固体中半整数四极核的自旋扩散

首先介绍固态中自旋扩散的一般理论，包括半经典描述和建立在投影算子理论上的密度矩阵描述. 接着以丰核环境中相互偶合的自旋-1/2系统以及自旋-3/2系统为典型列举了自旋扩散速率的计算. 最近藉助多量子魔角旋转(MQMAS)方法实现半整数四极核的多量子谱自旋扩散实验，可以测量固体粉末中半整数四极核体系四极张量相对方向. 结合作者最近的计算机模拟和实验测量结果对这一新兴方向作了重点介绍，尤其指出了射频
脉冲强度、宽度及样品旋转速度对交叉峰线型的影响.     

Initial conditions for carbon-13 MAS NMR 1D exchange involving chemically equivalent and inequivalent nuclei

A major problem in dynamic 1D ¹³C MAS NMR concerns the exchange between magnetically inequivalent, but chemically equivalent sites, whose signals are not resolved in the regular 1D spectrum. This difficulty may be overcome by properly preparing the initial nonequilibrium state of the spin system in the exchange experiments. In the present paper we discuss the advantages and limitations of several such experiments already in use and propose a new sequence, which we term SELDOM-ODESSA. Unlike the other 1D-exchange methods, this experiment yields pure absorption spectra that can more readily be analyzed quantitatively. The experiment is a hybrid comprising a SELDOM sequence, for selective excitation of one of the spinning sideband manifolds in the spectrum, followed by the ODESSA sequence, which induces alternate polarization in the excited sideband manifold. The evolution of the spectrum following this sequence provides information on both the exchange between congruent sites belonging to the same group of equivalent nuclei, and the exchange between inequivalent sites. Results are presented for a tropolone sample specifically enriched in carbon-13 at the carbonyl and hydroxyl sites. The dominant exchange mechanism in this sample involves spin diffusion. The various spin exchange processes in this sample, in the presence and absence of proton decoupling during the mixing time, are measured and discussed.     

The effect of Magic Angle Spinning on proton spin–lattice relaxation times in some organic solids

Proton spectra of solids are usually broadened by strong proton homonuclear dipolar interactions. However, substantial line narrowing may be achieved by Magic Angle Spinning (MAS) in systems of low proton density or in systems in which rapid molecular motions occur. In such conditions, T₁(H) measurements are often used to characterise the dynamics of each resolved proton site. We show that T₁(H) values measured for solid organic compounds with high proton abundance, such as adamantane and glycine, may be strongly dependent on the spinning rate employed, so that care is required when values are compared. The effects of molecular motion and proton density on T₁(H) and its dependence on spinning rate were investigated. We found that an increase in molecular motion leads to an increase of T₁(H) at higher spinning rates. The opposite is found for systems with low proton densities which show relatively lower T₁(H), at higher spinning rates. A possible interpretation is suggested in terms of the reduced spin diffusion efficiency at higher spinning rates.     

15N spin diffusion rate in solid-state NMR of totally enriched proteins: the magic angle spinning frequency effect

As demonstrated by means of the one-dimensional solid-state MAS exchange experiment (CODEX), the rate of the proton driven spin diffusion between backbone (15)N nuclei in totally enriched protein depends strongly on the magic angle spinning (MAS) frequency: spin diffusion at MAS frequency 16 kHz is about 4-5 times slower as compared to that at MAS frequency 1 kHz which is due to the averaging of the homo- and hetero-nuclear dipolar interactions by MAS. It is important that even at the highest MAS frequencies used in our experiments the spin diffusion rate is comparable or larger than typical values of the spin-lattice relaxation rates of backbone nitrogens in solid proteins. Thus, the precise quantitative analysis of (15)N T(1)'s in totally enriched solid proteins may lead to wrong quantitative results. On the other hand, the effectiveness of the (15)N-(15)N correlation and structure determination experiments making use of (15)N-(15)N distances can be increased by decreasing the MAS frequency as far as possible, which is counter intuitive to the commonly applied fast MAS conditions in order to reduce the dipolar-broadened line widths for increased spectral resolution.     

