Nuclear Magnetic Resonance

When the nuclear magnetic moment associated with a nuclear spin is placed in an external magnetic field, the different spin states are given different magnetic potential energies. In the presence of the static magnetic field which produces a small amount of spin polarization, a radio frequency signal of the proper frequency can induce a transition between spin states. This "spin flip" places some of the spins in their higher energy state. If the radio frequency signal is then switched off, the relaxation of the spins back to the lower state produces a measurable amount of RF signal at the resonant frequency associated with the spin flip. This process is called Nuclear Magnetic Resonance (NMR).

当与核自旋相关的核磁矩置于外部磁场中时，不同的自旋态将具有不同的磁势能。在存在产生少量自旋极化的静态磁场的情况下，适当频率的射频信号可以引起自旋态之间的跃迁。这种“自旋翻转”会使一些自旋处于较高能级。如果随后关闭射频信号，自旋弛豫回较低能级将产生与自旋翻转相关的共振频率的可测量射频信号。这个过程称为核磁共振（NMR）。

A magnetic dipole moment (usually just called "magnetic moment") in a magnetic field will have a potential energy related to its orientation with respect to that field.

在磁场中的磁偶极矩（通常简称为‘磁矩’）会因其方向与该磁场的相对取向而具有势能。

Note that the electron spin magnetic moment is opposite to the electron spin while the proton spin magnetic moment is in the direction of the proton spin. The electron spin or proton spin will tend to precess around the magnetic field with a frequency traditionally called the Larmor frequency. For a 1 Tesla magnetic field this Larmor frequency would be

需要注意的是，电子的自旋磁矩方向与电子自旋方向相反，而质子的自旋磁矩方向则与质子自旋方向一致。电子自旋或质子自旋会倾向于围绕磁场进行进动，这种进动频率传统上称为拉莫尔频率。在1特斯拉的磁场中，这种拉莫尔频率将是

The Larmor frequency can be visualized classically in terms of the precession of the magnetic moment around the magnetic field, analogous to the precession of a spinning top around the gravity field. It can also be visualized quantum mechanically in terms of the quantum energy of transition between the two possible spin states for spin 1/2. This can be expressed as a photon energy according to the Planck relationship. The magnetic potential energy difference is hυ = 2μB. The short table of Larmor frequencies below is from Hobbie, Ch 17 and Becker. An extensive list including the magnetic moments and Larmor frequencies of most elements can be found in Appendix A of Becker.

拉莫尔频率可以经典地通过磁矩围绕磁场的进动来可视化，类似于陀螺围绕重力场的进动。它也可以通过量子力学中自旋1/2的两个可能自旋态之间的量子能量跃迁来可视化。这可以表示为光子能量，根据普朗克关系。磁势能差为hυ = 2μB。下面的简表来自Hobbie，第17章和Becker。附录A of Becker中包含了一个详尽的列表，包括大多数元素的磁矩和拉莫尔频率。

电子自旋的拉莫尔频率位于电磁波的微波区域，并用于电子自旋共振。

The precession of the proton spin in the magnetic field is the interaction which is used in proton NMR. As a practical technique, a sample containing protons (hydrogen nuclei) is placed in a strong magnetic field to produce partial polarization of the protons. A strong RF field is also imposed on the sample to excite some of the nuclear spins into their higher energy state. When this strong RF signal is switched off, the spins tend to return to their lower state, producing a small amount of radiation at the Larmor frequency associated with that field. The emission of radiation is associated with the "spin relaxation" of the protons from their excited state. It induces a radio frequency signal in a detector coil which is amplified to display the NMR signal.

质子在磁场中的自旋进动是用于质子核磁共振的相互作用。作为一种实际技术，含有质子（氢核）的样品被置于强磁场中，以产生质子的部分极化。同时，样品上也施加了一个强的射频场，以激发一些核自旋跃迁到较高能级。当这个强射频信号关闭后，自旋倾向于返回较低能级，产生与该磁场相关的洛伦兹频率的少量辐射。辐射的发射与质子从激发态弛豫有关。这种弛豫在探测器线圈中诱导出无线电频率信号，该信号被放大以显示核磁共振信号。

Since the Larmor frequency of the detected signal is proportional to the applied magnetic field, changing the magnitude of that field produces a different detected frequency. Placing a magnetic field gradient across a sample allows you to locate the source of the proton NMR signal in the sample. This is used to great advantage in the medical imaging process known as Magnetic Resonance Imaging.

由于检测信号的拉莫尔频率与所施加的磁场成正比，改变该磁场的强度会得到不同的检测频率。在样品上施加一个磁场梯度可以用来确定样品中质子NMR信号的来源。这在称为磁共振成像的医学成像过程中得到了广泛应用。