Spin dynamics of superfluid<Superscript>3</Superscript>He in non-hydrodynamic regime

We review recent results of experimental and theoretical studies of superfluid³He spin dynamics at ultra low temperature, where density of the normal component is virtually zero. We describe a number of new phenomena: catastrophic relaxation, NMR in the Landau field, surface instability of homogeneous precession, persistent NMR signal etc. We propose that superfluid³He in the ultralow temperature limit may provide a system for the experimental modelling of nonequilibrium quantum field theories.     

<Superscript>29</Superscript>Si, <Superscript>27</Superscript>Al, <Superscript>1</Superscript>H and <Superscript>23</Superscript>Na MAS NMR Study of the Bonding Character in Aluminosilicate Inorganic Polymers

²⁹Si, ²⁷Al, ¹H and ²³Na solid-state magic-angle spinning (MAS) nuclear magnetic resonance (NMR) has been used to relate nominal composition, bonding character and compressive strength properties in aluminosilicate inorganic polymers (AIPs). The ²⁹Si chemical shift varies systematically with Si-to-Al ratio, indicating that the immediate structural environment of Si is altering with nominal composition. Fast ¹H MAS and ²⁹Si T _SiH/T _1ρ relaxation measurements demonstrated that occluded pore H₂O mobility within the disordered cavities is slow in comparison with H₂O mobility characteristics observed within the ordered channel structures of zeolites. The ²⁷Al MAS NMR data show that the Al coordination remains predominantly 4-coordinate. In comparison with the ²⁹Si MAS data, the corresponding ²⁷Al MAS line shapes are relatively narrow, suggesting that the AlO₄ tetrahedral geometry is largely unperturbed and the dominant source of structural disorder is propagated by large distributions of Si–O bond angles and bond lengths. Corresponding ²³Na MAS and multiple-quantum MAS NMR data indicate that Na speciation is dominated by distributions of hydration states; however, more highly resolved ²³Na resonances observed in some preparations supported the existence of short-range order. New structural elements are proposed to account for the existence of these Na resonances and an improved model for the structure of AIPs has also been proposed. Authors' address: John V. Hanna, NMR Facility, Institute of Materials and Engineering Science, Lucas Heights Research Laboratories, Australian Nuclear Science and Technology Organisation, Private Mail Bag 1, Menai, NSW 2234, Australia     

Temperature Dependence of <Superscript>1</Superscript>H and <Superscript>17</Superscript>O NMR Shifts of Water: Entropy Effect

Density functional theory together with statistical thermodynamics based on the equilibrium constants method and concept of orientational entropy were applied to reproduce the temperature dependences of ¹H and ¹⁷O nuclear magnetic resonance (NMR) chemical shifts in liquid water. Despite a rather simple theoretical model, a satisfactory agreement between calculated NMR quantities and corresponding experimental data was found. By using only a single adjustable parameter of arbitrary directionality, we succeeded to imitate the first-order temperature effect for both (¹H and ¹⁷O) NMR signals in the neat water. ¹H and ¹⁷O magnetic shielding tensors of water molecules in various water clusters have been calculated using the density functional theory. The full geometry optimization was performed using Becke's three-parameter hybrid method and the Lee–Yang–Parr correlation functional (B3LYP) combined with 6-311++G^** basis set. Magnetic shielding tensors have been calculated using the modified hybrid functional of Perdew, Burke and Ernzerhof, and the gauge-including atomic orbital approach was applied to ensure gauge invariance of the results. Solvent effects were taken into account by the polarized continuum model. Authors' address: Vytautas Balevicius, Faculty of Physics, Vilnius University, Sauletekio 9, Vilnius 10222, Lithuania     

<Superscript>23</Superscript>Na NMR in binary lithium-sodium cobaltite

Li_0.48Na_0.35CoO₂ lithium-sodium cobaltite was studied by means of wide-line ²³Na and ⁷Li NMR. A series of quantum-chemical calculations allowed to us determine the optimum positions of Li and Na atoms, to construct a map of the densities of electronic states near the Fermi level, and to estimate the electric field gradient on the Na nuclei. The results from these calculations are compared with experimental data from NMR and X-ray photoelectron spectroscopy     

Phase shift analysis of the <Superscript>6</Superscript>He+<Superscript>208</Superscript>Pb and the <Superscript>6</Superscript>He+<Superscript>197</Superscript>Au systems

We present the elastic scattering of the ⁶He+²⁰⁸Pb and the ⁶He+¹⁹⁷Au systems at the laboratory energy of E _lab=27 MeV within the framework of the McIntyre parametrization, and systematically investigate χ ²/N analysis of both systems to obtain an excellent agreement between the theoretical results and the experimental data. We find large diffusivity parameters indicating long range absorption mechanisms. We also show that both systems lack both the nuclear and the Coulomb rainbow scattering for obtained S-matrix parameters.     

