RUI: Path Integral Approach to Ion-Impact Collisions

对原子碰撞的研究提供了有关自然力之一的重要信息。原子碰撞的研究成果被广泛应用于等离子体物理、天体物理、生物物理等诸多领域。除了更好地全面了解重离子碰撞(这是这项工作的主要重点)外，这项工作还将把其他物理学领域的一项众所周知的技术引入原子和分子碰撞研究，并可能导致原子碰撞社区和其他相关领域之间更多的重叠和合作。这个项目的另一个重要方面是将本科生纳入前沿研究。通过参与这个项目，学生将通过代码开发和数据分析获得宝贵的实践研究经验。他们还将在地区和国家会议上展示他们的成果，这有望使他们对科学研究有更全面的看法。少体问题是物理学中最基本、最未解决的问题之一。当两个以上的粒子通过库仑力相互作用时，系统的动力学不能被精确描述。因此，理论必须求助于近似，而理论和实验之间的任何差异都必须是近似的结果。将现有的理论模型与最近的实验结果进行了比较，揭示了当前模型的一些明显的局限性。特别是，碰撞的动力学是不了解的，其中一些碰撞碎片是在完整的3维几何中发现的。众所周知，这些三维碰撞背后的潜在机制是量子力学效应的结果，但目前的理论无法准确描述碰撞动力学。本项目的目标是通过使用路径积分技术，发展一种新的量子力学理论模型，用于研究离子与原子的碰撞。路径积分方法是在其他物理领域中使用的一种众所周知的技术，但尚未应用于重离子碰撞的研究。这项特殊的技术将允许包括重要的量子力学相互作用，以及提供对碰撞期间粒子轨迹的直观理解。该项目的技术细节包括利用路径积分法为重离子射弹的电离和俘获过程开发一个计算模型。该方法将利用拉格朗日在经典路径周围的展开，其中与经典路径的偏差代表粒子的量子涨落。对于电子俘获碰撞，将研究弹核相互作用和靶电子关联的作用。我们还将研究高能、大散射角的电子俘获碰撞，以更好地理解Thomas机制，并确定在这些碰撞中是否存在可能的绕射效应。对于电离过程，将研究在散射面之外发现被抛出的电子的碰撞，重点是弹核相互作用以及弹核与目标核之间的近距离碰撞的作用。

The study of atomic collisions provides important information about one of the fundamental forces of nature. The results of atomic collisions research are widely used in fields such as plasma physics, astrophysics, biophysics, and many other areas. In addition to providing a better overall understanding of heavy-ion collisions, which is the principal focus of the effort, this work will bring a well-known technique from other areas of physics into atomic and molecular collisions research, and possibly lead to additional overlap and collaborations between the atomic collisions community and other related fields. Another important aspect of this project is the inclusion of undergraduate students in cutting-edge research. By participating in this project, students will gain valuable hands-on research experience through code development and data analysis. They will also present their results at regional and national conferences, which will hopefully give them a more global view of scientific research.The few-body problem is one of the most fundamental, unsolved problems in physics. When more than two particles interact through the Coulomb force, the dynamics of the system cannot be described exactly. As a result, theory must resort to approximations, and any discrepancies that result between theory and experiment must be a result of the approximations. A comparison of current theoretical models with recent experimental results reveals some striking limitations of the current models. In particular, the dynamics of collisions in which some of the collision fragments are found in a full 3-dimensional geometry is not understood. The underlying mechanism behind these 3-dimensional collisions is known to be a result of quantum mechanical effects, but current theories cannot accurately describe the collision dynamics. The objective of this project is to develop a novel quantum mechanical theoretical model for the study of ion-impact atomic collisions through the use of the path integral technique. The path integral method is a well-known technique used in other areas of physics, but has not been applied to the study of heavy-ion collisions. This particular technique will allow for the inclusion of important quantum mechanical interactions, as well as provide an intuitive understanding of particle trajectories during the collision. The technical details of the project include the development of a computational model using the path integral method for ionization and capture processes with heavy-ion projectiles. The method will utilize an expansion of the Lagrangian around the classical path, where the deviation from the classical path represents the quantum fluctuations of the particle. For electron capture collisions, the role of the projectile-nuclear interaction and target electron correlation will be studied. Electron capture collisions with high projectile energy and large scattering angle will also be studied with the objective of better understanding the Thomas mechanism, and determining if possible diffraction effects exist in these collisions. For ionization processes, collisions in which the ejected electron is found outside of the scattering plane will be studied, with a focus on projectile-nuclear interactions and the role of close collisions between the projectile and the target nucleus.