SBETHE: Stopping powers of materials for swift charged particles from the corrected Bethe formula

The Fortran program sbethe calculates the stopping power of materials for swift charged particles with small charges (electrons, muons, protons, their antiparticles, and alphas). The electronic stopping power is computed from the corrected Bethe formula, with the shell correction derived from numerical calculations with the plane-wave Born approximation (PWBA) for atoms, which were based on an independent-electron model with the Dirac–Hartree–Fock–Slater self-consistent potential for the ground-state configuration of the target atom. The density effect correction is evaluated from an empirical optical oscillator strength (OOS) model based on atomic subshell contributions obtained from PWBA calculations. For projectiles heavier than the electron, the Barkas correction is evaluated from the OOS model, and the Lindhard–Sørensen correction is estimated from an accurate parameterization of its numerical values. The calculated electronic stopping power is completely determined by a single empirical parameter, the mean excitation energy or I value of the material. The radiative stopping power for electrons, and positrons, is evaluated by means of Seltzer and Berger's cross section tables for bremsstrahlung emission. The program yields reliable stopping powers and particle ranges for arbitrary materials and projectiles with kinetic energy larger than a certain cutoff value E_cut, which is specific of each projectile kind. The program is accompanied by an extensive database that contains tables of relevant energy-dependent atomic quantities for all the elements from hydrogen to einsteinium. sbethe may be used to generate basic information for dosimetry calculations and Monte Carlo simulations of radiation transport, and as a pedagogical tool.

Fortran程序sbethe可计算高速小电荷带电粒子（电子、μ子、质子及其反粒子与α粒子）在材料中的阻止本领。电子阻止本领基于修正的贝特公式（Bethe formula）计算，其壳层修正源自针对原子的平面波玻恩近似（plane-wave Born approximation, PWBA）数值计算，该计算以独立电子模型为基础，并采用靶原子基态组态下的狄拉克-哈特里-福克-斯莱特（Dirac–Hartree–Fock–Slater）自洽势。密度效应修正通过经验光学振子强度（optical oscillator strength, OOS）模型进行评估，该模型依托由PWBA计算得到的原子亚壳层贡献。对于质量大于电子的入射粒子，巴克拉斯修正（Barkas correction）通过OOS模型计算，而林德哈德-瑟伦森修正（Lindhard–Sørensen correction）则通过其数值的精确参数化方法进行估算。所计算得到的电子阻止本领完全由单一经验参数决定，即材料的平均激发能（或称I值）。针对电子与正电子的辐射阻止本领，通过塞尔策（Seltzer）与伯杰（Berger）的轫致辐射发射截面表进行评估。该程序可针对任意材料以及动能高于特定截止值E_cut的入射粒子输出可靠的阻止本领与粒子射程，其中E_cut的取值因入射粒子种类而异。程序附带一套大型数据库，其中收录了从氢到锿所有元素的、与能量相关的关键原子物理量表格。sbethe可用于生成辐射输运的剂量学计算与蒙特卡洛模拟所需的基础信息，亦可作为教学工具使用。