Nonlinear NMR in a superfluid B phase of <Superscript>3</Superscript>He in aerogel

The properties of liquid ³He in a low-density aerogel preliminarily covered with a few monolayers of ⁴He were studied by pulsed and nonlinear CW NMR techniques. It was found that an NMR frequency shift from the Larmor value exhibits a sharp increase at a magnetization tilting angle exceeding 104°. Nonlinear CW NMR signals related to the formation of a macroscopic region featuring homogeneous precession of the magnetization (homogeneous precession domain) were observed. The experimental results confirm that the low-temperature superfluid ³He phase in the aerogel is analogous to the B-phase in bulk ³He and indicate that the spin supercurrents play an important role in the spin dynamics of superfluid ³He in aerogel.     

Structural investigation of non-stoichiometric CuInS<Subscript>2</Subscript> by <Superscript>63</Superscript>Cu and <Superscript>115</Superscript>In nuclear magnetic resonance

Results of studies of non-stoichiometric CuInS₂ semiconductor by ⁶³Cu and ¹¹⁵In nuclear magnetic resonance are presented. It was established that deviation of the composition from stoichiometry causes a quadrupolebroadened region of the NMR spectrum to change most. In this case a central peak whose shape is governed by the chemical shift anisotropy remains unaffected. NMR spectra reveal two types of structural distortions in the nearest surroundings of the In atoms.     

<Superscript>1</Superscript>H and <Superscript>19</Superscript>F NMR relaxation time studies in (NH<Subscript>4</Subscript>)<Subscript>2</Subscript>ZrF<Subscript>6</Subscript> superionic conductor

¹H and ¹⁹F spin-lattice relaxation times in polycrystalline diammonium hexafluorozirconate have been measured in the temperature range of 10–400 K to elucidate the molecular motion of both cation and anion. Interesting features such as translational diffusion at higher temperatures, molecular reorientational motion of both cation and anion groups at intermediate temperatures and quantum rotational tunneling of the ammonium group at lower temperatures have been observed. Nuclear magnetic resonance (NMR) relaxation time results correlate well with the NMR second moment and conductivity studies reported earlier.     

<Superscript>1</Superscript>H and<Superscript>13</Superscript>C chemical shift assignments and stereochemistry of matrine and oxymatrine

Matrine and oxymatrine were extracted fromSophora flavescens, and their¹H and¹³C nuclear magnetic resonances (NMR) were unambiguously assigned by a combination of different two-dimensional 2-D¹H-¹³C and¹H-¹H correlation experiments of HMQC, HMQC-TOCSY and MAXY. The technique of using those experiments to make the assignment of the heavily overlapped spectrum is demonstrated. The coupling constants of matrine were measured by 2-DJ-resolved spectrum and 1-D spectra extracted from the slices of 2-D MAXY spectrum. The stereochemistry of the titled compounds was established from the NMR spectroscopy.     

Investigation of the Mn-doped compound CuGaTe<Subscript>2</Subscript> by <Superscript>63</Superscript>Cu AND <Superscript>69</Superscript>Ga nuclear magnetic resonance techniques

The synthesized base compound CuGaTe₂ and the Mn-doped compounds Cu_0.97Ga_0.97Mn_0.06Te₂ and Cu_0.93Ga_0.93Mn_0.14Te₂ have been investigated by using ⁶³Cu and ⁶⁹Ga NMR spectroscopy. The NMR spectra obtained testify to substantial structural distortions near the cationic positions in the crystal lattice of Mndoped samples. The constants of quadrupole coupling between ⁶³Cu and ⁶⁹Ga nuclei in the compounds investigated have been estimated.     

