Showing papers on "Quadrupole published in 2010"

Gravitational radiative corrections from effective field theory

Abstract: In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures 'post-Minkowskian' corrections to the multipole expansion due to nonlinear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from nonrelativistic binaries, including long distance effects up to 3 post-Newtonian (v{sup 6}) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.

Testing the no-hair theorem with observations in the electromagnetic spectrum. I. Properties of a Quasi-Kerr spacetime

Abstract: According to the no-hair theorem, an astrophysical black hole is uniquely described by only two quantities, the mass and the spin. In this series of papers, we investigate a framework for testing the no-hair theorem with observations of black holes in the electromagnetic spectrum. We formulate our approach in terms of a parametric spacetime which contains a quadrupole moment that is independent of both mass and spin. If the no-hair theorem is correct, then any deviation of the black hole quadrupole moment from its Kerr value has to be zero. We analyze in detail the properties of this quasi-Kerr spacetime that are critical to interpreting observations of black holes and demonstrate their dependence on the spin and quadrupole moment. In particular, we show that the location of the innermost stable circular orbit and the gravitational lensing experienced by photons are affected significantly at even modest deviations of the quadrupole moment from the value predicted by the no-hair theorem. We argue that observations of black hole images, of relativistically broadened iron lines, as well as of thermal X-ray spectra from accreting black holes will lead in the near future to an experimental test of the no-hair theorem.

Constraining the quadrupole moment of stellar-mass black-hole candidates with the continuum fitting method

Abstract: Black holes in General Relativity are known as Kerr black holes and are characterized solely by two parameters, the mass $M$ and the spin $J$. All the higher multipole moments of the gravitational field are functions of these two parameters. For instance, the quadrupole moment is $Q=-J^2/M$, which implies that a measurement of $M$, $J$, and $Q$ for black hole candidates would allow one to test whether these objects are really black holes as described by General Relativity. While future gravitational-wave experiments will be able to test the Kerr nature of these objects with very high accuracy, in this paper we show that it is possible to put constraints on the quadrupole moment of stellar-mass black hole candidates by using presently available X-ray data of the thermal spectrum of their accretion disk.

Collective excitation of a Bose-Einstein condensate by modulation of the atomic scattering length

Abstract: We excite the lowest-lying quadrupole mode of a Bose-Einstein condensate by modulating the atomic scattering length via a Feshbach resonance. Excitation occurs at various modulation frequencies, and resonances located at the natural quadrupole frequency of the condensate and at the first harmonic are observed. We also investigate the amplitude of the excited mode as a function of modulation depth. Numerical simulations based on a variational calculation agree with our experimental results and provide insight into the observed behavior.

Domain bundle boundaries in single crystal BaTiO3 lamellae: searching for naturally forming dipole flux-closure/quadrupole chains.

Abstract: Naturally occurring boundaries between bundles of 90° stripe domains, which form in BaTiO3 lamellae on cooling through the Curie Temperature, have been characterized using both piezoresponse force microscopy (PFM) and scanning transmission electron microscopy (STEM). Detailed interpretation of the dipole configurations present at these boundaries (using data taken from PFM) shows that in the vast majority of cases they are composed of simple zigzag 180° domain walls. Topological information from STEM shows that occasionally domain bundle boundaries can support chains of dipole flux closure and quadrupole nanostructures, but these kinds of boundaries are comparatively rare; when such chains do exist, it is notable that singularities at the cores of the dipole structures are avoided. The symmetry of the boundary shows that diads and centers of inversion exist at positions where core singularities should have been expected.

How to adapt broad-band gravitational-wave searches for r-modes

Abstract: Up to now there has been no search for gravitational waves from the $r$-modes of neutron stars in spite of the theoretical interest in the subject. Several oddities of $r$-modes must be addressed to obtain an observational result: The gravitational radiation field is dominated by the mass current (gravitomagnetic) quadrupole rather than the usual mass quadrupole, and the consequent difference in polarization affects detection statistics and parameter estimation. To astrophysically interpret a detection or upper limit it is necessary to convert the gravitational-wave amplitude to an $r$-mode amplitude. Also, it is helpful to know indirect limits on gravitational-wave emission to gauge the interest of various searches. Here I address these issues, thereby providing the ingredients to adapt broad-band searches for continuous gravitational waves to obtain $r$-mode results. I also show that searches of existing data can already have interesting sensitivities to $r$-modes.

