Theoretical Investigation of Low-Energy Positron and Positronium Collisions

旋涡(或漩涡)是流体和气体的常见性质，因此在许多科学和工程领域都很重要，包括流体动力学、天体物理、凝聚态物理和非线性动力学。它们是搅拌系统中集体现象的例子，甚至在被称为玻色-爱因斯坦凝聚体的超冷原子气体中也观察到了。令人惊讶的是，最近在描述基本电子-原子碰撞过程的量子力学波函数中发现了涡旋，它们的出现与观测到的散射截面中的深极小值有关。情况仍然有些模糊，因为基本的碰撞过程似乎与液体和气体的集体性质相关的复杂得多的现象几乎没有共同点。该项目希望通过探索涉及正电子而不是电子的碰撞过程中涡旋的形成来揭示这一谜团。正电子是电子的反粒子，带有正电荷，因此与物质的相互作用非常不同。因此，对入射弹丸电荷的敏感性将通过直接的理论计算进行测试，有望澄清这些过程中涡旋形成的潜在机制。由于正电子现在被广泛应用于各种领域和应用，从凝聚态物理到正电子发射断层扫描(PET扫描)，涡旋的形成与涉及正电子的基本碰撞过程的相关性可能会产生广泛的影响。这项工作将使研究生参与到涉及基本量子力学碰撞过程的挑战性研究项目中。最近，研究人员已经证明，涡旋的形成是氦原子电子碰撞电离三重微分截面实验测量中观察到的深极小值的原因。还研究了原子碰撞中其他电离过程的涡旋。这个项目的第一个目标是分析正电子-氢和正电子-氦碰撞中的涡旋形成，看看涡旋是否影响正电子的形成速度。PI将指导研究生使用Kohn类型变分方法、多通道有效射程理论和Born近似详细分析这些过程中正电子的形成。目标是确定在正电子形成散射幅度中获得零所需的基本分量，在微分截面中获得相应的深极小值，以及在速度场中获得与散射幅度相对应的涡旋。第二个项目是研究正电子-正电子散射，因为这是一个基本的四体库仑问题，所以很有兴趣，并支持制造正电子玻色-爱因斯坦凝聚体的实验努力。PI将培训研究生使用Kohn类型的变分方法和Born近似与交换进行分析。一个目标是使用Kohn型变分方法获得基态正电子-基态正电子散射的基准结果。

Vortices (or whirlpools) are familiar properties of fluids and gases and so are important in a number of fields of science and engineering, including fluid dynamics, astrophysics, condensed-matter physics and non-linear dynamics. They are examples of collective phenomena in stirred systems, and have even been observed in the ultracold atomic gases known as Bose-Einstein condensates. Surprisingly, vortices have recently been discovered in the quantum mechanical wave function describing elementary electron-atom collision processes, where their appearance was correlated to deep minima in observed scattering cross sections. The situation is still somewhat murky, since elementary collision processes seem to have little in common with the much more complex phenomena associated with the collective properties of liquids and gases. This project hopes to shed light on this mystery by searching for vortex formation in collision processes involving positrons rather than electrons. Positrons are antiparticles of electrons, carry positive charge, and so interact very differently with matter. Sensitivity to the charge of an incident projectile will therefore be tested through direct theoretical calculations, hopefully clarifying the underlying mechanism of vortex formation in these processes. Since positrons are now commonly used in a variety of fields and applications, ranging from condensed matter physics to positron-emission tomography (PET scans), the relevance of vortex formation to elementary collision processes involving positrons could have wide-ranging impact. The work will engage graduate students in challenging research projects involving elementary quantum mechanical collision processes.Recently, researchers have demonstrated that vortex formation is responsible for deep minima observed in the experimental measurements of the triply differential cross sections for electron-impact ionization of helium atoms. Vortices have also been studied for other ionization processes in atomic collisions. The first goal of this project is to analyze vortex formation in positron-hydrogen and positron-helium collisions, to see whether or not vortices affect the rate of positronium formation. The PI will guide a graduate student through a detailed analysis of positronium formation in these processes using Kohn-type variational methods, multichannel effective range theories and the Born approximation. The goal is to determine basic components necessary to obtain a zero in the positronium formation scattering amplitude, the corresponding deep minimum in the differential cross section and the vortex in the velocity field that corresponds to the scattering amplitude. A second project is to study positronium-positronium scattering, which is of interest since it is a fundamental four-body Coulomb problem, and in support of experimental efforts to make a positronium Bose-Einstein Condensate. The PI will train a graduate student to use Kohn-type variational methods and the Born approximation with exchange for this analysis. A goal is to obtain benchmark results for ground-state positronium - ground-state positronium scattering using Kohn-type variational methods.