Suppression of artifacts induced by homonuclear decoupling in amino-acid-type edited methyl H–C correlation experiments

A detailed theoretical and experimental analysis of the artifacts induced by homonuclear band-selective decoupling during CT frequency labeling is presented. The effects are discussed in the context of an amino-acid-type editing filter implemented in ¹H–¹³C CT-HSQC experiments of methyl groups in proteins. It is shown that both Bloch–Siegert shifts and modulation sidebands are efficiently suppressed by using additional off-resonance decoupling as proposed by Zhang and Gorenstein [J. Magn. Reson. 132 (1998) 81], and appropriate adjustment of a set of pulse sequence parameters. The theoretical predictions are confirmed by experiments performed on ¹³C-labeled protein samples, yielding artifact-free amino-acid-type edited methyl spectra.     

Applications of the Bloch–Siegert Shift in Solid-State Proton-Dipolar-Decoupled19F MAS NMR

In solid-state proton-dipolar-decoupled¹⁹F MAS NMR spectroscopy,¹⁹F chemical-shift data need to be corrected for the Bloch–Siegert shift. Assigning the single sharp¹⁹F resonance of 2-fluoroadamantane to its proton-coupled¹⁹F shift of −174.4 ppm results in chemical-shift referencing that is independent of the amplitude of the proton-decoupling field. The Bloch–Siegert shift is also a useful tool to characterize the amplitude and homogeneity of the proton-decoupling field,H_1H, and to monitor probe performance. Considerable inhomogeneity inH_1Halong the long axis of the right-cylinder sample rotor was detected. In our commercial 7 mm H– F MAS probe, the proton field strength,[formula], decreases to 25% of the maximum value across the usable sample volume. Measurement of the Bloch–Siegert shift revealed that the proton-decoupling field strength decreases during the first few scans of an acquisition. Reductions in the proton field strengths can exceed 10%, and they are explained by the heating of the RF coil circuitry which is caused by high-power proton decoupling. The extent of reduction in field amplitude is a function of the decoupling duty cycle. Losses in[formula]can be avoided by tuning the probe proton RF circuitry at the operating temperature of the probe, using the Bloch–Siegert shift as an optimization parameter.     

Orientational dynamics of superfluid He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

"BEST" homonuclear adiabatic decoupling for 13C- and 15N-double-labeled proteins.

The cyclic irradiation sidebands appearing in homonuclear adiabatic decoupling are calculated in detail, which reveals the origin of the antisymmetric sidebands. The sidebands can be inverted by inserting an initial decoupling with a different period, but the same f1rms as the main decoupling that is required for Bloch-Siegert shift compensation. The sidebands can be eliminated in a broad decoupling range by adding spectra of opposite sidebands. Based on this scheme, an offset-independent double-adiabatic decoupling, named Bloch-Siegert Shift Eliminated and Cyclic Sideband Trimmed Double-Adiabatic Decoupling, or "BEST" decoupling for short, is constructed, which not only compensates the Bloch-Siegert shift as shown earlier by Zhang and Gorenstein (1998) but also eliminates residual sidebands effectively.     

Heteronuclear local field NMR spectroscopy under fast magic-angle sample spinning conditions

The acquisition of bidimensional heteronuclear nuclear magnetic resonance local field spectra under moderately fast magic-angle spinning (MAS) conditions is discussed. It is shown both experimentally and with the aid of numerical simulations on multispin systems that when sufficiently fast MAS rates are employed, quantitative dipolar sideband patterns from directly bonded spin pairs can be acquired in the absence of ¹H–¹H multiple-pulse homonuclear decoupling even for “real” organic solids. The MAS speeds involved are well within the range of commercially available systems (10–14 kHz) and provide sidebands with sufficient intensity to enable a reliable quantification of heteronuclear dipolar couplings from methine groups. Simulations and experiments show that useful information can be extracted in this manner even from more tightly coupled –CH₂– moieties, although the agreement with the patterns simulated solely on the basis of heteronuclear interactions is not in this case as satisfactory as for methines. Preliminary applications of this simple approach to the analysis of molecular motions in solids are presented; characteristics and potential extensions of the method are also discussed.     

K–K excitations on as “primary” superfields

We show that the K–K spectrum of IIB string on is described by “twisted chiral” superfields, naturally described in “harmonic superspace”, obtained by taking suitable gauge singlets polynomials of the D3-brane boundary superconformal field theory.To each p-order polynomial is associated a massive K–K short representation with states. The quadratic polynomial corresponds to the “supercurrent multiplet” describing the “massless” bulk graviton multiplet.     

