectra, which in NMR spectroscopy reveal the spin communication pathways. These are established by various forms of single quantum coherence connectivities, such as indirect coupling, chemical exchange, cross-relaxation, dipolar and quadrupolar coupling.If the functionals of the Volterra series are orthogonalized with respect to Gaussian white noise excitation, the Wiener series results. The Wiener kernels can be derived by multi-dimensional cross-correlation of the system response with different powers of the Gaussian white noise excitation.Cross-correlation of the transverse magnetization response to noise excitation in NMR leads to multi-dimensional time functions, the Fourier transforms of which closely resemble the nonlinear susceptibilities. The cross-correlation spectra differ from the susceptibilities in the governing Liouvillean and the dynamic density matrix, which are affected by saturation for continuous excitation. Cross-correlation spectra and susceptibilities converge for vanishing excitation power. Therefore the cross-correlation spectra are referred to as stochastic susceptibilities.In stochastic NMR spectroscopy only odd order susceptibilities exist for transverse magnetization. The first nonlinear order is the third, and the nonlinear spectral information is derived from the third order susceptibility. Higher order susceptibilities are not feasible to derive from experimental data. An important share of the nonlinear information is found on the six subdiagonal 2D cross-sections through the third order susceptibility. These cross-sections arise in three pairs, which carry distinct information, separated according to longitudinal magnetization and population effects, zero quantum coherences, and double quantum coherences.In practice a nonlinear 3D spectrum is computed from experimental data by an algorithm in the frequency domain, which yields access to selected regions in the 3D spectrum. This spectrum is the symmetrized stochastic third order susceptibility. All its sub-diagonal 2D cross-sections are equivalent. They are the average of the six different sub-diagonal 2D cross-sections through the asymmetric third order susceptibility.The stochastic excitation technique in NMR is characterized by several unique attributes. (1) There is no minimum time for a data acquisition cycle, so that, at the expense of signal-to-noise ratio, strong samples can be investigated faster with stochastic NMR than with pulsed FT NMR. (2) Stochastic excitation tests the sample extensively, and measures a maximum amount of information in a single experiment. This feature is of particular interest for investigation of short-lived samples and of samples with little a priori information. (3) An experiment with stochastic excitation is simple to perform, but the data processing is more complex than in FT spectroscopy. (4) The nonlinear information about spin communication pathways is derived for individual frequency regions only, which are identified in the stochastic ID spectrum. This information is located primarily on the sub-diagonal 2D cross-sections through the third order susceptibility. (5) Stochastic NMR spectra derived from random noise excitation are contaminated by systematic noise. In the sub-diagonal 2D cross-sections the noise is reduced by filtering and symmetrization during data processing. (6) Sub-diagonal 2D cross-sections are sensitive to experimental phase distortions in one direction only. They are readily adjusted in phase with the same parameters as the ID spectrum. (7) Stochastic multi-dimensional spectra can be computed at variable resolution from one and the same set of raw data.So far stochastic NMR spectroscopy is not applied routinely in analytical spectroscopy. More practical experience is needed to evaluate its merits in comparison with Fourier transform NMR.Stochastic excitation is distinguished from continuous wave and sparsely pulsed excitation by low input power in connection with large bandwidth. This important property cannot be exploited in high resolution NMR in liquids, because excitation power is not a restricting factor in this case. The situation is different in NMR imaging, where large field gradients require large bandwidths and the excitation power becomes a point of concern. For this reason stochastic RF excitation is being investigated in NMR imaging.The multi-dimensional cross-correlation functions obtained from random noise excitation generally are contaminated by systematic noise. The occurrence of systematic noise can be avoided if pseudo-random excitation is used in combination with a transformation of the system response to obtain the kernels. This technique is used successfully in Hadamard spectroscopy, where the linear Volterra kernel is the Hadamard transform of the linear response functional. Nonlinear transformations^(220,221) for retrieval of nonlinear kernels have not yet been realized in NMR spectroscopy.The cross-correlation technique underlying the data evaluation in stochastic nonlinear system analysis is equivalent to interferometry in optical spectroscopy. The Michelson interferometer is the most prominent optical correlator. The time resolution of the kernels derived by cross-correlation is determined by the inverse bandwidth of the excitation. With the Michelson interferometer a time resolution of 10⁻¹⁴ s is achieved in IR spectroscopy. Since the IR correlogramm is Fourier transformed for spectral analysis, the time resolution cannot be exploited otherwise. For analysis of fast time dependent processes a two-dimensional interferometer should be constructed, which performs a 2D cross-correlation of the system response to two in general different noise inputs. One input pumps the time dependent process, the other is used to investigate the time dependence spectroscopically. This technique is introduced by the name of ‘two-dimensional interferometry’. It uses low excitation power, but provides high time resolution at large response energy. Related work is pursued in nonlinear optical spectroscopy with incoherent excitation. In this area the use of broad band lasers is investigated for generation of echoes and for correlation based measurements of relaxation times.     

