Development of a General and Effective B-spline R-matrix Computer Program for Electron and Photon Collisions with Atoms, Ions, and Molecules

此外，还将利用非正交轨道的B-样条法，进一步开发电子与原子和二子碰撞的通用有效程序。该方法基于R矩阵方法的扩展版本，其中非正交轨道被广泛用于描述目标状态和散射函数。新方法基本上避免了将最常用的一套R矩阵代码应用于真正复杂的目标时经常出现的三个主要问题。R矩阵代码主要是在过去30年里在贝尔法斯特开发的，目前在全球范围内使用。这些问题包括i)以足够的精度描述给定计算的所有感兴趣的目标状态的困难，ii)当试图解决前一个问题时可能出现非物理结构，即所谓的伪共振，以及iii)由于病态正交化过程和修改所谓的Buttle校正的需要而造成的数值困难。用于描述内部区域中的连续状态的B样条基的优良的数值特性允许高计算精度，而基的完备性将确保不需要对R矩阵元素进行Buttle校正。利用非正交轨道技术，可以通过紧凑的组态展开，从独立的计算中产生靶态。在资助期内，将进行以下扩展：1)将代码并行化，以允许处理更具挑战性的问题；2)包括足够数量的伪态来模拟与电离连续统的耦合，从而允许在中等能量下产生准确的结果；3)使用上面的扩展2)生成电离过程的结果；4)用相对论Hartree-Fock方法生成目标轨道；5)处理带电粒子碰撞和多光子单电离和双原子电离；6)处理电子与双原子分子的碰撞。

Further development of a general and effective program for electron collisions with atoms andions using a B-spline approach with non-orthogonal orbitals will be undertaken. The approach is based upon an extended version of the R-matrix method, in which non-orthogonalorbitals are extensively used for describing both the target states and the scattering functions.The new approach is essentially free of the three major problems that often arise when the most frequently used suite of R-matrix codes, mostly developed over the past three decades in Belfast and currently used world-wide, is applied to truly complex targets such as heavy noble gases or open-shell transition elements. These problems include i) the difficulties in describing all target states of interest for a given calculation to sufficient accuracy, ii) the likely occurrence of unphysical structures, so-called pseudo-resonances, when an attempt is made to address the former problem, and iii) numerical difficulties due to an ill-conditioned orthogonalization procedure and the need to modify the so called Buttle correction.The excellent numerical properties of a B-spline basis used for the description of the continuumstates in the inner region allow for high computational accuracy, while the completeness of the basis will ensure that no Buttle correction to the R-matrix elements is required. With the non-orthogonal orbital technique the target states can be generated from independent calculations, with compact configuration expansions. During the funding period, the following extensions will be undertaken:1) parallelize the code to allow for the treatment of even more challenging problems;2) include a sufficient number of pseudo-states to simulate coupling to the ionization continuum,thereby allowing for accurate results to be generated at intermediate energies;3) use extention 2) above to generate results for ionization processes;4) generate the target orbitals by the relativistic Hartree-Fock method;5) treat charged-particle impact and multi-photon single- and double-ionization;6) treat electron collisions with diatomic molecules.