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.     

自旋与手征动力学的输运模拟研究

自旋相关的物理是多个研究领域的热门课题。核子和夸克都是自旋为1/2的费米子，在非对心重离子碰撞中受到自旋-轨道相互作用以及磁场的影响，会产生有趣的自旋动力学，特别是在垂直于反应平面方向上会出现自旋极化。在相对论重离子碰撞中，由于产生了极端的高温高密环境，夸克可以近似看作无质量粒子，此时自旋动力学过渡为手征动力学。在外界电磁场、涡旋场作用下以及在电荷与手征荷不对称的条件下，会产生一系列手征反常效应。本文介绍我们课题组基于输运模拟在自旋与手征动力学方面开展的一系列研究工作，包括中能重离子碰撞及相对论重离子碰撞中粒子的自旋极化、理想体系及相对论重离子碰撞中的手征磁波等。     

伪自旋对称情形下Rosen-Morse类型势场中相对论粒子的束缚态

在伪自旋对称情形下研究了Rosen-Morse类型势场中相对论粒子的束缚态,利用Nikiforov-Uvarov方法求解了伪自旋对称情形下的Klein-Gordon和Dirac方程,得到了相对论粒子被束缚在Rosen-Morse类型势场的精确束缚态解.     

相对论核－核碰撞中产生的Λ粒子的横向极化度与横向动量的关联

对在相对论能量下重核反应中产生的粒子的横向极化度进行了测定．对粒子自旋磁矩与磁场相互作用所造成的自旋进动效应进行了修正，得到了粒子的零横向极化度及其与横动量的无关联关系．与较低能量时核－核反应中产生的粒子的极化情况进行了比较．结果表明，在相对论重核反应下的粒子的产生机制有别于高能质子引起的反应和较低能时的核－核反应中产生粒子的机制．     

整数自旋协变波函数

对高自旋态的Bargmann-Wigner方程的解进行了改造,给出了一套系统地构造高自旋态(整数自旋)协变波函数的新方法.利用这种方法,分别构造了任意整数自旋粒子的协变波函数.     

相对论核–核碰撞中产生的Λ粒子的横向极化度与横向动量的关联

对在相对论能量下重核反应中产生的Λ粒子的横向极化度进行了测定．对粒子自旋磁矩与磁场相互作用所造成的自旋进动效应进行了修正，得到了Λ粒子的零横向极化度及其与横动量的无关联关系．与较低能量时核－核反应中产生Λ的粒子的极化情况进行了比较．结果表明，在相对论重核反应下的Λ粒子的产生机制有别于高能质子引起的反应和较低能时的核－核反应中产生Λ粒子的机制．     

自旋不是轨道角动量的相对论效应——与许方官和高春媛商榷

对《大学物理》2000年第11期上发表的《氢原子的磁矩－对自旋的讨论之一》一提出了不同的看法，认为该错把相对论的流密度当成了非相对论的流密度，前不能在非相对论近似下过滤到后，在相对论情况下，自旋和轨道耦合在一起，不能互相独立，在非相对论情况下自旋独立于轨道运动而存在；因而，自旋不是轨道角动量的相对论效应。     

整数自旋粒子的方程和波函数

从高自旋态的Bargmann-Wigner方程出发,建立了整数自旋粒子的运动方程,通过求解方程得到了一套整数自旋粒子波函数,并建立了等效Largrange形式.     

量子场论中的自旋算符

从量子场论的角度对相对论粒子的运动自旋概念作了进一步深入研究.构造了场量子自旋以及场系统运动自旋两个新算符.给出了场量子自旋动量空间的显式表达式以及用Poincar啨群生成元表示的场系统运动自旋的显式表达式.借助这两个算符,可以干净地解决有关场自旋的问题,表明它们才是场自旋的恰当的算符.     

