Zeeman Interaction
塞曼相互作用
An external magnetic field will exert a torque on a magnetic dipole and the magnetic potential energy which results in
一个外磁场会对磁偶极子施加力矩，并产生相应的磁势能。
The magnetic dipole moment associated with the orbital angular momentum is given by
与轨道角动量相关的磁偶极矩由
For a magnetic field in the z-direction this gives
对于沿z方向的磁场，这给出
Considering the quantization of angular momentum, this gives
equally spaced energy levels displaced from the zero field level by
考虑角动量的量子化，这给出了等间距的能级，这些能级相对于零场电平被位移。
This displacement of the energy levels gives the uniformly spaced multiplet splitting of the spectral lines which is called the Zeeman effect.
这种能量级的位移导致谱线出现均匀间隔的多重线分裂，这种现象称为塞曼效应。
The magnetic field also interacts with the electron spin magnetic moment, so it contributes to the Zeeman effect in many cases. The electron spin had not been discovered at the time of Zeeman's original experiments, so the cases where it contributed were considered to be anomalous. The term "anomalous Zeeman effect" has persisted for the cases where spin contributes. In general, both orbital and spin moments are involved, and the Zeeman interaction takes the form
磁场也与电子自旋磁矩相互作用，因此在许多情况下会贡献给塞曼效应。在塞曼最初的实验时期，电子自旋尚未被发现，因此其贡献的案例被视作异常。术语‘异常塞曼效应’一直用于描述自旋贡献的案例。通常情况下，轨道和自旋磁矩都涉及其中，塞曼相互作用的形式为
The factor of two multiplying the electron spin angular momentum comes from the fact that it is twice as effective in producing magnetic moment. This factor is called the spin g-factor or gyromagnetic ratio. The evaluation of the scalar product between the angular momenta and the magnetic field here is complicated by the fact that the S and L vectors are both precessing around the magnetic field and are not in general in the same direction. The persistent early spectroscopists worked out a way to calculate the effect of the directions. The resulting geometric factor gL in the final expression above is called the Lande g factor. It allowed them to express the resultant splittings of the spectral lines in terms of the z-component of the total angular momentum, mj.
乘以电子自旋角动量的二倍因子来源于它在产生磁矩方面是两倍有效的。这个因子称为自旋g因子或旋磁比。在这里，角动量与磁场之间的标量积的计算变得复杂，因为S和L向量都在磁场周围进动，并且通常不在同一方向上。早期的光谱学家们找到了一种计算方向影响的方法。最终表达式中的几何因子g_L称为兰德自旋g因子。它使他们能够将谱线的分裂用总角动量的z分量m_j来表示。
The above treatment of the Zeeman effect describes the phenomenon when the magnetic fields are small enough that the orbital and spin angular momenta can be considered to be coupled. For extremely strong magnetic fields this coupling is broken and another approach must be taken. The strong field effect is called the Paschen-Back effect.
上述关于塞曼效应的处理描述了当磁场足够弱时，轨道角动量和自旋角动量可以被视为耦合的现象。对于极强的磁场，这种耦合会被打破，必须采用另一种方法。这种强磁场效应被称为帕森-巴克效应。
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