Solid-State 127I NMR and GIPAW DFT Study of Metal Iodides and Their Hydrates: Structure, Symmetry, and Higher-Order Quadrupole-Induced Effects

Abstract: Central-transition 127I solid-state nuclear magnetic resonance (SSNMR) spectra are presented for several anhydrous group 2 metal iodides (MgI2, CaI2, SrI2, and BaI2), hydrates (BaI2·2H2O and SrI2·6H2O), and CdI2 (4H polytype). Variable offset cumulative spectrum data acquisition coupled with echo pulse sequences and an ‘ultrahigh’ applied field of 21.1 T were usually suitable to acquire high-quality spectra. Spectral analysis revealed iodine-127 nuclear quadrupole coupling constants (CQ(127I)) ranging in magnitude from 43.5 (CaI2) to 214 MHz (one site in SrI2). For very large CQ, analytical second-order perturbation theory could not be used to reliably extract chemical shifts and a treatment which includes quadrupolar effects exactly was required (Bain, A. D. Mol. Phys. 2003, 101, 3163). Differences between second-order and exact modeling allowed us to observe ‘higher-order’ quadrupole-induced effects for the first time. This finding will have implications for the interpretation of SSNMR spectra of quadru...

Nuclear spins, magnetic moments, and quadrupole moments of Cu isotopes from N=28 to N=46: Probes for core polarization effects

Abstract: Measurements of the ground-state nuclear spins and magnetic and quadrupole moments of the copper isotopes from $^{61}\mathrm{Cu}$ up to $^{75}\mathrm{Cu}$ are reported. The experiments were performed at the CERN online isotope mass separator (ISOLDE) facility, using the technique of collinear laser spectroscopy. The trend in the magnetic moments between the $N=28$ and $N=50$ shell closures is reasonably reproduced by large-scale shell-model calculations starting from a $^{56}\mathrm{Ni}$ core. The quadrupole moments reveal a strong polarization of the underlying Ni core when the neutron shell is opened, which is, however, strongly reduced at $N=40$ due to the parity change between the $\mathit{pf}$ and $g$ orbits. No enhanced core polarization is seen beyond $N=40$. Deviations between measured and calculated moments are attributed to the softness of the $^{56}\mathrm{Ni}$ core and weakening of the $Z=28$ and $N=28$ shell gaps.

One-sided outflows/jets from rotating stars with complex magnetic fields

Abstract: We present for the first time axisymmetric magnetohydrodynamic simulations which show the formation of intrinsically asymmetric or one-sided outflows or jets from disc accretion on to a rotating star with a complex magnetic field. The intrinsic magnetic field of the star is assumed to consist of a superposition of an aligned dipole and an aligned quadrupole in different proportions. The star is assumed to be rapidly rotating in the sense that the star's magnetosphere is in the propeller regime where strong outflows occur. Our simulations show that for conditions where there is a significant quadrupole component in addition to the dipole component, then a dominantly one-sided conical wind tends to form on the side of the equatorial plane with the larger value of the intrinsic axial magnetic field at a given distance. For cases where the quadrupole component is absent or very small, we find that dominantly one-sided outflows also form, but the direction of the flow ‘flip-flops’ between upward and downward on a time-scale of ∼30 d for a protostar. The average outflow will thus be symmetrical. In the case of a pure quadrupole field we find symmetric outflows in the upward and downward directions.

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum: II. Black-Hole Images

Abstract: According to the no-hair theorem, all astrophysical black holes are fully described by their masses and spins. This theorem can be tested observationally by measuring (at least) three different multipole moments of the spacetimes of black holes. In this paper, we analyze images of black holes within a framework that allows us to calculate observables in the electromagnetic spectrum as a function of the mass, spin, and, independently, the quadrupole moment of a black hole. We show that a deviation of the quadrupole moment from the expected Kerr value leads to images of black holes that are either prolate or oblate depending on the sign and magnitude of the deviation. In addition, there is a ring-like structure around the black-hole shadow with a diameter of about 10 black-hole masses that is substantially brighter than the image of the underlying accretion flow and that is independent of the astrophysical details of accretion flow models. We show that the shape of this ring depends directly on the mass, spin, and quadrupole moment of the black hole and can be used for an independent measurement of all three parameters. In particular, we demonstrate that this ring is highly circular for a Kerr black hole with a spin a<0.9M, independent of the observer's inclination, but becomes elliptical and asymmetric if the no-hair theorem is violated. Near-future very-long baseline interferometric observations of Sgr A* will image this ring and may allow for an observational test of the no-hair theorem.

