MASAP: A package for atomic scattering amplitude in solids

We present the MsSpec Atomic Scattering Amplitude Package (MASAP), composed of a computation program and a graphical interface to generate atomic scattering amplitude (ASA) of an atom, either isolated or embedded in an environment, at any chosen energy of the impinging electron up to ≈15 KeV. The ASA is calculated using an effective, complex optical potential which provides damping effects in the scattering process in a fully relativistic framework. Optionally, scalar relativistic and non-relativistic approximations are also available to assess their applicability to a given problem. In order to describe electron propagation in solids we suggest to replace ASA's based on Plane Waves (PW) scattering with effective ASA's based on curved Spherical Waves (SW) using truncated-overlapped potentials of the Muffin-Tin (MT) type constructed according to the Mattheiss prescription. The graphical user interface generates not only ASA data files providing atomic Differential Cross Sections (DCS) but also files of related quantities such as total Cross Section (CS), both elastic and inelastic, atomic t_l-matrices and phase shifts. We found in general that the imaginary part of the optical potential enhances the calculated elastic DCSs in the forward direction compared to the same potential without the imaginary part, a feature related to the optical theorem, but gives rise to a lower intensity at all other directions as expected due to the damping effect of the complex part of the potential. We show calculated differential and transport Cross Sections for aluminum and gold atoms both in isolation and in crystals with the Face-Centered-Cubic (FCC) structure.

我们提出了MsSpec原子散射振幅程序包（MsSpec Atomic Scattering Amplitude Package，MASAP），该程序包包含计算程序与图形界面，可针对孤立原子或处于环境中的原子，在入射电子能量最高可达约15 keV的任意选定能量下生成原子散射振幅（Atomic Scattering Amplitude，ASA）。原子散射振幅采用有效复光学势进行计算，该势可在全相对论框架下描述散射过程中的阻尼效应。此外，还支持标量相对论近似与非相对论近似两种可选模式，用于评估其在特定问题中的适用性。为描述电子在固体中的传播，我们建议将基于平面波（Plane Waves，PW）散射的原子散射振幅，替换为基于弯曲球面波（Spherical Waves，SW）的有效原子散射振幅；后者采用依据Mattheiss规则构建的Muffin-Tin（MT）型截断重叠势。该图形用户界面不仅可生成包含原子微分截面（Differential Cross Sections，DCS）的ASA数据文件，还可生成各类相关物理量的文件，包括弹性与非弹性总截面（Cross Section，CS）、原子t_l矩阵以及相移等。我们的研究结果总体表明，与不含虚部的等效光学势相比，光学势的虚部会提升正向方向的计算弹性微分截面，这一特性与光学定理相符；但如预期般，由于复势的阻尼效应，其余所有方向的散射强度均会出现降低。我们展示了孤立态以及面心立方（Face-Centered-Cubic，FCC）结构晶体中铝原子与金原子的微分截面与输运截面的计算结果。