--- title: "怎样知道原子核遇到了共振" description: "束流减少、无线电波被吸收、线圈出现电压，为什么都能告诉我们原子核有多强的磁性？" canonical_url: "https://sandboxphysics.com/zh/stories/quantum-evidence/magnetic-resonance-beams-absorption-induction/" language: "zh-CN" page_type: "story" alternate_languages: en: "https://sandboxphysics.com/stories/quantum-evidence/magnetic-resonance-beams-absorption-induction/" last_modified: "2026-10-24" --- [量子物理：读懂证据](https://sandboxphysics.com/zh/stories/quantum-evidence/) 诺奖 A · 证据与操控 # 怎样知道原子核遇到了共振 Sandbox Physics · 2026-10-15 束流减少、无线电波被吸收、线圈出现电压，为什么都能告诉我们原子核有多强的磁性？ ## 先让分子重新回到探测器 1938 年，Rabi、Zacharias、Millman 和 Kusch 让分子束穿过两段偏转磁场。装置调好以后，选中的分子会重新聚焦到探测器上。他们在中间的均匀磁场区，又叠加一个弱振荡磁场。频率碰对时，部分分子改变内部磁态，经过后半段磁铁便走了另一条路，抵达探测器的分子随之减少。 那篇通信以氯化锂为例，固定射频、扫描静磁场，画出束流强度随磁铁电流的变化。共振在图上表现为凹下去的信号。作者还说明，最终磁矩数值要等磁场重新标定；找到共振和测准磁性之间，隔着这一步。 证据阅读：I. I. Rabi, J. R. Zacharias, S. Millman and P. Kusch (1938), A New Method of Measuring Nuclear Magnetic Moment, Phys. Rev. 53, 318 — original scan ## 原子核也有自己的节拍 有磁矩的原子核在静磁场里，会发生一种称为进动的运动。可以先借陀螺来想象：倾斜的陀螺轴绕竖直方向缓缓转圈。原子核的进动有自己的频率，外加的振荡磁场与它节拍合适，就容易诱发内部状态变化。 最简单的关系是，进动频率随静磁场成正比。式里的 B 是静磁场，旋磁比表示这种原子核对磁场有多敏感；普通频率数每秒多少圈，角频率数每秒多少弧度。原子核所处的化学环境和邻近磁性会修正这个简单关系，测量时需要一并考虑。 $$ \omega_{\mathrm L}=|\gamma|B_0=2\pi\nu_{\mathrm L} $$ 证据阅读：I. I. Rabi, J. R. Zacharias, S. Millman and P. Kusch (1938), A New Method of Measuring Nuclear Magnetic Moment, Phys. Rev. 53, 318 — original scan E. M. Purcell, H. C. Torrey and R. V. Pound (1946), Resonance Absorption by Nuclear Magnetic Moments in a Solid, Phys. Rev. 69, 37–38 F. Bloch, W. W. Hansen and M. Packard (1946), Nuclear Induction, Phys. Rev. 69, 127 ## 把分子束换成一块石蜡 到 1946 年，Purcell、Torrey 和 Pound 换了样品和读法。他们把含有大量质子的石蜡放进射频谐振器，用电路观察样品吸收了多少无线电波。扫描静磁场到共振附近，平衡电路的输出出现明显变化。原子核被看见的方式，从分子少了多少，变成了电路多损失多少能量。 室温下，两种自旋状态中的质子数目只差一点点。低能态稍多，向上吸收的机会便略多于向下受激发射，合起来才有净吸收。射频太强会把人数差抹平，信号趋于饱和；周围环境又会让分布恢复，这个恢复过程叫弛豫。吸收信号正是驱动和恢复共同作用的结果。 证据阅读：E. M. Purcell, H. C. Torrey and R. V. Pound (1946), Resonance Absorption by Nuclear Magnetic Moments in a Solid, Phys. Rev. 69, 37–38 ## 水里的质子也能在线圈里留下电压 同在 1946 年，Bloch、Hansen 和 Packard 用室温的水研究核磁共振。横向振荡场驱动样品，许多原子核的磁性合起来形成宏观磁化；它的变化在线圈里感应出电压。团队比较了两个驱动频率对应的共振磁场，还与已有的质子磁性数据对照。 这次早期实验持续施加驱动场。后来常见的做法，是先打一段射频脉冲，再听样品自己发出逐渐衰减的感应信号，称为自由感应衰减。后者发展了新的测量方式，读这段历史时要保留两种操作之间的年代差别。 证据阅读：F. Bloch, W. W. Hansen and M. Packard (1946), Nuclear Induction, Phys. Rev. 69, 127 ## 同一个共振，可以有不同的出口 三项实验都把磁场和共振频率联系起来。探测器各有不同，分别报告束流数目、射频吸收和线圈电压。Rabi 于 1944 年获奖，Bloch 和 Purcell 于 1952 年获奖。这些方法把原子核极小的磁性，变成了可以反复扫描的信号。 要把信号换成磁矩，还得知道样品真正经历的磁场，考虑线宽、局部环境和驱动强度。今天医院里的磁共振成像继续利用核磁信号，再用空间梯度和重建方法辨认信号来自身体哪里。早期这三项实验完成的是共振测量，空间编码是后续发展的另一步。 证据阅读：I. I. Rabi, J. R. Zacharias, S. Millman and P. Kusch (1938), A New Method of Measuring Nuclear Magnetic Moment, Phys. Rev. 53, 318 — original scan E. M. Purcell, H. C. Torrey and R. V. Pound (1946), Resonance Absorption by Nuclear Magnetic Moments in a Solid, Phys. Rev. 69, 37–38 F. Bloch, W. W. Hansen and M. Packard (1946), Nuclear Induction, Phys. Rev. 69, 127 Nobel Prize in Physics 1944 — official award record Nobel Prize in Physics 1952 — official award record ## 接着操作模型 下面这些教学 Lab 产生的是模拟数据，和上文讨论的历史观测不是一回事。 - [扫描磁场，测量共振吸收](https://sandboxphysics.com/zh/labs/cw-nmr-spectrometer/) - [记录脉冲后的感应信号，再把它变成频谱](https://sandboxphysics.com/zh/labs/nmr-free-induction-spectrometer/) ## 来源与阅读说明 Rabi、Zacharias、Millman、Kusch 1938 年的通信和两篇 1946 年的 APS 报告，都有完整扫描件可读。三项工作的样品和探测方式各不相同，本文分开叙述。下面的 Larmor 关系只是孤立自旋的参考，不是拟合出的化学位移，也不是成像模型。 1. [I. I. Rabi, J. R. Zacharias, S. Millman and P. Kusch (1938), A New Method of Measuring Nuclear Magnetic Moment, Phys. Rev. 53, 318 — original scan](https://physics.umd.edu/grt/taj/623e/Rabi_etal_1938_letter.pdf) 2. [E. M. Purcell, H. C. Torrey and R. V. Pound (1946), Resonance Absorption by Nuclear Magnetic Moments in a Solid, Phys. Rev. 69, 37–38](https://journals.aps.org/pr/pdf/10.1103/PhysRev.69.37) 3. [F. Bloch, W. W. Hansen and M. Packard (1946), Nuclear Induction, Phys. Rev. 69, 127](https://journals.aps.org/pr/pdf/10.1103/PhysRev.69.127) 4. [Nobel Prize in Physics 1944 — official award record](https://www.nobelprize.org/prizes/physics/1944/summary/) 5. 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