Asymptotic Similarity of Time Correlation Functions and Shape of the <Superscript>13</Superscript>C and <Superscript>29</Superscript>Si NMR Spectra in Diamond and Silicon

Based on the proposed theory, we have investigated the shape of the NMR absorption spectra for ¹³C and ²⁹Si nuclei in diamond and silicon crystals attributable to the internuclear dipole–dipole interaction. In accordance with the available experimental data, we have considered both crystals with a 100% content of magnetoactive isotopes and crystals with a comparatively low dilution by nonmagnetic nuclei. The time correlation functions (the first of which is the Fourier transform of the NMR spectrum) arising in an infinite chain of coupled differential equations are shown to be mutually similar with a slight time delay. The proposed theory allows the spectrum to be calculated analytically. The results obtained agree satisfactorily with the experimental ones. It is noted that the mutual similarity of the time correlation functions is probably a corollary of the development of dynamical chaos in the system     

Crystalline Aluminium Borates with the Mullite Structure: A <Superscript>11</Superscript>B and <Superscript>27</Superscript>Al Solid-State NMR Study

²⁷Al magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectra were acquired at 8.45, 14.1 and 16.45 T for a series of aluminium borates with the mullite structure (Al_6−x B _x O₉, where x has nominal values of 1 to 4) augmented with ²⁷Al multiple-quantum MAS NMR spectra at 8.45 T. Even though the ²⁷Al NMR spectra are complex, simulation of the combined set of data produced a relatively well-defined set of parameters (e.g., quadrupolar interaction, isotropic chemical shift, etc.) for each site. The ¹¹B MAS NMR spectra of the same compounds were also acquired at 14.1 T. Linear changes in the X-ray a-, b- and c-cell parameters with composition suggest that these compounds constitute a continuous series. Based on a Rietveld structural refinement of the compound synthesized as Al₄B₂O₉, the resulting site occupancies and relative site distortions allow the identification of particular sites with specific NM resonances. Changes in the ²⁷Al and ¹¹B MAS NMR spectra of the related compounds with x = 1–4 show at the lowest Al contents a greater degree of asymmetry in the Al sites of the octahedral chains. A fairly distorted cross-linking tetrahedral site, which persists throughout the composition range, is accompanied in the lower Al compositions by two 5-fold coordinated Al–O units which are replaced by two more-regular tetrahedral Al–O sites as the Al content increases. In the compounds of lowest Al composition (i.e., highest B content) both the tetrahedral and trigonal cross-linking sites are distinguishable, but as the Al content increases, the BO₄ units progressively disappear. Authors' address: Kenneth J. D. MacKenzie, School of Chemical and Physical Sciences, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand     

<Superscript>23</Superscript>Na spin-lattice relaxation in powder Rochelle salt

The temperature dependence of ²³Na spin-lattice relaxation in the polycrystalline Rochelle salt was studied by NMR within the range from 235 to 320 K covering both Curie points. The spin-relaxation time t ₁ versus temperature curve showed noticeable dips near the phase transitions against the background of the regular decrease in the relaxation time upon increasing temperature. The dips observed were ascribed to critical contributions to sodium spin-lattice relaxation caused by the slowdown of the correlation time for one of two relaxation modes in the Rochelle salt. The ²³Na NMR parameters were also measured for the melted Rochelle salt. This article was submitted by the authors in English.     

<Superscript>57</Superscript>Fe NMR study of multiferroic BiFeO<Subscript>3</Subscript>

The effects of the ⁵⁷Fe isotope content and high-frequency magnetic field amplitude h ₁ on the shape of the NMR spectrum of multiferroic BiFeO₃ at T = 4.2 K are studied by pulsed nuclear magnetic resonance. The NMR spectrum shape and transverse relaxation time T ₂ are found to depend strongly on the ⁵⁷Fe isotope content and h ₁ in multiferroic BiFeO₃ in the presence of a spatial spin-modulated structure of a cycloid type. In a sample with a high ⁵⁷Fe isotope content, the Suhl-Nakamura interaction contributes substantially to T ₂. When these dynamic effects are taken into account for analysis of the NMR spectrum shape, an undisturbed (without an anharmonicity effect) spatial spin-modulated structure of a cycloid type is shown to exist in BiFeO₃.     

Mapping of the <Superscript>12</Superscript>C* states via the <Superscript>10</Superscript>B(<Superscript>3</Superscript>He,pααα) reaction

We have studied ¹²C in full kinematics via the ¹⁰B(³He,pααα) reaction at an energy of 2.45 MeV. In our data we have identified states in ¹²C from the ground state up to about 18 MeV, with spins ranging from 0 to 4. Due to the very good resolution, we are able to determine properties of these ¹²C resonances, such as their energy, width, and spin. In this contribution preliminary results from the ongoing analysis are presented. Main focus on the precise determination of the breakup spectra for all resonances.     

