Showing papers on "Quadrupole published in 2015"

Unified picture of the post-merger dynamics and gravitational wave emission in neutron star mergers

Abstract: We introduce a classification scheme of the postmerger dynamics and gravitational wave emission in binary neutron star mergers, after identifying a new mechanism by which a secondary peak in the gravitational wave spectrum is produced. It is caused by a spiral deformation, the pattern of which rotates slower with respect to the double-core structure in the center of the remnant. This secondary peak is typically well separated in frequency from the secondary peak produced by a nonlinear interaction between a quadrupole and a quasiradial oscillation. The new mechanism allows for an explanation of low-frequency modulations seen in a number of physical characteristics of the remnant, such as the central lapse function, the maximum density and the separation between the two cores, but also in the gravitational wave amplitude. We find empirical relations for both types of secondary peaks between their gravitational wave frequency and the compactness of nonrotating individual neutron stars, that exist for fixed total binary masses. These findings are derived for equal-mass binaries without intrinsic neutron star spin analyzing hydrodynamical simulations without magnetic field effects. Our classification scheme may form the basis for the construction of detailed gravitational wave templates of the postmerger phase. We find that the quasiradial oscillation frequency of the remnant decreases with the total binary mass. For a given merger event, our classification scheme may allow one to determine the proximity of the measured total binary mass to the threshold mass for prompt black hole formation, which can, in turn, yield an estimate of the maximum neutron star mass.

Fano Resonance-Induced Negative Optical Scattering Force on Plasmonic Nanoparticles

Abstract: We demonstrate theoretically that Fano resonance can induce a negative optical scattering force acting on plasmonic nanoparticles in the visible light spectrum when an appropriate manipulating laser beam is adopted. Under the illumination of a zeroth-order Bessel beam, the plasmonic nanoparticle at its Fano resonance exhibits a much stronger forward scattering than backward scattering and consequently leads to a net longitudinal backward optical scattering force, termed Fano resonance-induced negative optical scattering force. The extinction spectra obtained based on the Mie theory show that the Fano resonance arises from the interference of simultaneously excited multipoles, which can be either a broad electric dipole mode and a narrow electric quadrupole mode, or a quadrupole and an octupole mode mediated by the broad electric dipole. Such Fano resonance-induced negative optical scattering force is demonstrated to occur for core–shell, homogeneous, and hollow metallic particles and can therefore be expe...

Gas flow in barred potentials - III. Effects of varying the quadrupole

Abstract: We run hydrodynamical simulations of a 2D isothermal non self-gravitating inviscid gas flowing in a rigidly rotating externally imposed potential formed by only two components: a monopole and a quadrupole We explore systematically the effects of varying the quadrupole while keeping fixed the monopole and discuss the consequences for the interpretation of longitude-velocity diagrams in the Milky Way We find that the gas flow can constrain the quadrupole of the potential and the characteristics of the bar that generates it The exponential scale length of the bar must be at least $15\rm\, kpc$ The strength of the bar is also constrained Our global interpretation favours a pattern speed of $\Omega=40\,\rm km s^{-1} {kpc}^{-1}$ We find that for most observational features, there exist a value of the parameters that matches each individual feature well, but is difficult to reproduce all the important features at once Due to the intractably high number of parameters involved in the general problem, quantitative fitting methods that can run automatic searches in parameter space are necessary

Collinear laser spectroscopy of atomic cadmium

Abstract: Hyperfine structure A and B factors of the atomic 5s 5p 3 P2 → 5s 6s 3 S1 transition are deter- mined from collinear laser spectroscopy data of 107�123 Cd and 111m�123m Cd. Nuclear magnetic moments and electric quadrupole moments are extracted using reference dipole moments and calculated electric field gradients, respectively. The hyperfine structure anomaly for isotopes with s1/2 and d5/2 nuclear ground states and isomeric h11/2 states is evaluated and a linear relationship is observed for all nuclear states except s1/2. This corresponds to the Moskowitz-Lombardi rule that was established in the mercury region of the nuclear chart but in the case of cadmium the slope is distinctively smaller than for mercury. In total four atomic and ionic levels were analyzed and all of them exhibit a similar behaviour. The electric field gradient for the atomic 5s 5p 3 P2 level is derived from multi-configuration Dirac-Hartree-Fock calculations in order to evaluate the spectroscopic nuclear quadrupole moments. The results are consistent with those obtained in an ionic transition and based on a similar calculation.