Modified Kolmogorov wave turbulence in QCD matched onto “Bottom-up” thermalization

We investigate modification of Kolmogorov wave turbulence in QCD calculating gluon spectra as functions of time in the presence of a low energy source which feeds in energy density in the infrared region at a time-dependent rate. Then considering the picture of saturation constraints as has been constructed in the “bottom-up” thermalization approach we revisit that picture for RHIC center-mass energy, W=130 GeV, and also extend it to LHC center-mass energy, W=5500 GeV, thus for two cases having an opportunity to calculate the equilibration time, τ_eq|therm, of the gluon system produced in a central heavy ion collision at mid-rapidity region. Thereby, at RHIC and LHC energies we can match the equilibration time, obtained from the late stage gluon spectrum of the modified Kolmogorov wave turbulence, onto that of the “bottom-up” thermalization and other evolutional approaches as well. In addition, from the revised “bottom-up” approach we find the gluon liberation coefficient to be on the average, ε0.81–1.06 at RHIC and ε0.50–0.56 at LHC. We also present other phenomenological estimates of τ_therm which, at QCD realistic couplings, yield 0.45–0.65 fmτ_therm0.97–2.72 fm at RHIC and 0.31–0.40 fmτ_therm0.86–2.04 fm at LHC. We show that the second upper-bounds of τ_therm in both cases are due to the late stage gluon spectrum of the original Kolmogorov wave turbulence in QCD, previously deduced with a low energy source which feeds in energy density at a constant rate. On the other hand, the lower-bounds and first upper-bounds of τ_therm are due to the late stage gluon spectrum of the modified QCD wave turbulence, deduced here at the specific time-dependent rate. In the latter case, at certain conditions, taking also into account both very small and realistic couplings we give estimates: 0.65 fmτ_therm1.29 fm at RHIC and 0.52 fmτ_therm1.16 fm at LHC, as well as at realistic couplings we find 0.53<τ_therm<0.7 fm at RHIC and 0.41<τ_therm<0.65 fm at LHC.     

Fluorine-19 Solid-State NMR Magic-Angle-Turning Experiments Using Multiple-Pulse Homonuclear Decoupling

For compounds giving “crowded” 1-dimensional magic-angle-spinning spectra, information about the local atomic environment in the form of the chemical shift anisotropy (CSA) is sacrificed for high resolution of the less informative isotropic chemical shift. Magic-angle-turning (MAT) NMR pulse sequences preserve the CSA information by correlating it to the isotropic chemical shift in a 2-dimensional experiment. For low natural abundance nuclei such as ¹³C and ¹⁵N and under ¹H heteronuclear dipolar decoupling conditions, the dominant NMR interaction is the chemical shift. For abundant nuclei such as ¹H, ¹⁹F, and ³¹P, the homonuclear dipolar interaction becomes a significant contribution to the observed linewidth in both F₁ and F₂ dimensions. We incorporate MREV8 homonuclear multiple-pulse decoupling sequences into the MAT experiment to give a multiple-pulse MAT (MP-MAT) experiment in which the homonuclear dipolar interaction is suppressed while maintaining the chemical shift information. Extensive use of computer simulation using GAMMA has guided the pulse sequence development. In particular, we show how the MREV8 pulses can be incorporated into a quadrature-detected sequence such as MAT. The MP-MAT technique is demonstrated for a model two-site system containing a mixture of silver trifluoroacetate and calcium difluoride. The resolution in the isotropic evolution dimension is improved by faster sample spinning, shorter MREV8 cycle times in the evolution dimension, and modifications of the MAT component of the pulse sequence.     

Recoupled Polarization-Transfer Methods for Solid-State H–C Heteronuclear Correlation in the Limit of Fast MAS