A method for detection of spectral spin diffusion from minor peaks, and its application to F MAS NMR of antimony(III)-doped fluorapatite

A new technique for detecting spectral spin diffusion in solids under MAS NMR conditions that is particularly well suited for accurately measuring cross-relaxation from minor spectral components is presented. The pulse sequence, SINK (Saturation Inter-Nuclear Kinetics), selectively saturates the magnetization of a minor spectral component with a series of rotor-synchronized DANTE pulse trains and monitors spin diffusion to other peaks with a non-selective 90° pulse. We have used SINK with ¹⁹F MAS NMR on samples of calcium fluorapatite doped with Sb³⁺ to measure spin diffusion between a weak peak at 68.6 ppm due to fluoride ions associated with Sb³⁺ and other peaks in the spectrum. The SINK experiment clearly demonstrates that spin diffusion from the former peak to the main resonance of fluorapatite at 64.0 ppm is faster than spin diffusion to a second antimony-related peak at 65.6 ppm. These results strengthen our previous conclusion that antimony(III) occupies a phosphate site in the apatite lattice, with an SbO₃³⁻ group replacing a PO₄³⁻ group. The SINK experiment also enables the detection of a “hidden” peak at approximately 62.9 ppm that is otherwise obscured by the intense main peak at 64.0 ppm.     

瞬态自旋光栅系统的建设及其在自旋输运研究中的应用

简要介绍了瞬态光栅系统原理及光路的建设,包括瞬态光栅的产生与探测.采用了外差探测法（heterodyne detection）,大大提高了信噪比.利用瞬态自旋光栅系统,研究了(110)方向生长的本征GaAs/AlGaAs单量子阱中自旋输运特性,测得室温下电子自旋的扩散常数D_s=551 cm/s. 关键词： 瞬态自旋光栅 自旋扩散 自旋输运 自旋弛豫     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

Spin Dependent Quark Forces and the Spin Content of the Nucleon

The spin crisis of the nucleon is that the quark spin contribution is only a small fraction of the nucleon spin. A relativistic Dirac equation approach is followed assuming three low mass current quarks in the nucleon described by a (1/2⁺)³ configuration. If the lower component contribution to the normalization of the quark wave function is about 0.18, then the axial charge of the nucleon can be reproduced. However including the same lower component to every quark wave function is not enough to resolve the spin crisis. The net u quark spin z component is predicted as 1.0 and the net d quark spin z component is predicted as –0.25, both in disagreement with experiment. These predictions can be brought into agreement with experiment if flavor independent but spin dependent forces are assumed between the quarks. The strength of the spin dependent force found by empirically fitting the nucleon spin data is shown to be comparable to the spin dependence that can explain the -nucleon mass difference. The spin content of the ⁺ is then predicted using the interactions that reproduce the spin content of the proton.     

NQR Spin Diffusion in an Inhomogeneous Internal Field

The theory of NQR spin diffusion is extended to the case of spin lattice relaxation and spin diffusion in an inhomogeneous field. Two coupled equations describing the mutual relaxation and the spin diffusion of the nuclear magnetization and dipolar energy were obtained by using the method of nonequilibrium state operator. The equations were solved for short and long times approximation corresponding to the direct and diffusion relaxation regimes.     

Spin-Dependent Forces and Current Quark Masses

The J = (3/2) , J = 1/2 Nucleon mass difference shows the quark energies can be spin dependent. It is natural to expect that the quark wave functions also depend on spin. A spin-dependent quark force is fitted to the proton and neutron magnetic moments, axial charge, and spin content using a (1/2⁺)³ configuration for the quarks and assuming only zero mass u and d quarks are in the nucleon. In the octet, such spin-dependent forces lead to different wave functions for quarks with spin parallel or antiparallel to the nucleon spin. The eigen-energy of this potential is 0.15 GeV higher for quark spin parallel than for the quark spin antiparallel to the proton spin. This potential predicts a single quark energy of 0.37 GeV for mass-less quarks in the Delta. Assuming the quark forces are flavor independent, this potential predicts magnetic moments of a bound strange quark to be very close to those determined empirically from the octet magnetic moments.     

Particle Spin Described by Quantum Hamilton Equations

The anomalous Zeeman effect made it clear that charged particles like the electron possess a magnetic dipole moment. Classically, this could be understood if the charged particle possesses an eigenrotation, that is, spin. Within Nelson's stochastic mechanics, it was shown that the model of a rotating charged ball is able to reproduce the well-known spin expectation values. This classically motivated model of intrinsic rotation described in terms of a stochastic process is revisited here within the formalism of stochastic optimal control theory. Quantum Hamilton equations (QHE) for spinning particles are derived, which reduce to their classical counterpart in the zero quantum noise limit. These equations enable the calculation of the common spin expectation values without the use of the wave function. They also offer information on the orientation dynamics of the magnetic moment of charged particles beyond the behavior of the spin averages.     