A NEMO potential that includes the dipole-quadrupole and quadrupole-quadrupole polarizability.

Abstract: To increase the accuracy of molecular force fields a systematical and balanced improvement of the various terms included is needed. In this work, we have followed this strategy to improve the quality of the NEMO potential for the formaldehyde dimer by introducing local quadrupole moments and higher-order polarizabilities. It is found that inclusion of the quadrupole moment significantly improves the interaction potential. Furthermore, the inclusion of higher-order polarizabilities up to quadrupole-quadrupole polarizability is shown to give a better description of the intermolecular interaction. In addition, it is demonstrated that localized properties based on MP2 densities reproduces the BSSE corrected MP2 interaction energy at large intermolecular separations. This is not the case for HF-SCF based properties.

Ion ring in a linear multipole trap for optical frequency metrology

Abstract: A ring crystal of ions trapped in a linear multipole trap is studied as a basis for an optical frequency standard. The equilibrium conditions and cooling possibilities are discussed through an analytical model and molecular dynamics simulations. A configuration which reduces the frequency sensitivity to the fluctuations of the number of trapped ions is proposed. The systematic shifts for the electric quadrupole transition of calcium ions are evaluated for this ring configuration. This study shows that a ring of 10 or 20 ions allows to reach a short term stability better than for a single ion without introducing limiting long term fluctuations.

Trapping ultracold atoms in a time-averaged adiabatic potential

Abstract: This thesis describes the trapping and manipulation of ultracold atoms in time-averaged adiabatic potentials (TAAP). The time-averaged adiabatic potential, proposed in [Phys. Rev. Lett. 99, 083001 (2007)], uses resonant radio frequency (rf) radiation to couple the different magnetic substates of a hyperfine level manifold. The resultant dressed states are time-averaged and produce smooth and versatile trapping geometries. More specifically, we apply rf-radiation (MHz) to a quadrupole magnetic field, which results in an ellipsoidal trapping potential for rubidium-87 atoms in the F=1 manifold. This geometry is time-averaged with the help of oscillating (kHz) Helmholtz fields. We develop a convenient loading scheme for the TAAP which uses a standard TOP trap and suffers negligible atom losses and heating. Subsequently we characterize the TAAP trap itself and observe low heating rates and sufficient lifetimes (>3s). Furthermore it is possible to use a second, weaker rf-field to evaporatively cool the atoms to quantum degeneracy [Phys. Rev. A. 81, 031402 (2010)]. This opens up a route for further experiments in this potential: we show how atoms can be trapped in a double well potential and a ring trap geometry. Additionally a process to instigate rotation in these potentials by rotating the polarization of the rf-radiation is developed and implemented. This allows us to impart angular momentum onto the atomic cloud and spin it into a ring.

Relativistic energy density functionals: Low-energy collective states of Pu 240 and Er 166

Abstract: The empirical relativistic density-dependent, point-coupling energy density functional, adjusted exclusively to experimental binding energies of a large set of deformed nuclei with A≈150– 180 and A≈230–250, is tested with spectroscopic data for 166Er and 240Pu. Starting from constrained self-consistent triaxial relativistic Hartree-Bogoliubov calculations of binding energy maps as functions of the quadrupole deformation in the β–γ plane, excitation spectra and E2 transition probabilities are calculated as solutions of the corresponding microscopic collective Hamiltonian in five dimensions for quadrupole vibrational and rotational degrees of freedom and compared with available data on low-energy collective states.