Systematic Calculations of Energy Levels and Transition Rates of Be-like Ions with Z=10–30 Using a Combined Configuration Interaction and Many-body Perturbation Theory Approach

Abstract: We report calculations of energy levels and radiative rates for transitions among the lowest 116 fine-structure levels arising from the configurations in Be-like ions with Z = 10–30. The wavelengths, oscillator strengths, line strengths, and radiative rates for all possible electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transitions among the 116 levels have been calculated using the combined configuration interaction and many-body perturbation method. The accuracy of the results is determined through extensive comparisons with existing laboratory measurements and theoretical results. The present complete set of results should be of great help in line identification and the interpretation of spectra, as well as in the modeling and diagnostics of astrophysical and fusion plasmas.

Gamma-ray timing of redback psr j2339–0533: hints for gravitational quadrupole moment changes

Abstract: We present the results of precision gamma-ray timing measurements of the binary millisecond pulsar PSR J2339–0533, an irradiating system of the "redback" type, using data from the Fermi Large Area Telescope. We describe an optimized analysis method to determine a long-term phase-coherent timing solution spanning more than six years, including a measured eccentricity of the binary orbit and constraints on the proper motion of the system. A major result of this timing analysis is the discovery of an extreme variation of the nominal 4.6 hr orbital period over time, showing alternating epochs of decrease and increase. We inferred a cyclic modulation of with an approximate cycle duration of 4.2 yr and a modulation amplitude of . Considering different possible physical causes, the observed orbital-period modulation most likely results from a variable gravitational quadrupole moment of the companion star due to cyclic magnetic activity in its convective zone.

Use of a Continuous Wave Laser and Pockels Cell for Sensitive High-Resolution Collinear Resonance Ionization Spectroscopy

Abstract: New technical developments have led to a 2 orders of magnitude improvement of the resolution of the collinear resonance ionization spectroscopy (CRIS) experiment at ISOLDE, CERN, without sacrificing the high efficiency of the CRIS technique. Experimental linewidths of 20(1) MHz were obtained on radioactive beams of francium, allowing us for the first time to determine the electric quadrupole moment of the short lived [t_{1/2}=22.0(5) ms] ^{219}Fr Q_{s}=-1.21(2) eb, which would not have been possible without the advantages offered by the new method. This method relies on a continuous-wave laser and an external Pockels cell to produce narrow-band light pulses, required to reach the high resolution in two-step resonance ionization. Exotic nuclei produced at rates of a few hundred ions/s can now be studied with high resolution, allowing detailed studies of the anchor points for nuclear theories.

Multipolar electromagnetic fields around neutron stars: exact vacuum solutions and related properties

Abstract: The magnetic field topology in the surrounding of neutron stars is one of the key questions in pulsar magnetospheric physics. A very extensive literature exists about the assumption of a dipolar magnetic field but very little progress has been made in attempts to include multipolar components in a self-consistent way. In this paper, we study the effect of multipolar electromagnetic fields anchored in the star. We give exact analytical solutions in closed form for any order $l$ and apply them to the retarded point quadrupole ($l=2$), hexapole ($l=3$) and octopole ($l=4$), a generalization of the retarded point dipole ($l=1$). We also compare the Poynting flux from each multipole and show that the spin down luminosity depends on the ratio $R/r_{\rm L}$, $R$ being the neutron star radius and $r_{\rm L}$ the light-cylinder radius. Therefore the braking index also depends on $R/r_{\rm L}$. As such multipole fields possess very different topology, most importantly smaller length scales compared to the dipolar field, especially close to the neutron star, we investigate the deformation of the polar caps induced by these multipolar fields. Such fields could have a strong impact on the interpretation of the pulsed radio emission suspected to emanate from these polar caps as well as on the inferred geometry deduced from the high-energy light-curve fitting and on the magnetic field strength. Discrepancies between the two-pole caustic model and our new multipole-caustic model are emphasized with the quadrupole field. To this respect, we demonstrate that working with only a dipole field can be very misleading.

Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order

Abstract: This paper is motivated by the need to improve the post-Newtonian (PN) amplitude accuracy of waveforms for gravitational waves generated by inspiralling compact binaries, both for use in data analysis and in the comparison between post-Newtonian approximations and numerical relativity computations. It presents (i) the non-linear couplings between multipole moments of general post-Newtonian matter sources up to order 3.5PN, including all contributions from tails, tails-of-tails and the non-linear memory effect; and (ii) the source mass-type octupole moment of (non-spinning) compact binaries up to order 3PN, which permits completion of the expressions of the octupole modes (3, 3) and (3, 1) of the gravitational waveform to order 3.5PN. On this occasion we reconfirm by means of independent calculations our earlier results concerning the source mass-type quadrupole moment to order 3PN. Related discussions on factorized resummed waveforms and the occurence of logarithmic contributions to high order are also included.

Measurement of the dipole in the cross-correlation function of galaxies

Abstract: It is usually assumed that in the linear regime the two-point correlation function of galaxies contains only a monopole, quadrupole and hexadecapole. Looking at cross-correlations between different populations of galaxies, this turns out not to be the case. In particular, the cross-correlations between a bright and a faint population of galaxies contain also a dipole. In this paper we present the first attempt to measure this dipole. We discuss the four types of effects that contribute to the dipole: relativistic distortions, evolution effect, wide-angle effect and large-angle effect. We show that the first three contributions are intrinsic anti-symmetric contributions that do not depend on the choice of angle used to measure the dipole. On the other hand the large-angle effect appears only if the angle chosen to extract the dipole breaks the symmetry of the problem. We show that the relativistic distortions, the evolution effect and the wide-angle effect are too small to be detected in the LOWz and CMASS sample of the BOSS survey. On the other hand with a specific combination of angles we are able to measure the large-angle effect with high significance. We emphasise that this large-angle dipole does not contain new physical information, since it is just a geometrical combination of the monopole and the quadrupole. However this measurement, which is in excellent agreement with theoretical predictions, validates our method for extracting the dipole from the two-point correlation function and it opens the way to the detection of relativistic effects in future surveys like e.g. DESI.

Ion implantation apparatus

Abstract: A multistage quadrupole lens system in an ion implantation apparatus includes a first quadrupole lens and a third quadrupole lens. A first bore radius of the first quadrupole lens may be smaller than a third bore radius of the third quadrupole lens. The multistage quadrupole lens system may further include a second quadrupole lens placed between the first quadrupole lens and the third quadrupole lens. A second bore radius of the second quadrupole lens may take a value lying between the first bore radius of the first quadrupole lens and the third bore radius of the third quadrupole lens (i.e., an intermediate value between them).

All-dielectric nanoantennas for unidirectional excitation of electromagnetic guided modes

Abstract: Engineering of intensity and direction of radiation from a single quantum emitter by means of structuring of their environment at the nanoscale is at the cornerstone of modern nanophotonics. Systems exhibiting spin–orbit coupling of light are of particular interest in this context. In this letter, we have demonstrated that the asymmetrical excitation of a high-index subwavelength ( λ/3−λ/2) dielectric nanoparticle by a point dipole source located in a notch at its surface results in formation of a chiral near field, which is similar to that of a circularly polarized dipole or quadrupole. Using numerical simulations, we have shown that this effect is the result of a higher multipole (quadrupole and octupole) modes excitation within the nanoparticle. We have applied this effect for unidirectional excitation of dielectric waveguide and surface plasmon-polariton modes. We have achieved the value of front–to–back ratio up to 5.5 for dielectric waveguide and to 7.5 for the plasmonic one. Our results are importa...

