Dirac方程中有效质量随空间变化的相对论散射
Relativistic scattering with spatially-dependent effective mass in the Dirac equation
摘要：
基于J-矩阵方法，我们提出了一种求解空间依赖质量系统散射问题的代数相对论方法。参考哈密顿量是三维狄拉克哈密顿量，但具有与位置相关的质量，并且具有恒定的渐近极限。此外，该有效质量分布在有限维函数子空间中局部表示。旋量耦合到短程的球对称矢量势和伪标量势，使得它们在相同的有限维子空间中由它们的矩阵元素精确地表示。我们计算了相对论性相移作为能量的函数对于一个给定的配置和研究的能量共振结构上的质量的空间变化的效果。
英文摘要：
We formulate an algebraic relativistic method of scattering for systems with spatially dependent mass based on the J-matrix method. The reference Hamiltonian is the three-dimensional Dirac Hamiltonian but with a mass that is position-dependent and having a constant asymptotic limit. Additionally, this effective mass distribution is locally represented in a finite dimensional function subspace. The spinor couples to spherically symmetric vector and pseudo scalar potentials that are short-range such that they are accurately represented by their matrix elements in the same finite dimensional subspace. We calculate the relativistic phase shift as a function of energy for a given configuration and study the effect of spatial variation of the mass on the energy resonance structure.
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