Search for critical-point nuclei in terms of the sextic oscillator

Abstract: The spherical to deformed gamma-unstable shape transition in nuclei is discussed in terms of the sextic oscillator as a gamma-independent potential in the Bohr Hamiltonian. The wave functions, energy eigenvalues, and electric quadrupole and monopole transition rates are calculated in closed analytical form for the lowest-lying energy levels. It is shown that the locus of critical points for the spherical to deformed gamma-unstable shape phase transition corresponds to a parabola in the parameter space of the model. The ratios of energy eigenvalues and electromagnetic transition probabilities are constant along this parabola. It is thus possible to associate parameter-free benchmark values to the ratios of relevant observables at the critical point of the transition that can be compared to experimental data. In addition, systematic studies of the shape evolution in isotope chains can be performed within the model. As an application, the model parameters are fitted to the energy spectra of the chains of even-even Ru, Pd, and Cd isotopes and the electric quadrupole transition probabilities are calculated. It is found that {sup 104}Ru, {sup 102}Pd, and {sup 106,108}Cd nuclei, which are usually considered to be good candidates for the E(5) symmetry, lie rather close to the critical parabola that separatesmore » the spherical and deformed gamma-unstable domains. The isotope {sup 116}Cd is proposed as a new candidate for a similar critical-point nucleus.« less

First identification of the a1Δg–X3Σg− electric quadrupole transitions of oxygen in solar and laboratory spectra

Abstract: Electric quadrupole transitions in the a 1 Δ g – X 3 Σ g − band of 16O2 near 1.27 μm are reported for the first time. They were first detected in atmospheric solar spectra acquired with a ground-based Fourier transform spectrometer (FTS) in Park Falls, WI. Subsequently high-sensitivity CW—cavity ring down spectroscopy (CW-CRDS) experiments were carried out at Grenoble University in the 7717–7917 cm−1 region in order to provide quantitative intensity information for the electric quadrupole transitions. Measured intensities were used as input data for the calculation of the complete list of electric quadrupole transitions with ΔJ=±2, ±1 and 0. The calculation was carried out for the intermediate coupling case and assuming that these transitions are possible only through mixing of the Ω=0 component of the ground electronic state and b 1 Σ g + state induced by spin–orbit coupling. The calculated line list agrees well with experimental measurements and was used to improve the residuals of the fitted solar atmospheric spectrum. Emission probability for the electric quadrupole band was determined to be (1.02±0.10)×10−6 s−1.

Cold chemistry with electronically excited Ca + Coulomb crystals

Abstract: Rate constants for chemical reactions of laser-cooled Ca+ ions and neutral polar molecules (CH3F, CH2F2, or CH3Cl) have been measured at low collision energies (⟨Ecoll⟩/kB=5–243 K). Low kinetic energy ensembles of C40a+ ions are prepared through Doppler laser cooling to form “Coulomb crystals” in which the ions form a latticelike arrangement in the trapping potential. The trapped ions react with translationally cold beams of polar molecules produced by a quadrupole guide velocity selector or with room-temperature gas admitted into the vacuum chamber. Imaging of the Ca+ ion fluorescence allows the progress of the reaction to be monitored. Product ions are sympathetically cooled into the crystal structure and are unambiguously identified through resonance-excitation mass spectrometry using just two trapped ions. Variations of the laser-cooling parameters are shown to result in different steady-state populations of the electronic states of C40a+ involved in the laser-cooling cycle, and these are modeled by s...

A transferable classical potential for the water molecule.

Abstract: We developed a new model for the water molecule which contains only three Gaussian charges. Using the gas-phase geometry the dipole moment of the molecule matches, the quadrupole moment closely approximates the experimental values. The negative charge is connected by a harmonic spring to its gas-phase position. The polarized state is identified by the equality of the intermolecular electrostatic force and the spring force acting on the negative charge. In each timestep the instantaneous position of the massless negative charge is determined by iteration. Using the technique of Ewald summation, we derived expressions for the potential energy, the forces, and the pressure for Gaussian charges. The only properties to be fitted are the half-width values of the Gaussian charge distributions and the parameters of the nonelectrostatic repulsion-attraction potential. We determined the properties of gas-phase clusters up to six molecules, the internal energy and density of ambient water and hexagonal ice. We calcu...

X-ray spectroscopy of E2 and M3 transitions in Ni-like W

Abstract: The electric quadrupole (E2) and magnetic octupole (M3) ground-state transitions in Ni-like W46+ have been measured using high-resolution crystal spectroscopy at the LLNL electron-beam ion trap facility. The lines fall in the soft x-ray region near 7.93 angstrom and were originally observed as an unresolved feature in tokamak plasmas. Using flat ammonium dihydrogen phosphate and quartz crystals, the wavelengths, intensities, and polarizations of the two lines have been measured for various electron-beam energies and compared to intensity and polarization calculations performed using the Flexible Atomic Code (FAC).