Clustering fossil from primordial gravitational waves in anisotropic inflation

Abstract: Inflationary models can correlate small-scale density perturbations with the long-wavelength gravitational waves (GW) in the form of the Tensor-Scalar-Scalar (TSS) bispectrum. This correlation affects the mass-distribution in the Universe and leads to the off-diagonal correlations of the density field modes in the form of the quadrupole anisotropy. Interestingly, this effect survives even after the tensor mode decays when it re-enters the horizon, known as the fossil effect. As a result, the off-diagonal correlation function between different Fourier modes of the density fluctuations can be thought as a way to probe the large-scale GW and the mechanism of inflation behind the fossil effect. Models of single field slow roll inflation generically predict a very small quadrupole anisotropy in TSS while in models of multiple fields inflation this effect can be observable. Therefore this large scale quadrupole anisotropy can be thought as a spectroscopy for different inflationary models. In addition, in models of anisotropic inflation there exists quadrupole anisotropy in curvature perturbation power spectrum. Here we consider TSS in models of anisotropic inflation and show that the shape of quadrupole anisotropy is different than in single field models. In fact, in these models, quadrupole anisotropy is projected into the preferred direction and its amplitude is proportional to g* Ne where Ne is the number of e-folds and g* is the amplitude of quadrupole anisotropy in curvature perturbation power spectrum. We use this correlation function to estimate the large scale GW as well as the preferred direction and discuss the detectability of the signal in the galaxy surveys like Euclid and 21 cm surveys.

Interaction of Strain and Nuclear Spins in Silicon: Quadrupolar Effects on Ionized Donors.

Abstract: The nuclear spins of ionized donors in silicon have become an interesting quantum resource due to their very long coherence times Their perfect isolation, however, comes at a price, since the absence of the donor electron makes the nuclear spin difficult to control We demonstrate that the quadrupolar interaction allows us to effectively tune the nuclear magnetic resonance of ionized arsenic donors in silicon via strain and determine the two nonzero elements of the S tensor linking strain and electric field gradients in this material to S(11)=15×10(22) V/m2 and S(44)=6×10(22) V/m2 We find a stronger benefit of dynamical decoupling on the coherence properties of transitions subject to first-order quadrupole shifts than on those subject to only second-order shifts and discuss applications of quadrupole physics including mechanical driving of magnetic resonance, cooling of mechanical resonators, and strain-mediated spin coupling

Relativistic Coulomb excitation within the time dependent superfluid local density approximation.

Abstract: Within the framework of the unrestricted time-dependent density functional theory, we present for the first time an analysis of the relativistic Coulomb excitation of the heavy deformed open shell nucleus 238U. The approach is based on the superfluid local density approximation formulated on a spatial lattice that can take into account coupling to the continuum, enabling self-consistent studies of superfluid dynamics of any nuclear shape. We compute the energy deposited in the target nucleus as a function of the impact parameter, finding it to be significantly larger than the estimate using the Goldhaber-Teller model. The isovector giant dipole resonance, the dipole pygmy resonance, and giant quadrupole modes are excited during the process. As a result, the one-body dissipation of collective dipole modes is shown to lead a damping width Γ↓≈0.4 MeV and the number of preequilibrium neutrons emitted has been quantified.

Giant enhancement of dipole-forbidden transitions via lattices of plasmonic nanoparticles

Abstract: We demonstrate theoretically that electric dipole-forbidden atomic transitions can be excited by the interaction of the quadrupole moment of the transition with the electric near-field in the vicinity of an illuminated periodic array of core–shell metallic nanoparticles via surface-plasmon excitation. The rate of the quadrupole transition is enhanced by nine orders of magnitude relative to the illumination of the atom by a plane wave rendering the transition experimentally observable. At the same time, the enhancement of the quadrupole transition rate means an enhancement of the quadrupole force at the same level, enabling the subwavelength trapping of the atom at the optical near-field landscape. The calculations are based on rigorous electrodynamic calculations based on the layer-multiple-scattering theory for periodic nanostructures of spherical scatterers. The quadrupole transition is studied by means of electromagnetic multipole angular momentum theory which provides a closed formula for the correspo...

The consequences of improperly describing oscillator strengths beyond the electric dipole approximation

Abstract: The interaction between a quantum mechanical system and plane wave light is usually modeled within the electric dipole approximation. This assumes that the intensity of the incident field is constant over the length of the system and transition probabilities are described in terms of the electric dipole transition moment. For short wavelength spectroscopies, such as X-ray absorption, the electric dipole approximation often breaks down. Higher order multipoles are then included to describe transition probabilities. The square of the magnetic dipole and electric quadrupole are often included, but this results in an origin-dependent expression for the oscillator strength. The oscillator strength can be made origin-independent if all terms through the same order in the wave vector are retained. We will show the consequences and potential pitfalls of using either of these two expressions. It is shown that the origin-dependent expression may violate the Thomas-Reiche-Kuhn sum rule and the origin-independent expression can result in negative transition probabilities.

