Electron Scattering from Nuclei

The scattering of electrons from nuclei has given us the most precise information about nuclear size and charge distribution. The electron is a better nuclear probe than the alpha particles of Rutherford scattering because it is a point particle and can penetrate the nucleus.

电子散射提供了关于核尺寸和电荷分布最精确的信息。相比于卢瑟福散射中的α粒子，电子作为点粒子能够穿透核，因此是更优良的核探测工具。

For low energies and under conditions where the electron does not penetrate the nucleus, the electron scattering can be described by the Rutherford formula. The Rutherford formula is an analytic expression for the differential scattering cross section, and for a projectile charge of 1, it is

在低能条件下，且电子不穿透核的情况下的电子散射可由卢瑟福公式描述。卢瑟福公式是散射截面的解析表达式，对于入射电荷为1的情况，其形式为

As the energy of the electrons is raised enough to make them an effective nuclear probe, a number of other effects become significant, and the scattering behavior diverges from the Rutherford formula. The probing electrons are relativistic, they produce significant nuclear recoil, and they interact via their magnetic moment as well as by their charge. When the magnetic moment and recoil are taken into account, the expression is called the Mott cross section:

当电子的能级足够高，使其成为有效的核探针时，一些其他效应变得显著，散射行为偏离了Rutherford公式。探测电子是相对论性的，它们会产生显著的核反冲，并且它们还通过其磁矩以及电荷进行相互作用。当考虑磁矩和反冲时，这个表达式被称为Mott散射截面：

A major period of investigation of nuclear size and structure occurred in the 1950's with the work of Robert Hofstadter and others who compared their high energy electron scattering results with the Mott cross section. The illustration below from Hofstadter's work shows the divergence from the Mott cross section which indicates that the electrons are penetrating the nucleus - departure from point-particle scattering is evidence of the structure of the nucleus.

20世纪50年代，核尺寸和结构的研究进入了一个重要阶段，霍夫斯塔特等人的工作起到了关键作用。他们将高能电子散射的结果与Mott散射截面进行比较。下面来自霍夫斯塔特工作的图示显示了与Mott散射截面的偏离，这表明电子穿透了核——偏离点粒子散射的证据表明了核的结构。

This productive period of research with electron scattering built the picture of the nucleus as a spherical distribution of positive charge of essentially constant density, so that the nuclear radius could be modeled by the relationship:

这一时期利用电子散射进行的研究构建了核的图像，即核内的正电荷呈近似恒定密度的球形分布，因此核半径可以由以下关系式来描述：