Two-dimensional exchange nuclear quadrupole resonance spectroscopy of molecular crystals

A theoretical treatment of the 2D exchange NQR pulse sequence is presented and applied to the quantitative study of exchange processes in molecular crystals. It takes into account the off-resonance irradiation, which critically influences the spin dynamics. The response of a system of spins I = 3/2 in zero applied field, experiencing electric quadrupole couplings, to the three-pulse sequence is analysed. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. The mixing dynamics by exchange and the expected cross-peak intensities as a function of the frequency offset have been derived. The theory is illustrated by a study of the optimization procedure, which is of crucial importance for the detection of the cross- and diagonalpeaks in a 2D exchange spectrum. The systems investigated here were hexachloroethane and tetrachloroethylene, which show threefold and twofold reorientational jumps about the carbon-carbon axis, respectively.     

Chemisorption and surfaces studied by nuclear magnetic resonance spectroscopy

This paper presents an introduction to the study of surfaces and chemically adsorbed species with nuclear magnetic resonance (NMR) spectroscopy. The analysis is based on nuclear magnetic interactions in the solid state: dipole-dipole couplings, chemical shift anisotropy, Knight shifts, and quadrupolar splitting. The physical origins and characteristics of each interaction, as well as relative intensities for different nuclei, are discussed. In particular, emphasis is placed on the relation of these interactions to quantities of interest to studies in adsorption and catalysis: motional properties of the adsorbate, the distribution of adsorption sites, the chemical state of atoms adsorbed at the surface, electrostatic field gradients, and the metallic character of surface atoms. Techniques to observe these interactions are described; subdivided by the type of nucleus: strongly coupled nuclei (e.g. ¹H, ¹⁹F), weakly coupled nuclei (e.g. ¹³C, ¹⁵N, ²⁹Si, ¹⁹⁵Pt), and quadrupolar nuclei (e.g. ²H, ¹⁴N, ²⁷Al). The techniques described to isolate and identify the overlapping effects in the spectra include multiple-pulse spin echoing and decoupling, double-resonance irradiation, multiple-quantum excitation, and mechanical sample spinning. A review of the recent application of these techniques to studies of adsorption and surfaces illustrates the potentials and limitations. Finally, a procedure for formulating a NMR study of surface samples is proposed, with respect to sample composition and character, and the type of information desired.     

Study of natural diamonds by dynamic nuclear polarization-enhanced C nuclear magnetic resonance spectroscopy

The results of a study of two types of natural-diamond crystals by dynamic nuclear polarization (DNP)-enhanced high-resolution solid-state ¹³C nuclear magnetic resonance (NMR) are reported. The home-built DNP magic-angle spinning (MAS) ¹³C NMR spectrometer operates at 54 GHz for electrons and 20.2 MHz for carbons. The power of the microwave source was about 30 W and the highest DNP enhancement factor came near to 10³. It was shown that in the MAS spectra the ¹³C NMR linewidths of the I_b-type diamond were broader than those of I_aB3-type diamond. From the hyperfine structure of the DNP enhancement as a function of frequency, four kinds of nitrogen-centred and one kind of carbon-centred free radicals could be identified in the I_b-type diamond. The hyperfine structures of the DNP enhancement curve that originated from the anisotropic hyperfine interaction between electron and nuclei could be partially averaged out by MAS. The ¹³C polarization time of DNP was rather long, i.e. 1500 s, and the spin—lattice relaxation time (without microwave irradiation) was about 300 s, which was somewhat shorter than anticipated. Discussions on these experimental results have been made in this report.     

Study of diamond film by dynamic nuclear polarization-enhanced13C nuclear magnetic resonance spectroscopy

Three chemical vapor deposited diamond films were studied by dynamic nuclear polarization (DNP)-enhanced high-resolution solid-state¹³C nuclear magnetic resonance (NMR) spectroscopy. Enhanced¹³C direct-polarization spectra of diamond films were obtained by irradiating the samples with microwaves at or near electron spin resonance Larmor frequency of carbon center free radicals. No NMR signal for sp² hybridized carbons could be observed. From the curve of the DNP enhancement as a function of frequency, it is found that the dominant DNP mechanism is the solid-state effect. The¹³C cross-polarization spectrum, which is an evidence for existence of the proton defect in the lattice of diamond films, is much broader than the¹³C single pulse spectrum. The reason is discussed shortly.     