Core/shell/shell spherical quantum dot with Kratzer confining potential: Impurity states and electrostatic multipoles

Abstract: An exactly solvable problem of impurity states is considered in core/shell/shell spherical quantum dot. Kratzer molecular potential is taken for confinement potential. The analytical expressions are obtained for the energy spectrum and wave functions of the impurity electron. The dependencies of the total energy and the binding energy of the impurity on the parameters of the confining potential are investigated. The possibility of the impurity electron leakage is shown in the external environment, due to the specific form of the Kratzer potential. The character of the electrostatic field created by the impurity and the electron is observed on the basis of obtained results. The multipole corrections caused by the dipole and quadrupole moments of the electron are calculated. It is shown that the dipole moment is absent, and the problem reduces to the calculation of only z component for the average values of the diagonal elements of the quadrupole moment tensor. The dependencies of the average values of the quadrupole moment on the Kratzer potential parameters are studied.

Investigation into the semimagic nature of the tin isotopes through electromagnetic moments

Abstract: A complete set of electromagnetic moments, B(E2;0+1 2+1), Q(2+1), and g(2+1), have been measured from Coulomb excitation of semi-magic 112,114,116,118,120,122,124Sn (Z = 50) on natural carbon and titanium targets. The magnitude of the B(E2) values, measured to a precision of ~4%, disagree with a recent lifetime study [Phys. Lett. B 695, 110 (2011)] that employed the Doppler- shift attenuation method. The B(E2) values show an overall enhancement compared with recent theoretical calculations and a clear asymmetry about midshell, contrary to naive expectations. A new static electric quadrupole moment, Q(2+1), has been measured for 114Sn. The static quadrupole moments are generally consistent with zero but reveal an enhancement near midshell; this had not been previously observed. The magnetic dipole moments are consistent with previous measurements and show a near monotonic decrease in value with neutron number. The current theory calculations fail to reproduce the electromagnetic moments of the tin isotopes. The role of 2p-2h and 4p-4h intruders, which are lowest in energy at mid shell and outside of current model spaces, needs to be investigated in the future.

The Surface Potential of the Water-Vapor Interface from Classical Simulations.

Abstract: The electrochemical surface potential across the water-vapor interface provides a measure of the orientation of water molecules at the interface. However, the large discrepancies between surface potentials calculated from ab initio (AI) and classical molecular dynamics (MD) simulations indicate that what is being calculated may be relevant to different test probes. Although a method for extracting the electrochemical surface potential from AIMD simulations has been given, methods for MD simulations have not been clarified. Here, two methods for extracting the surface potential relevant to electrochemical measurements from MD simulations are presented. This potential is shown to be almost entirely due to the dipole contribution. In addition, the molecular origin of the dipole contribution is explored by using different potential energy functions for water. The results here show that the dipole contribution arises mainly from distortions in the hydration shell of the full hydrogen bonded waters on the liquid side of the interface, which is determined by the charge distribution of the water model. Disturbingly, the potential varies by 0.4 eV depending on the model. Although there is still no consensus on what that charge distribution should be, recent results indicate that it contains both a large quadrupole and negative charge out of the molecular plane, i.e., three-dimensional (3D) charge. Water models with 3D charge give the least distortion of the hydration shell and the best agreement with experimental surface potentials, although there is still uncertainty in the experimental values.

Tuning ultracold collisions of excited rotational dipolar molecules

Abstract: We investigate the ultracold collisions of rotationally excited dipolar molecules in free-space, taking the hetero-nuclear bi-alkali molecule of KRb as an example. We show that we can sharply tune the elastic, inelastic and reactive rate coefficients of lossy molecular collisions when a second rotationally excited colliding channel crosses the threshold of the initial colliding channel, with the help of an applied electric field, as found by Avdeenkov et al for non-lossy molecules (Phys. Rev. A 73 022707). We can increase or decrease the inelastic and reactive processes whether the second channel is above or below the initial channel. This is seen for both bosonic and fermionic molecules. Additionally, we include the electric quadrupole and octopole moment to the dipole moment in the expression of the long-range multipole–multipole interaction. We found that for processes mediated by the incident channel, such as elastic and reactive collisions, the inclusion of quadrupole and octopole moments is not important at ultralow energies. The moments are important for processes mediated by state-to-state transitions like inelastic collisions.