硼原(离)子内壳激发高自旋态能级和辐射跃迁

采用Rayleigh-Ritz变分方法计算了B原子(离子)内壳层激发高自旋态(~(4,5,6)L,L=S,P)里德伯系列的能量和精细结构劈裂,利用截断变分方法改进非相对论能量,并利用一阶微扰理论计算了相对论能量修正和质量极化效应修正,利用屏蔽的类氢公式计算了量子电动力学效应和高阶相对论效应,从而得到了高精度的组态能量.利用精确计算的波函数,计算了这些高自旋态的电偶极辐射跃迁波长、振子强度和辐射跃迁概率.通过长度规范和速度规范计算的振子强度的一致性证明了本文计算的波函数是精确的.相比其他理论计算结果,本文计算的高自旋态的能级及跃迁波长数据与实验数据符合得更好.对于一些高位的内壳层激发高自旋态,相关的能级和跃迁数据为首次报道,本文的计算结果对相关实验光谱谱线标定具有重要意义.     

Relativistic Spin Operators

A systematic theory on the appropriate spin operators for the relativistic states is developed.For a massive relativistic particle with arbitrary nonzero spin,the spin operator should be replaced with the relativistic one,which is called in this paper as moving spin.Further the concept of moving spin is discussed in the quantum field theory.A new operator,field quanta spin is defined and in terms of the generators of Poincare group the moving spin of field system is constructed.It is shown that,in virtue of the two operators,problems in quantum field concerned spin can be neatly settled.     

相对论性无自旋氢原子的散射态

研究获得了相对论性无自旋氢原子散射态的精确解,给出了精确的相移表达式和按"k/2π标度"归一化的散射态的径向波函数,讨论了散射振幅的解析性质 .     

Wavefunctions for Particles with Arbitrary Spin

By solving rigorously the relativistic wave equations derived from Bargmann-Wigner equation for arbitrary spin,the relativistic wavefunctions in momentum representation for particles with arbitrary spin are deduced.     

Test of spin symmetry in anti-nucleon spectra

The spin symmetry in antinucleon spectra of a nucleus is tested by investigating the relations between the Dirac wave functions of the spin doublets and examining these relations in realistic nuclei within the relativistic mean-field model. In addition to the fact that the dominant components of the Dirac spinors of the spin doublet are nearly identical to each other, there is a differential relation between the smaller components which is found to be almost exactly fulfilled.     

Solution to the Rarita-Schwinger equations

A systematical method is presented for solving the relativistic wave equations for particles of arbitrary spin. Explicit helicity relativistic wave functions for particles with arbitrary spin are derived rigorously. Received: 22 August 2001 / Revised version: 5 July 2002 / Published online: 9 December 2002 RID="a" ID="a" Corresponding author.     

Solutions of Dirac equations with the Pöschl-Teller potential

By using the basic concepts of the supersymmetric quantum mechanics formalism and the function analysis method, we solve the Dirac equation with vector and scalar potentials and obtain the bound-state solutions for the nuclei in the relativistic P?schl-Teller potential. All of the analyses are prepared under the conditions of the exact spin symmetry and pseudospin symmetry. The exact energy equation and corresponding two-component spinor wave functions for s -wave bound states are obtained analytically.     

Static observables of relativistic three-fermion systems with instantaneous interactions

We show that static properties like the charge radius and the magnetic moment of relativistic three-fermion bound states with instantaneous interactions can be formulated as expectation values with respect to intrinsically defined wave functions. The resulting operators can be given a natural physical interpretation in accordance with relativistic covariance. We also indicate how the formalism may be generalized to arbitrary moments. The method is applied to the computation of static baryon properties with numerical results for the nucleon charge radii and the baryon octet magnetic moments. In addition, we make predictions for the magnetic moments of some selected nucleon resonances and discuss the decomposition of the nucleon magnetic moments in contributions of spin and angular momentum, as well as the evolution of these contributions with decreasing quark mass.     

The nucleon wave function in light-front dynamics

The general spin structure of the relativistic nucleon wave function in the 3q-model is found. It contains 16 spin components, in contrast to the 8 already known. This follows from the fact that in a many-body system parity conservation does not reduce the number of components. The explicitly covariant form of the wave function automatically takes into account the relativistic spin rotations, without introducing any Melosh rotation matrices. It also reduces the calculations to the standard routine of the Dirac matrices and of the trace techniques. In examples of the proton magnetic moment and of the axial nucleon form factor, with a particular wave function, we reproduce the results of the standard approach. Calculations beyond the standard assumptions give different results.     

自旋为2的Bargmann-Wigner方程的严格解

在坐标表象中严格求解自旋为2的Bargmann-Wigner方程,导出了自旋为2的场（m≠0）的相对论性场方程和动量表象波函数。