Computational studies on boron nitride and boron phosphide nanotubes: Density functional calculations of boron-11 electric field gradient tensors

Abstract: We have performed density functional theory (DFT) calculations employing BLYP exchange functional and 6–31 G * standard basis set by GAUSSIAN 98 package of program The electronic structure properties of representative zigzag and armchair models of boron nitride nanotube (BNNT) and boron phosphide nanotube (BPNT) have been studied The (6,0) and (4,4) structures have been optimized and the electric field gradient (EFG) tensors have been calculated at the sites of various boron-11 nuclei The calculated EFG tensors have been converted to the equivalent experimental nuclear quadrupole resonance (NQR) parameters, quadrupole coupling constant and asymmetry parameter The results revealed that the boron atoms at the edges of nanotubes play dominant roles in determining the electronic behaviors of BNNT and BPNT The average of the calculated values of quadrupole coupling constants at the sites of boron-11 nuclei is in good agreement with experiments

Experimental study of the electric dipole strength in the even Mo nuclei and its deformation dependence

Abstract: Two methods based on bremsstrahlung were applied to the stable even Mo isotopes for the experimental determination of the photon strength function covering the high excitation energy range above 4 MeV with its increasing level density. Photon scattering was used up to the neutron separation energies S{sub n} and data up to the maximum of the isovector giant resonance (GDR) were obtained by photoactivation. After a proper correction for multistep processes the observed quasicontinuous spectra of scattered photons show a remarkably good match to the photon strengths derived from nuclear photoeffect data obtained previously by neutron detection and corrected in absolute scale by using the new activation results. The combined data form an excellent basis to derive a shape dependence of the E1 strength in the even Mo isotopes with increasing deviation from the N=50 neutron shell (i.e., with the impact of quadrupole deformation and triaxiality). The wide energy coverage of the data allows for a stringent assessment of the dipole sum rule and a test of a novel parametrization developed previously which is based on it. This parametrization for the electric dipole strength function in nuclei with A>80 deviates significantly from prescriptions generally used previously. In astrophysical network calculationsmore » it may help to quantify the role the p-process plays in cosmic nucleosynthesis. It also has impact on the accurate analysis of neutron capture data of importance for future nuclear energy systems and waste transmutation.« less

Microwave spectrum, structural parameters, and quadrupole coupling for 1,2-dihydro-1,2-azaborine.

Abstract: The first microwave spectrum for 1,2-dihydro-1,2-azaborine has been measured in the frequency range 7−18 GHz, providing accurate rotational constants and nitrogen and boron quadrupole coupling strengths for three isotopomers, H6C411B14N, H6C410B14N, and H5DC411B14N. The measured rotational constants were used to accurately determine coordinates for the substituted atoms and provide sufficient data to determine most of the important structural parameters for this molecule. The spectra were obtained using a pulsed beam Fourier transform microwave spectrometer, with sufficient resolution to allow accurate measurements of 14N, 11B, and 10B nuclear quadrupole hyperfine interactions. High-level ab initio calculations provided structural parameters and quadrupole coupling strengths that are in very good agreement with measured values. The rotational constants for the parent compound are A = 5657.335(1), B = 5349.2807(5), and C = 2749.1281(4) MHz, yielding the inertial defect Δ0 = 0.02 amu·A2 for the ground-state...

Large scale directional anomalies in the WMAP 5yr ILC map

Abstract: We study the alignments of the low multipoles of CMB anisotropies with specific directions in the sky (i.e. the dipole, the north Ecliptic pole, the north Galactic pole and the north Super Galactic pole). Performing 105 random extractions we have found that: 1) separately quadrupole and octupole are mildly orthogonal to the dipole but when they are considered together, in analogy to Copi2006, we find an unlikely orthogonality at the level of 0.8% C.L.; 2) the multipole vectors associated to l = 4 are unlikely aligned with the dipole at 99.1% C.L.; 3) the multipole vectors associated to l = 5 are mildly orthogonal to the dipole but when we consider only maps that show exactly the same correlation among the multipoles as in the observed WMAP 5yr ILC, these multipole vectors are unlikely orthogonal to the dipole at 99.7% C.L..