Analysis methods of safe Coulomb-excitation experiments with radioactive ion beams using the gosia code

Abstract: With the recent advances in radioactive ion beam technology, Coulomb excitation at safe energies becomes an important experimental tool in nuclear-structure physics. The usefulness of the technique to extract key information on the electromagnetic properties of nuclei has been demonstrated since the 1960's with stable beam and target combinations. New challenges present themselves when studying exotic nuclei with this technique, including dealing with low statistics or number of data points, absolute and relative normalisation of the measured cross sections and a lack of complimentary experimental data, such as excited-state lifetimes and branching ratios. This paper addresses some of these common issues and presents analysis techniques to extract transition strengths and quadrupole moments utilising the least-squares fit code, {\rmfamily \textsc{gosia}}.

Intriguing Electrostatic Potential of CO: Negative Bond-ends and Positive Bond-cylindrical-surface.

Abstract: The strong electronegativity of O dictates that the ground state of singlet CO has positively charged C and negatively charged O, in agreement with ab initio charge analysis, but in disagreement with the dipole direction. Though this unusual phenomenon has been fairly studied, the study of electrostatic potential (EP) for noncovalent interactions of CO is essential for better understanding. Here we illustrate that both C and O atom-ends show negative EP (where the C end gives more negative EP), favoring positively charged species, whereas the cylindrical surface of the CO bond shows positive EP, favoring negatively charged ones. This is demonstrated from the interactions of CO with Na(+), Cl(-), H2O, CO and benzene. It can be explained by the quadrupole driven electrostatic nature of CO (like N2) with very weak dipole moment. The EP is properly described by the tripole model taking into account the electrostatic multipole moments, which has a large negative charge at a certain distance protruded from C, a large positive charge on C, and a small negative charge on O. We also discuss the EP of the first excited triplet CO.

Spontaneous multipole ordering by local parity mixing

Abstract: Broken spatial inversion symmetry in spin-orbital coupled systems leads to a mixing between orbitals with different parity, which results in unusual electronic structures and transport properties. We theoretically investigate the possibility of multipole ordering induced by a parity mixing. In particular, we focus on the system in which the parity mixing appears in a sublattice-dependent form. Starting from the periodic Anderson model with such a local parity mixing, we derive an extended Kondo lattice model with sublattice-dependent antisymmetric exchange couplings between itinerant electrons and localized spins. By the variational calculation, simulated annealing, and Monte Carlo simulation, we show that the model on a quasi-one-dimensional zig-zag lattice exhibits an odd-parity multipole order composed of magnetic toroidal and quadrupole components at and near half filling. The multipole order causes a band deformation with the band bottom shift and a magnetoelectric response. The results suggest that unusual odd-parity multipole orders will be widely observed in multi-orbital systems with local parity mixing.

Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules

Abstract: For slowly tumbling entities or quasi-rigid lattices, we derive very simple analytical expressions of the quadrupole relaxation enhancement (QRE) of the longitudinal relaxation rate R1 of nuclear spins I due to their intramolecular magnetic dipolar coupling with quadrupole nuclei of arbitrary spins S ≥ 1. These expressions are obtained by using the adiabatic approximation for evaluating the time evolution operator of the quantum states of the quadrupole nuclei S. They are valid when the gyromagnetic ratio of the spin S is much smaller than that of the spin I. The theory predicts quadrupole resonant peaks in the dispersion curve of R1 vs magnetic field. The number, positions, relative intensities, Lorentzian shapes, and widths of these peaks are explained in terms of the following properties: the magnitude of the quadrupole Hamiltonian and the asymmetry parameter of the electric field gradient (EFG) acting on the spin S, the S-I inter-spin orientation with respect to the EFG principal axes, the rotational correlation time of the entity carrying the S-I pair, and/or the proper relaxation time of the spin S. The theory is first applied to protein amide protons undergoing dipolar coupling with fast-relaxing quadrupole (14)N nuclei and mediating the QRE to the observed bulk water protons. The theoretical QRE agrees well with its experimental counterpart for various systems such as bovine pancreatic trypsin inhibitor and cartilages. The anomalous behaviour of the relaxation rate of protons in synthetic aluminium silicate imogolite nano-tubes due to the QRE of (27)Al (S = 5/2) nuclei is also explained.