当能级间隔较小时三能级核四极共振自旋系统对脉冲的响应

用虚拟自旋-1/2算符理论考察了I=1的核四极共振自旋系统在其能级间隔较小时对1-2个脉冲的响应.由于核四极相互作用表象中的射频场与核自旋的相互作用(H_rf)包含时间,因而用Dyson时序算符来计算密度算符在H_rf作用下的演化.     

￣（14）N核四极共振的偏共振效应

用虚拟１／２自旋算符讨论了核四极共振（ＮＱＲ）中自旋Ｉ＝１的自旋系统对激发脉冲宽度和频率偏置的响应。用单脉冲和双脉冲来观测的核四极共振信号与理论预期相符合。此外还证明，若只考虑射频场在分子电场梯度（ＥＰＧ）张量主轴坐标系（ＰＡＳ）中的一个轴上的分量（即有效射频场分量）的作用，就可用ＮＭＲ矢量模型来处理Ｉ＝１的核自旋系统。     

14N核四极共振的偏共振效应

用虚拟１／２自旋算符讨论了核四极共振（ＮＱＲ）中自旋Ｉ＝１的自旋系统对激发脉冲宽度和频率偏置的响应。用单脉冲和双脉冲来观测的核四极共振信号与理论预期相符合。此外还证明，若只考虑射频场在分子电场梯度（ＥＰＧ）张量主轴坐标系（ＰＡＳ）中的一个轴上的分量（即有效射频场分量）的作用，就可用ＮＭＲ矢量模型来处理Ｉ＝１的核自旋系统。 关键词：     

《量子力学》自学辅导之十一——电子自旋（续）

《量子力学》自学辅导之十一──电子自旋（续）宋宇辰，曾心愉，裴文杰（１）复旦大学理论物理骨干教师班；２）复旦大学物理系，上海２００４３３）２．３自旋算符的矩阵形式自旋函数是２×１的矩阵，作用在自旋函数上的自旋算符应该是２×２的矩阵．设泡利算符的矩阵形...     

14N核四极共振中自旋锁定的偏共振效应

用虚拟自旋-1/2算符理论计算了核四极共振自旋系统在自旋锁定脉冲序列作用下的时间演化,获得了自旋锁定信号随锁定脉冲长度和射频频率偏置的变化关系。如果不考虑准备脉冲期间射频频率偏置的影响,那么可简单地用核磁共振中的矢量模型来解释自旋锁定这一现象。 关键词：     

￣（14）N核四极共振自旋系统自旋－晶格弛豫时间的测量

￣１４Ｎ核四极共振自旋系统的自旋－晶格弛豫是一种双指数弛豫。本文介绍了￣１４Ｎ核四极共振自旋系统的自旋－晶格弛豫时间的３种测量方法，利用可变多面体方法对实验数据进行拟合，获得了￣１４Ｎ核四极共振自旋系统的自旋－晶格弛豫时间Ｔ＿１ｓ和Ｔ＿１１，对有关文献中关于核四极共振弛豫时间的测量的３个观点提出了质疑。     

化学位移各向导性对半整数自旋四极核的2D NMR章动的影响(英文)

考察了化学位移各向异性对半整数自旋四极核2DNMR章动的影响．用数值方法对2DNMR章动实验的演化期的Hamiltonian矩阵进行对角化，然后用帐篷法进行粉末平均，获得了自旋为I＝3／2、5／2、7／2和9／2的四极核在不同化学位移各向异性下的2DNMR章动谱．实验结果与理论计算符合较好．     

关于核相的分析和核相图

本文讨论了原子核内单粒子能级与两类残余相互作用,(长程的四极—四极相互作用与短程的成对相互作用)之间的相互交织所导致的相变。类比于普通空间中对I～ω关系的分析,进行了规范空间中N～λ_n(或Z～λ_p)关系的分析。并进一步深入探讨了这两类分析各自的特点。综合从这两个侧面所获得的知识,可以达到关于核相变的更全面的理解,建立起一个核相图。于是核结构的相特征随着核子数(N或Z)及自旋的变化规律就可以通过这样的核相图而显示出它的全貌。这样的思想和分析方法近两年来引起了国际高自旋界的较大兴趣。     