Soft-core Interaction for the <Superscript>4,6</Superscript>He + <Superscript>64</Superscript>Zn Fusion Reactions

In this paper, the cross section of the ⁴He + ⁶⁴Zn and ⁶He + ⁶⁴Zn reactions, at bombarding energies above and below the fusion barrier, has been investigated. Soft-core nucleon-nucleon interaction and the Monte Carlo method have been employed for studying the nuclear potential of the projectile-target system. One adjustable parameter has been chosen in this study. This parameter can change the depth of the soft-core potential. It has to be adjusted so that the calculated elastic scattering and fusion cross sections are in acceptable agreement with experimental data. Our results indicate that an increase in energy decreases the depth parameter of the soft-core nucleon-nucleon potential obtained from careful analysis the ⁴He + ⁶⁴Zn and ⁶He + ⁶⁴Zn reactions. Likewise, by comparing the results obtained from both reactions, one can observe that the calculated depth parameter for the reaction related to ⁶He is larger than that for ⁴He at the same energy, in particular at the sub-barrier energies. We try to explain this behavior.     

Spin Kinetics of Liquid <Superscript>3</Superscript>He in Contact with a DyF<Subscript>3</Subscript> Micropowder at Ferromagnetic Ordering of Dy<Superscript>3+</Superscript> Ions

The spin kinetics of liquid ³He in contact with a mixture of LaF₃ (99.67%) and DyF₃ (0.33%) micropowders at temperatures of 1.5–3 K has been studied by pulsed nuclear magnetic resonance (NMR). The DyF3 is a dipolar dielectric ferromagnet with the phase transition temperature T_c= 2.55 K, whereas the diamagnetic fluoride LaF₃ is a diluting substance for the optimal observation conditions of ³Не NMR in powder pores. The magnetic phase transition in DyF₃ is accompanied by a considerable change in the character of fluctuations of the magnetic moments of dysprosium ions, which affect the spin kinetics of ³Не in contact with the substrate. Significant changes in the relaxations rates of the longitudinal and transverse magnetizations of 3Не have been discovered in the region of magnetic ordering of the solid matrix. The technique of studying the static and fluctuating magnetic fields of a solid matrix at low temperatures using liquid ³He as a probe has been proposed.     

<Superscript>77</Superscript>Se Low-Temperature NMR in the Bi<Subscript>2</Subscript>Se<Subscript>3</Subscript> Single Crystalline Topological Insulator

⁷⁷Se nuclear magnetic resonance (NMR) measurements in the Bi₂Se₃ topological insulator single crystal were carried out at temperatures 15.8, 88, and 293 K. Bismuth selenide single crystalline plate was studied in the orientation when the crystallographic c-axis was parallel to the external magnetic field B₀. We observed two component NMR spectra at the three temperatures. It was shown that the NMR spectrum almost did not move with decreasing temperature and the density of charge carriers did not follow the thermal activation law.     

Nuclear level densities in <Superscript>47</Superscript>V, <Superscript>48</Superscript>V, <Superscript>49</Superscript>V, <Superscript>53</Superscript>Mn,and <Superscript>54</Superscript>Mn from neutron evaporation spectra

The spectra of neutrons from the (p, n) reactions on ⁴⁷Ti, ⁴⁸Ti, ⁴⁹Ti, ⁵³Cr, and ⁵⁴Cr nuclei were measured in the proton-energy range 7–11 MeV. The measurements were performed with the aid of a fast-neutron spectrometer by the time-of-flight method over the base of the EGP-15 tandem accelerator of the Institute for Physics and Power Engineering (IPPE, Obninsk). Owing to a high resolution and a high stability of the time-of-flight spectrometer used, low-lying discrete levels could be identified reliably along with a continuum section of neutron spectra. An analysis of measured data was performed within the statistical equilibrium and preequilibrium models of nuclear reactions. The relevant calculations were performed by using the exact formalism of Hauser-Feshbach statistical theory supplemented with the generalized model of a superfluid nucleus, the back-shifted Fermi gas model, and the Gilbert-Cameron composite formula for the nuclear level density. The nuclear level densities for ⁴⁷V, ⁴⁸V, ⁴⁹V, ⁵³Mn, and ⁵⁴Mn were determined along with their energy dependences and model parameters. The results are discussed together with available experimental data and recommendations of model systematics.