High-Speed Magic-Angle SpinningC MAS NMR Spectra of Adamantane: Self-Decoupling of the Heteronuclear Scalar Interaction and Proton Spin Diffusion

We have investigated the carbon line shape of solid adamantane under high-speed magic-angle sample spinning (MAS) acquired without proton decoupling. The CH-group shows a spinning-speed-dependent line broadening while the CH₂-group consists of a spinning-speed-independent sharp component and a spinning-speed-dependent broader part. These phenomena can be explained by self-decoupling of theJ-interaction due to proton spin diffusion. Such a self-decoupling process can be described by a magnetization exchange process between the multiplet lines. Changing the spin-diffusion rate constant by off-resonance irradiation of the protons allows us to observe the full range from slow exchange to coalescence to fast exchange of the carbon spectra. One of the multiplet components in the CH₂-group corresponds to a group spin of the protons of zero and therefore does not couple to the other protons. This gives rise to the sharp central line. The magnetization exchange rate constant between the different multiplet lines can be determined from the spectra and is a measure for the spinning-speed-dependent proton spin-diffusion rate constant. Even at an MAS speed of 30 kHz, proton spin diffusion is still observable despite the relatively weak intermolecular proton dipolar-coupling network in adamantane which results in a static proton line width of only 14 kHz (full width at half height).     

Phonon-assisted spin diffusion in solids

The spin flip-flop transition rate is calculated for the case of spectral spin diffusion within a system of dipolarly coupled spins in a solid where the lattice vibrations are present. Long-wavelength acoustic phonons time-modulate the interspin distance r_ij and enhance the transition rate via the change of the 1/r³_ij term in the coupling dipolar Hamiltonian. The phonon-assisted spin diffusion rate is calculated by the golden rule in the Debye approximation of the phonon density of states. The coupling of the spins to the phonons introduces temperature dependence into the transition rate, in contrast to the spin diffusion in a rigid lattice, where the rate is temperature-independent. The direct (one-phonon absorption or emission) processes introduce a linear temperature dependence into the rate at temperatures not too close to T = 0. Two-phonon processes introduce a more complicated temperature dependence that again becomes simple analytical for temperatures higher than the Debye temperature, where the rate is proportional to T², and in the limit T → 0, where the rate varies as T⁷. Raman processes (one-phonon absorption and another phonon emission) dominate by far the phonon-assisted spin flip-flop transitions.     

相对论粒子的自旋算符

发展了关于相对论态自旋算符的系统理论.考虑了具有非零静质量的粒子情况.对带自旋的相对论粒子,通常的自旋算符需换为相对论的自旋算符.在Poincar啨群不可约表示的框架里,构造了适用于粒子任意正则态的自旋算符,称为运动自旋.本文的讨论限于量子力学.随后将在量子场论中对此作进一步深入研究.     

Symmetries and motions in manifolds

In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependent co-ordinate transformations naturally leads to the concept of Killing tensors. Via their Poisson brackets these tensors generate an a priori infinite-dimensional Lie algebra. The nature of such infinite algebras is clarified using the example of flat space-time. Next the formalism is extended to spinning space, which in addition to the standard real co-ordinates is parametrised also by Grassmann-valued vector variables. The equations for extremal trajectories (“geodesics”) of these spaces describe the pseudo-classical mechanics of a Dirac fermion. We apply the formalism to solve for the motion of a pseudo-classical electron in Schwarzschild space-time.     

C–H dipolar recoupling under very fast magic-angle spinning using virtual pulses

A new solid-state NMR pulse sequence for recoupling ¹³C–¹H dipolar interactions under magic-angle spinning is proposed, which works under a spinning speed of a few to several tens kilohertz. The sequence is composed of two different frequency switched Lee–Goldburg sequences, and the modulation of the spin part of the ¹³C–¹H dipolar interaction is introduced by a virtual pulse sequence consisting of unitary operators connecting the rotating frame and the tilted rotating frame. When the cycle time of the spinning is equal to or twice the cycle time of the sequence, the ¹³C–¹H dipolar interactions can be recoupled. The sequence is insensitive to experimental imperfections such as rf inhomogeneity or frequency offset, and the resulting lineshape can be represented by a simple analytical equation based on the zeroth-order average Hamiltonian. Experimental results for [2-¹³C] -valine·HCl are reported.     

Rotating frame proton spin relaxation in viscous glycerol

The observation of a rotating frame Larmor frequency dependence in the proton spin relaxation of glycerol lends support to a recent study of proton spin relaxation in this substance. Comparison of the data to recent theories describing spin relaxation by translational diffusion strongly suggest that this is the dominant relaxation process in glycerol near room temperature. In addition, the measurement of the self-diffusion coefficient of glycerol, at a temperature lower than has been previously reported, indicates that this rotating frame technique may be useful in the study of diffusion in viscous media.