Continuous-wave gravitational radiation from pulsar glitch recovery

Abstract: Non-axisymmetric, meridional circulation inside a neutron star, excited by a glitch and persisting throughout the post-glitch relaxation phase, emits gravitational radiation. Here, it is shown that the current quadrupole contributes more strongly to the gravitational wave signal than the mass quadrupole evaluated in previous work. We calculate the signal-to-noise ratio for a coherent search and conclude that a large glitch may be detectable by second-generation interferometers like the Laser Interferometer Gravitational-Wave Observatory. It is shown that the viscosity and compressibility of bulk nuclear matter, as well as the stratification length-scale and inclination angle of the star, can be inferred from a gravitational wave detection in principle.

Thermal Casimir-Polder shifts in Rydberg atoms near metallic surfaces

Abstract: The Casimir-Polder (CP) potential and transition rates of a Rydberg atom above a plane metal surface at finite temperature are discussed. As an example, the CP potential and transition rates of a rubidium atom above a copper surface at 300 K are computed. Close to the surface we show that the quadrupole correction to the force is significant and increases with increasing principal quantum number $n$. For both the CP potential and decay rates one finds that the dominant contribution comes from the longest wavelength transition and the potential is independent of temperature. We provide explicit scaling laws for potential and decay rates as functions of atom-surface distance and principal quantum number of the initial Rydberg state.

Oscillator strengths of the transitions in a spherically confined hydrogen atom

Abstract: Dipole and quadrupole oscillator strengths have been calculated for the series of transitions nl → n'l' (n ≤ 5) in a hydrogen atom confined in the centre of a sphere with impenetrable walls. The non-monotonic dependence of the oscillator strengths on the radius of confinement has been discussed through their general forms obtained with a properly chosen radial wavefunction. It was qualitatively ascribed to variation of the radial electron density distributions of the states involved in the transitions. The effect of the confinement on the use of the dipole approximation has been studied, introducing a correction through the octupole term as well as performing the calculation with the full form of the interaction term.

The quadrupole enhanced 1H spin-lattice relaxation of the amide proton in slow tumbling proteins.

Abstract: An analysis, based on the stochastic Liouville approach, is presented of the R(1)-NMRD or field dependent spin-lattice relaxation rate of amide protons. The proton relaxivity, displayed as R(1)-NMRD profiles, is calculated for a reorienting (1)H-(14)N spin group, where the inter spin coupling is due to spin dipole-dipole coupling or the scalar coupling. The quadrupole nucleus (14)N has an asymmetry parameter eta = 0.4 and a quadrupole interaction which is modulated by the overall reorientational motion of the protein. In the very slow reorientational regime, omega(Q)tau(R)>> 1 and tau(R)>/= 2.0 mus, both the dipole-dipole coupling and the scalar coupling yield a T(1)-NMRD profile with three marked peaks of proton spin relaxation enhancement. These peaks appear when the proton Larmor frequency, omega(I), matches the nuclear quadrupole spin transition frequencies: omega(1) = omega(Q)2eta/3, omega(2) = omega(Q)(1 -eta/3) and omega(3) = omega(Q)(1 + eta/3), and the quadrupole spin system thus acts as a relaxation sink. The relative relaxation enhancements of the peaks are different for the dipole-dipole and the scalar coupling. Considering the dipole-dipole coupling, the low frequency peak, omega(1), is small compared to the high field peaks whereas for the scalar coupling the situation is changed. For slow tumbling proteins with a correlation time of tau(R) = 400 ns, omega(2) and omega(3) are not resolved but become one relatively broad peak. At even faster reorientation, tau(R) < 60 ns, the marked peaks disappear. In this motional regime, the main effect of the cross relaxation phenomenon is a subtle perturbation of the main amide proton T(1) NMRD dispersion. The low field part of it can be approximately described by a Lorentzian function: R(DD,SC)(0.01)/(1 + (omega(I)tau(R)3/2)(2)) whereas the high field part coincides with R(DD,SC)(0.01)/(1 + (omega(I)tau(R))(2)).