An in-depth account of the effects of homonuclear couplings and multiple heteronuclear couplings is given for a recently published technique for ¹H–¹³C dipolar correlation in solids under very fast MAS, where the heteronuclear dipolar coupling is recoupled by means of REDOR π-pulse trains. The method bears similarities to well-known solution-state NMR techniques, which form the framework of a heteronuclear multiple-quantum experiment. The so-called recoupled polarization-transfer (REPT) technique is versatile in that rotor-synchronized ¹H–¹³C shift correlation spectra can be recorded. In addition, weak heteronuclear dipolar coupling constants can be extracted by means of spinning sideband analysis in the indirect dimension of the experiment. These sidebands are generated by rotor encoding of the reconversion Hamiltonian. We present generalized variants of the initially described heteronuclear multiple-quantum correlation (HMQC) experiment, which are better suited for certain applications. Using these techniques, measurements on model compounds with ¹³C in natural abundance, as well as simulations, confirm the very weak effect of ¹H–¹H homonuclear couplings on the spectra recorded with spinning frequencies of 25–30 kHz. The effect of remote heteronuclear couplings on the spinning-sideband patterns of CH_n groups is discussed, and ¹³C spectral editing of rigid organic solids is shown to be practicable with these techniques.     

Compositionally asymmetrical multiquantum wells: “Pseudo-molecules” for giant optical nonlinearities in the infrared (9–11 μm)

Intersubband transitions in quantum well have extremely large oscillator strengths and induce strong nonlinear effects in structures where inversion symmetry is broken, realized by growing AlGaAs quantum wells with asymmetrical A1 gradients. These compositionally asymmetrical multiquantum wells may thus be viewed as giant “quasimolecules” optimized for optimal nonlinearities in the mid infrared. Optical rectification as well as second harmonic generation have been measured in those structures using a continuous CO₂ laser. At 10.6 μm the nonlinear coefficients are more than 3 orders of magnitude higher in these samples than for bulk GaAs (i.e. χ₀⁽²⁾ = 5.3 × 10⁻⁶m/V, χ_2ω⁽²⁾ = 7.2 × 10⁻⁷ m/V) and are in good agreement with theoretical predictions. We present more complex “pseudo-molecules” involving weakly coupled quantum wells. The optical rectification effects in these devices are so large χ₀⁽²⁾ = 1.6 × 10⁻³ m/V) that application to infrared detection may be envisioned.     

Generic phase diagram of “electron-doped” T′ cuprates

We investigated the generic phase diagram of the electron doped superconductor, Nd_2−xCe_xCuO₄, using films prepared by metal organic decomposition. After careful oxygen reduction treatment to remove interstitial O_ap atoms, we found that the T_c increases monotonically from 24 K to 29 K with decreasing x from 0.15 to 0.00, demonstrating a quite different phase diagram from the previous bulk one. The implication of our results is discussed on the basis of tremendous influence of O_ap “impurities” on superconductivity and also magnetism in T′ cuprates. Then we conclude that our result represents the generic phase diagram for oxygen-stoichiometric Nd_2−xCe_xCuO₄.     

Effect of dipolar forces on the response functions of ordered magnetic crystals and their light scattering spectra

Response functions for ferromagnets and antiferromagnets are calculated using the linearized Bloch's equations for the spin system including dipole-dipole interaction. This calculation has proved to be equivalent to the simplest random-phase decoupling approximation when dipolar forces are not considered. Light scattering cross-sections have been calculated on the basis of the response functions obtained. The effect of dipole-dipole forces has been shown to be important when the shift in the magnon spectrum introduced by them is of the same order of magnitude as the magnon energy in the absence of such forces. Y.I.G. and MnF₂ have been considered as examples of ferromagnetic and antigerromagnetic crystals respectively, for which the variation of the scattering cross-section with temperature and external magnetic field is given     

Effective spin susceptibility, electron mass and Landé factor in two-dimensional (2D) Si inversion layers

We have studied the silicon (Si) band-structure, electron–electron and electron-ionized donor interaction effects on our accurate and approximate results (AcR and ApR) for renormalized effective spin susceptibitity (RESS), electron mass (EEM), Landé factor and spin polarization in the impure 2D Si (electron system), showing that:(i) our ApR, being strongly deviated from our AcR, reproduces approximately all the data obtained recently by Pudalov et al. (Phys. Rev. Lett. 88 (2002) 196404) [in particular, RESS =4.7 at the critical value of Wigner–Seitz radius r_s: r_s=r_c≈8.5 at which occur the “apparent” metal–insulator transition (MIT)] and can also be compared with other ApRs found in the recent literature,(ii) both the RESS and EEM produce physical singularities at the same critical value: r_s=r_c11.05661 (weakly disordered samples) at which occurs the “true” MIT; the existence of such two “apparent and true” critical values in this impure system agrees with a recent discussion by Abrahams et al. (Rev. Mod. Phys. 73 (2001) 251), and(iii) at r_s=r_c=8.5, at which occurs the “apparent” MIT, our AcR for effective spin polarization and the corresponding result, obtained using a disordered Hubbard model and a determinant quantum Monte Carlo method by Denteneer and Scalettar (Phys. Rev. Lett. 90 (2003) 246401), both give the same result: ξ_eff.=ξ_c0.31 at B0.4 T, which is found to be lower than the critical parallel magnetic field for full spin polarization, B_c=1.29 T, supporting thus the existence of such an “apparent” MIT.     