关于核相的分析和核相图

本文讨论了原子核内单粒子能级与两类残余相互作用,(长程的四极—四极相互作用与短程的成对相互作用)之间的相互交织所导致的相变。类比于普通空间中对I～ω关系的分析,进行了规范空间中N～λ_n(或Z～λ_p)关系的分析。并进一步深入探讨了这两类分析各自的特点。综合从这两个侧面所获得的知识,可以达到关于核相变的更全面的理解,建立起一个核相图。于是核结构的相特征随着核子数(N或Z)及自旋的变化规律就可以通过这样的核相图而显示出它的全貌。这样的思想和分析方法近两年来引起了国际高自旋界的较大兴趣。     

随机电报过程引起的光失相的计算

本文计算了红宝石中Ａｌ核自旋跳变引起的Ｒ１［４Ａ２（Ｓ＝－３／２）→２Ｅ（Ｓ＝－１／２）］回波衰减．用随机电报过程描述每个Ａｌ核自旋（ｉ）跳变引起Ｃｒ共振频率的起伏Δｉ，这个过程对光子回波衰减的贡献〈Ｅｉ（ｔ２１）〉可以用解析式表示．首先计算核自旋（ｉ）跳变的总速率Ｗｉ及它引起的Δｉ，求出〈Ｅｉ（ｔ２１）〉．设对Ｃｒ光失相起主要贡献的每个Ａｌ核自旋跳变近似是独立的，所以总的回波强度是所有Ａｌ引起的〈Ｅｉ（ｔ）２１〉的乘积．计算得到非指数的回波衰减，以Ｉ＝Ｉ０ｅｘｐ〔－（４ｔ／ｔｍ）ｘ〕拟合，ｘ＝２．５６，ｔｍ＝５０．６μｓ，与实验及计算机模拟的结果一致     

Nuclear spin echo model based on Floquet–Lyapunov theory

The method of nuclear spin-echo amplitude calculation based on the density matrix technique is improved. The Floquet–Lyapunov theorem for a system of the ordinary differential equations with coefficients periodically dependent on time is used to find the solution of the Schrödinger equation for the time-evolution operator which describes behavior of a nuclear spin in the presence of a radiofrequency pulsed magnetic field. NQR spin echo for the case of nuclear spin I?=?1 and NMR spin echo for I?=?1/2 are considered as the simplest illustrations of the approach. The appearance of multiple spin echoes is predicted in the case of strong radiofrequency field.     

The nuclear spin interaction with paramagnetic impurities in antiferromagnets

The influence of paramagnetic impurities on the relaxation frequencies of the nuclear subsystem in antiferromagnets is investigated. In the framework of the spin operator diagram technique the nuclear spin-spin as well as spin-lattice relaxation rates are calculated. The correlation effects due to indirect spin-spin interaction via magnons both in nuclear and impurity subsystems are taken into account.     

Multiple-quantum dynamics of one-dimensional nuclear spin systems in solids

Multiple-quantum spin dynamics is studied using analytic and numerical methods for one-dimensional finite linear chains and rings of nuclear spins 1/2 coupled by dipole-dipole interactions. An approximation of dipole-dipole interaction between nearest neighbors having the same constants is used to obtain exact expressions for the intensities of the multiple-quantum coherences in the spin systems studied, which are initially in thermal equilibrium and whose evolution is described by a two-spin two-quantum Hamiltonian. An approximation of nearest neighbors with arbitrary dipole-dipole interaction constants is used to establish a simple relationship between the multiple-quantum dynamics and the dynamics of spin systems with an XY Hamiltonian. Numerical methods are developed to calculate the intensities of multiple-quantum coherences in multiple-quantum NMR spectroscopy. The integral of motion is obtained to expand the matrix of the two-spin two-quantum Hamiltonian into two independent blocks. Using the nearest-neighbor approximation the Hamiltonian is factorized according to different values of the projection operator of the total spin momentum on the direction of the external magnetic field. Results of calculations of the multiple-quantum dynamics in linear chains of seven and eight nuclear spins and a six-spin ring are presented. It is shown that the evolution of the intensities of the lowest-order multiple-quantum coherences in linear chains is accurately described allowing for dipole-dipole interaction of nearest and next-nearest neighbors only. Numerical calculations are used to compare the contributions of nearest and remote spins to the intensities of the multiple-quantum coherences.     

Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator

Relaxation plays a crucial role in the spin dynamics of dynamic nuclear polarisation. We review here two different strategies that have recently been used to incorporate relaxation in models to predict the spin dynamics of solid effect dynamic nuclear polarisation. A detailed explanation is provided on how the Lindblad–Kossakowski form of the master equation can be used to describe relaxation in a spin system. Fluctuations of the spin interactions with the environment as a cause of relaxation are discussed and it is demonstrated how the relaxation superoperator acting in Liouville space on the density operator can be derived in the Lindblad–Kossakowski form by averaging out non-secular terms in an appropriate interaction frame. Furthermore we provide a formalism for the derivation of the relaxation superoperator starting with a choice of a basis set in Hilbert space. We show that the differences in the prediction of the nuclear polarisation dynamics that are found for certain parameter choices arise from the use of different interaction frames in the two different strategies. In addition, we provide a summary of different relaxation mechanisms that need to be considered to obtain more realistic spin dynamic simulations of solid effect dynamic nuclear polarisation.     

Effect of the nuclear hyperfine field on the 2D electron conductivity in the quantum Hall regime

The effect of the nuclear hyperfine interaction on the dc conductivity of 2D electrons under quantum Hall effect conditions at filling factor ν=1 is observed for the first time. The local hyperfine field enhanced by dynamic nuclear polarization is monitored via the Overhauser shift of the 2D conduction electron spin resonance in AlGaAs/GaAs multiquantum-well samples. The experimentally observed change in the dc conductivity resulting from dynamic nuclear polarization is in agreement with a thermal activation model incorporating the Zeeman energy change due to the hyperfine interaction. The relaxation decay time of the dc conductivity is, within experimental error, the same as the relaxation time of the nuclear spin polarization determined from the Overhauser shift. These findings unequivocally establish the nuclear spin origins of the observed conductivity change. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 58–63 (10 January 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Anisotropic Spin Cluster as a Qubit

We study an anisotropic spin cluster of 3 spin S=1/2 particles with antiferromagnetic exchange interaction with non-uniform coupling constants. A time-dependent magnetic field is applied to control the time evolution of the cluster. It is well known that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. The universal one-qubit logic gate can be constructed from the time evolution operator of the non-autonomous many-body system, and the six basic one-qubit gates can be realized by adjusting the applied time-dependent magnetic field.     

Anisotropic Spin Cluster as a Qubit

We study an anisotropic spin cluster of 3 spin S=1/2 particles with antiferromagnetic exchange interaction with non-uniform coupling constants. A time-dependent magnetic field is applied to control the time evolution of the cluster. It is well known that for an odd number og sites a spin cluster qubit can be defined in terms of the ground state doublet. The universal one-qubit logic gate can be constructed from the time evolution operator of the non-autonomous many-body system, and the six basic one-qubit gates can be realized by adjusting the applied time-dependent magnetic field.     

The NSW interaction with nuclear local modes in antiferromagnets

The nuclear spin wave (NSW) relaxation rates due to the interaction with nuclear impurity local modes (NILM) in antiferromagnets are considered in the framework of the Keldysh formalism based on the spin operator diagram technique. It is shown that the NSW relaxation frequency due to the scattering on the fluctuations of impurity nuclear spins is of resonance character. The NSW damping due to the resonance absorption by NILM depends strongly on the NSW amplitude N, which accounts for the “hard” excitation of NSW's in parallel pumping experiments /6/. The NSW relaxation rates due to the processes involving two NSW's and one impurity nuclear excitation are also calculated.     

Isobar giant resonance formation in self-conjugate nuclei

The production of isobars with concomitant giant resonance excitations due to peripheral collisions of relativistic heavy ions is investigated. The interaction is described by a modified form of the central term in the one-pion-exchange potential (OPEP) where the projectile ordinary spin operator is replaced by a transition spin operator which describes the creation of an isobar from a nucleon. The scattering is analyzed using time-dependent harmonic perturbation theory to determine the reaction total cross sections. The results obtained, which are valid for reactions involving self-conjugate nuclei, are applied to the specific collison of 2.1 $\text{GeV}\text{nucleon}$¹⁶O projectiles with ¹²C targets at rest. Cross sections are investigated using two different models for the nuclear spin states. In the first model, the many-body nuclear spin state is reduced, in the spirit of a particle-hole state, to an equivalent two-body state called a particle-core state. In the second model, the many-body spin states are described by unsymmetrized products of individual particle spins. Properties of the spin giant resonance and isobar giant resonance states are investigated. Finally, isobar decay and isobar/pion absorption effects are discussed.