Forces in the Nucleus | 原子核内的力

📚 Forces in the Nucleus | 原子核内的力

The atomic nucleus is held together by a delicate competition between repulsive electrostatic forces and the attractive strong nuclear force. Understanding this competition explains nuclear stability, binding energy, and decay processes.

原子核依靠强核力与静电斥力之间的微妙平衡结合在一起。理解这种竞争关系可以解释核稳定性、结合能以及各种衰变过程。

1. Inside the Nucleus: Protons and Neutrons | 核内粒子：质子与中子

The nucleus consists of nucleons: positively charged protons and electrically neutral neutrons. Protons carry charge +e ≈ 1.60 × 10⁻¹⁹ C, while neutrons have no net charge.

原子核由核子组成：带正电的质子和电中性的中子。质子带电荷 +e ≈ 1.60 × 10⁻¹⁹ C，而中子净电荷为零。

A nucleus with Z protons and N neutrons has mass number A = Z + N. Nuclear radii are of order 10⁻¹⁵ m = 1 femtometre (fm), so quantum effects and short-range forces dominate.

含有 Z 个质子和 N 个中子的原子核，其质量数为 A = Z + N。原子核半径约为 10⁻¹⁵ m = 1 飞米（fm），因此量子效应和短程力起主导作用。

2. Coulomb Repulsion Between Protons | 质子间的库仑斥力

Protons repel one another by Coulomb’s law. At a typical separation of 1 fm, the repulsive force between two protons is approximately 230 N, which is enormous for nuclear particles.

质子之间通过库仑定律相互排斥。在典型的 1 fm 距离上，两个质子之间的斥力约为 230 N，这对核粒子而言非常巨大。

F = k q₁q₂ / r²

Because this electrostatic force acts over long range, it tries to blow the nucleus apart. Some additional attractive force must overcome it.

由于这种静电力作用范围很长，它会试图将原子核炸开。必须有某种额外的吸引力来克服它。

3. The Strong Nuclear Force | 强核力

The strong nuclear force is the attractive interaction between nucleons that binds the nucleus together. It is much stronger than the electrostatic force at nucleon separations around 1–2 fm.

强核力是核子之间的吸引相互作用，它将原子核束缚在一起。在核子间距约 1–2 fm 时，它比静电力强得多。

Unlike gravity or electromagnetism, the strong force is a short-range force: it is negligible beyond about 3 fm and saturates with nearest neighbours.

与引力或电磁力不同，强核力是一种短程力：在约 3 fm 以外可忽略，并且具有饱和性，主要作用于最近邻核子。

4. Range and Sign of the Strong Force | 强核力的作用范围与方向

The strong force has three distance regimes. At separations greater than about 3 fm, it is effectively zero. Around 1–2 fm it is strongly attractive. Below about 0.5 fm it becomes strongly repulsive.

强核力有三个距离区间。在大于约 3 fm 时，它实际上为零；在 1–2 fm 附近表现为强吸引；在小于约 0.5 fm 时表现为强排斥。

This short-range repulsion stops nucleons from collapsing into each other, giving the nucleus a nearly constant density of about 2.3 × 10¹⁷ kg m⁻³.

这种短程排斥阻止核子坍缩到一起，使原子核具有近似恒定的密度，约为 2.3 × 10¹⁷ kg m⁻³。

5. Charge Independence of the Strong Force | 强核力与电荷无关

Experiments show that the strong nuclear force is almost the same between proton–proton, neutron–neutron and proton–neutron pairs, after removing electrostatic effects.

实验表明，在扣除静电效应后，质子–质子、中子–中子以及质子–中子之间的强核力几乎相同。

This charge independence means the strong force depends on the nucleon configuration, not on electric charge. It is one reason why mirror nuclei have similar energy levels.

这种电荷无关性意味着强核力取决于核子的排布，而不是电荷。这正是镜像核具有相似能级的原因之一。

6. Why Neutrons Matter for Stability | 中子为何对稳定性至关重要

Adding protons increases both the attractive strong force and the repulsive Coulomb force. Adding neutrons increases the strong force without adding electrostatic repulsion.

增加质子会同时增大吸引性的强核力和排斥性的库仑力。增加中子则只增大强核力，而不增加静电斥力。

Heavy nuclei therefore need a neutron excess to remain stable. For example, lead-208 has Z = 82 protons and N = 126 neutrons, so N > Z.

因此，重核需要中子过剩才能保持稳定。例如，铅-208 有 Z = 82 个质子和 N = 126 个中子，即 N > Z。

7. Nuclear Stability and the N/Z Curve | 核稳定性与 N/Z 曲线

Stable nuclei follow a band on a plot of neutron number N against proton number Z. Light stable nuclei lie close to N = Z, but heavier stable nuclei require N > Z.

在以中子数 N 对质子数 Z 作图的坐标系中，稳定核素分布在一个带状区域。轻的稳定核素接近 N = Z，但较重的稳定核素需要 N > Z。

Nuclei that lie too far above the band have excess neutrons and tend to undergo beta-minus decay; nuclei too far below the band tend to undergo beta-plus decay or electron capture.

位于稳定带上方过远的核素中子过多，倾向于发生 β⁻ 衰变；位于稳定带下方过远的核素则倾向于发生 β⁺ 衰变或电子俘获。

8. Binding Energy and Mass Defect | 结合能与质量亏损

The mass of a nucleus is always less than the total mass of its separate nucleons. This difference is called the mass defect Δm.

原子核的质量总是小于其全部分散核子的总质量。这一差值称为质量亏损 Δm。

E = Δm c²

The binding energy is the energy required to separate a nucleus into its individual nucleons. A larger binding energy per nucleon means a more stable nucleus.

结合能是将原子核拆分为单个核子所需的能量。每个核子的结合能越大，原子核就越稳定。

9. The Binding Energy Curve | 结合能曲线

The average binding energy per nucleon rises sharply for light nuclei, reaches a maximum of about 8.8 MeV near iron-56, and then decreases slowly for heavy nuclei.

平均每个核子的结合能在轻核区迅速上升，在铁-56 附近达到约 8.8 MeV 的最大值，然后对重核缓慢下降。

Energy can be released by fusion of light nuclei or by fission of very heavy nuclei, because both processes move products towards the maximum of the binding energy curve.

轻核聚变或极重核裂变都能释放能量，因为这两种过程都使生成物向结合能曲线的最大值方向移动。

10. Alpha Decay and the Coulomb Barrier | α 衰变与库仑势垒

In a heavy nucleus, the Coulomb repulsion between the alpha particle and the daughter nucleus is large. Classical physics would forbid the alpha particle from escaping, but quantum tunnelling allows it to leak through the Coulomb barrier.

在重核中，α 粒子与子核之间的库仑斥力很大。经典物理会认为 α 粒子无法逃逸，但量子隧穿效应允许它穿过库仑势垒泄漏出去。

This is why alpha decay occurs with a wide range of half-lives: a small change in barrier height or particle energy can greatly change the tunnelling probability.

这就是 α 衰变半衰期差异巨大的原因：势垒高度或粒子能量的微小变化都会极大地改变隧穿概率。

11. Beta Decay and the Weak Nuclear Force | β 衰变与弱核力

Beta decay is not caused by the strong force but by the weak nuclear force. In beta-minus decay a neutron changes into a proton, emitting an electron and an antineutrino.

β 衰变不是由强

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Forces in the Nucleus | 原子核内的力