Noncommutative theories, the axial anomaly, Fujikawa's method and the Atiyah–Singer index

Fujikawa's method is employed to compute at first order in the noncommutative parameter the U(1)_A anomaly for noncommutative SU(N). We consider the most general Seiberg–Witten map which commutes with hermiticity and complex conjugation and a noncommutative matrix parameter, θ^μν, which is of “magnetic” type. Our results for SU(N) can be readily generalized to cover the case of general nonsemisimple gauge groups when the symmetric Seiberg–Witten map is used. Connection with the Atiyah–Singer index theorem is also made.     

Small-x behavior of the structure function and its slope for “frozen” and analytic strong-coupling constants

Using the leading-twist approximation of the Wilson operator product expansion with “frozen” and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F₂ and its slope ∂lnF₂/∂ln(1/x) at small values of x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA.     

Multiple-Photon Dynamics in Molecules: A New Approach to High Resolution Spectroscopy of Highly Excited Vibrational States

Multi-photon transitions with two simultaneously interacting IR laser fields lead to final excited states with frequenciesnν = n₁ν₁+ n₂ν₂, withnthe total number of photons absorbed and (n,n₁,n₂) = (2, 1, 1), (3, 2, 1), (4, 1, 3), etc. The nature of the actual transition is determined by shift measurements, where the lasers are frequency-tuned by δν_iin opposite directions keeping the sum frequency,nν, resonant with the molecular transition. This technique opens a new spectral range for multi-photon transitions and a unique identification of the observed features. Forn₁andn₂both positive the excitation will lead to a “normal” up–up multi-photon transition. Many three- and four-photon transitions in the ν₃vibrational ladder of SF₆could be resolved with a resolution of 1 MHz, as well as four new two-photon transitions. As long asn₁+ n₂≥ 0, one of the twon_imay be negative resulting in an, e.g., up–down excitation pathway with its particular selection rules. The up–down excitations are demonstrated both for one- and two-photon transitions using the frequency shift technique. The different possible excitation schemes which meet the resonance condition for these transitions lead to interference effects and local couplings to highly excited states. Changes in resonance frequency for a one-photon transition (n= 1), due to these effects, are demonstrated. Evidently, the radiative coupling of participating levels to high-lying or quasi-continuum states may drastically change for different δν_ileading both to ac Stark shift and transition probability variations.     

Effect of Sweep Direction on Sidebands in Adiabatic Decoupling

The appearance of sidebands in adiabatic decoupling can be substantially reduced simply by matching the sweep rate and direction of adiabatic pulses with the evolution of differentJcouplings. Alternatively, a matched adiabatic defocusing pulse is applied just before the decoupling is turned on, providing an efficient means for complete suppression of sidebands.     

Fast acquisition of multi-dimensional spectra in solid-state NMR enabled by ultra-fast MAS

The advantages offered by ultra-fast (>60 kHz) magic angle spinning (MAS) rotation for the study of biological samples, notably containing paramagnetic centers are explored.It is shown that optimal conditions for performing solid-state ¹³C NMR under 60 kHz MAS are obtained with low-power CW ¹H decoupling, as well as after a low-power ¹H,¹³C cross-polarization step at a double-quantum matching condition. Acquisition with low-power decoupling highlights the existence of rotational decoupling sidebands. The sideband intensities and the existence of first and second rotary conditions are explained in the framework of the Floquet–van Vleck theory.As a result, optimal ¹³C spectra of the oxidized, paramagnetic form of human copper zinc superoxide dismutase (SOD) can be obtained employing rf-fields which do not exceed 40 kHz during the whole experiment. This enables the removal of unwanted heating which can lead to deterioration of the sample. Furthermore, combined with the short ¹H T₁s, this allows the repetition rate of the experiments to be shortened from 3 s to 500 ms, thus compensating for the sensitivity loss due to the smaller sample volume in a 1.3 mm rotor. The result is that 2D ¹³C–¹³C correlation could be acquired in about 24 h on less than 1 mg of SOD sample.