Study of synthetic diamonds by dynamic nuclear polarization-enhanced13C nuclear magnetic resonance spectroscopy

Four I_b-type synthetic diamond crystals were studied by dynamic nuclear polarization (DNP)-enhanced high resolution solid state¹³C nuclear magnetic resonance (NMR) spectroscopy. The home built DNP magic-angle-spinning (MAS) NMR spectrometer operates at a field strength of 1.9 T and the highest DNP enhancement factor of synthetic diamonds came near to 10³. Comparing with I_b-type natural diamonds, the¹³C NMR linewidths of synthetic diamonds in static spectra are broader. The¹³C spin-lattice relaxation time and DNP polarization time of synthetic diamond are shorter than those of I_b-type natural diamond. From the hyperfine structure of the DNP enhancement curve, four kinds of nitrogen-centred free radicals could be identified in synthetic diamond.     

Magnetic field distribution in superconducting niobium by nuclear magnetic resonance fourier spectroscopy

Nuclear magnetic resonance measurements of the superconducting mixed-state field distribution in niobium metal are reported. It is demonstrated that pulsed NMR Fourier spectroscopy (defined in the text) can resolve considerable detail in the field distribution functionf(h). A simple analytic model forf(h) was used for numerical calculation of the expected spectrum shape. An ordered vortex lattice was always observed. Far from the transition the spectra were most consistent with triangular lattice symmetry. The temperature variation of the Maki parameter? ₂ was measured. The shift of spectrum position is compatible with appreciable reduction of spin susceptibility in the superconducting state.     

Therapeutic response of tumors by in-vitro proton nuclear magnetic resonance spectroscopy

Proton NMR spectra of perchloric acid extracts of methyl cholantherene induced tumors grown in rats have been analyzed and compared with the normal and the treated tumor tissue samples. Well-resolved resonances from numerous low-molecular weight compounds including various amino acids, nucleotides, choline, creatine, phosphocreatine etc. were observed and assigned using pH titration, 2D NMR and by comparison with the spectra of model compounds. Significant differences were noticed in the spectra of the tumor and the normal tissue samples. Ratios of metabolite levels were calculated for the normal, tumor and treated tumor tissues which are shown as good markers to assess the state of the tumor and their response to treatment.     

Studies of ion-solvent and ion-ion interactions using nuclear magnetic resonance spectroscopy

Chemical shifts of the fluorine nuclear resonance have been measured for fluoride ion in a variety of environments. The shift varies linearly with the mole-fraction of organic solvent and is dependent upon the nature and concentration of added cations and anions. In contrast, the value for the caesium resonance from solutions of caesium salts is independent of the choice of solvent. Large, linear, chemical shifts are observed when other electrolytes are added, the effect being almost entirely due to the anions.     

An eight-coil high-frequency probehead design for high-throughput nuclear magnetic resonance spectroscopy

In order to increase the throughput of high-resolution nuclear magnetic resonance spectroscopy a multiple-coil probe, which enables the simultaneous analysis of eight different samples, was designed. The probe, consisting of eight identical solenoidal coils, was constructed for operation at 600 MHz. By using four receivers and radiofrequency switches, spectra from eight different chemical solutions were acquired in the time normally required for one. Two-dimensional COSY, gradient COSY, and TOCSY data have been acquired. Intercoil electrical isolation was between 25 and 45 dB, with signal cross-talk between approximately 1 and 5% measured by NMR. The spectral linewidths for the eight coils were between 3 and 6Hz for a single optimized shim setting.     

Quantum computation based on magic-angle-spinning solid state nuclear magnetic resonance spectroscopy

Magic-angle spinning (MAS) solid state nuclear magnetic resonance (NMR) spectroscopy is shown to be a promising technique for implementing quantum computing. The theory underlying the principles of quantum computing with nuclear spin systems undergoing MAS is formulated in the framework of formalized quantum Floquet theory. The procedures for realizing state labeling, state transformation and coherence selection in Floquet space are given. It suggests that by this method, the largest number of qubits can easily surpass that achievable with other techniques. Unlike other modalities proposed for quantum computing, this method enables one to adjust the dimension of the working state space, meaning the number of qubits can be readily varied. The universality of quantum computing in Floquet space with solid state NMR is discussed and a demonstrative experimental implementation of Grover's search is given. Received 19 April 2001