物理学 1935

论基本粒子的相互作用

汤川秀树

核力之所以短程，是因为它的传递者有质量——一种新粒子，介子。

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In depth · the introduction

把原子核拢在一起的那种力，强到足以压住质子之间的相互排斥——可只要离开一根头发丝那么远，它就消失得无影无踪。汤川用一个大胆的猜想同时解释了这两件事：这种力，是由一种全新的粒子来传递的，而那粒子，很重。

核心想法

到 1935 年，物理学家已经知道原子核里挤满了质子和中子，却卡在一个悖论上。把它们黏在一起的力必定极其巨大——远比那本该把原子核炸开的电斥力还强。可这种力，伸不出原子核本身半步；离开一丁点，它就干脆没有了。究竟什么样的力，近在咫尺时威猛无比、稍远一步就荡然无存？

汤川的回答，借用了电磁学里的一幅图景。在那里，两个电荷之所以能「感觉」到彼此，是因为它们在交换光子——光的粒子。他说，也许，两个核子之所以能感觉到核力，也是因为它们在交换一种属于它们自己的新粒子。妙处就在这里：光子没有质量，这正是电力与磁力能横跨整个宇宙的原因。倘若这种新粒子有质量，那么它所传递的力，就会在极短的距离之外迅速消亡。仅凭已知的原子核大小，汤川甚至能预言出这粒子的质量——约为电子的 200 倍。他只是从「一种力能伸多远」出发，就凭空唤出了一个从未有人见过的粒子。

它是如何诞生的

汤川秀树，是大阪一位年轻的理论物理学家，身处一个那时才刚刚开始被国际听见的日本物理学界。欧洲的巨匠们——海森堡、费米——曾试图让粒子交换电子和中微子来解释核的束缚，可算出来的数字实在太弱了。汤川为这道难题度过了许多不眠之夜，而他那惊人的一跃，是不再翻用已知的粒子、而是发明出那个正确的粒子。

他于 1935 年用英文、在一份日本刊物上发表了此文，此后好几年几乎无人留意。到 1936 年，宇宙射线中冒出了一种质量大致相符的粒子，人们一阵兴奋——可当那粒子被发现几乎不碰原子核、因而不可能是那团黏合剂时，兴奋又变了味。真正的那个粒子——π 介子——直到 1947 年才被捕获。两年后，汤川获得了诺贝尔奖，那是史上第一次有日本科学家获此殊荣。

它为何重要

汤川改变了「力」这个词本身的含义。在他之后，自然界中每一种基本力，都被理解为粒子的交换——而一条简单的规则，把传递者的轻重与力的伸展联系了起来：传递者越重，力程越短。正是这一个洞见，整理了整部现代的「力」之目录，从那让光横跨星系的无质量光子，到那躲在放射性背后的有质量粒子。他还证明了：一位审慎的理论家，仅凭一个悖论和一个波动方程，就能在任何仪器找到它之前，预言出宇宙的一块新拼图。

一个可以想象的画面

想象湖上有两条船，彼此把一个沉甸甸的药球抛来抛去。每一次投掷，都把投的人往后一推、把接的人往前一送——这一来一回的交换，本身就像两条船之间的一种力。再注意一点：因为球很重，你只能把它抛出很短一段，它就「扑通」落了水。两条船必须靠得很近，这游戏才玩得起来。换成一个轻飘飘的沙滩球，你就能把它一抛抛过整个湖面——那便是一种长程的力。汤川的核力，是那场重球游戏；电磁力，则是那个沙滩球。所抛之物的轻重，定下了力能伸多远。

它的位置

汤川站在一场漫长接力赛的中途。麦克斯韦把电磁作用铸成了一个场；量子论又把那个场的量子定为光子；汤川则把这一步推广到一种需要有质量量子的力上，由此开启了「粒子交换」的时代。从他的想法，有一条直线通向弱力的 W 与 Z 粒子、通向夸克与胶子，也通向希格斯玻色子——而正是它的「汤川耦合」（这个以他命名的词，从此固定下来），让其他粒子获得了质量。他当年追寻的那团核黏合剂，如今被看作更深层力的残余；但他所开创的那种思考方式，至今仍是整个粒子物理共用的语言。

The original document

Original source text

导言——核力的难题

H. Yukawa · On the Interaction of Elementary Particles · Proc. Phys.-Math. Soc. Japan, 3rd ser., 17 (1935) 48–57 · Received 1935

At the present stage of the quantum theory little is known about the nature of interaction of elementary particles. Heisenberg considered the interaction of “Platzwechsel” between the neutron and the proton to be of importance to the nuclear structure.

Recently Fermi treated the problem of β-disintegration on the hypothesis of “neutrino”. According to this theory, the neutron and the proton can interact by emitting and absorbing a pair of neutrino and electron. Unfortunately the interaction energy calculated on such assumption is much too small to account for the binding energies of neutrons and protons in the nucleus.

To remove this defect, it seems natural to modify the theory of Heisenberg and Fermi in the following way. The transition of a heavy particle from neutron state to proton state is not always accompanied by the emission of light particles, i.e., a neutrino and an electron, but the energy liberated by the transition is taken up sometimes by another heavy particle, which in turn will be transformed from proton state into neutron state.

Now such interaction between the elementary particles can be described by means of a field of force, just as the interaction between the charged particles is described by the electromagnetic field. … In the quantum theory this field should be accompanied by a new sort of quantum, just as the electromagnetic field is accompanied by the photon.

描述相互作用的场

Field Describing the Interaction

In analogy with the scalar potential of the electromagnetic field, a function U(x, y, z, t) is introduced to describe the field between the neutron and the proton. This function will satisfy an equation similar to the wave equation for the electromagnetic potential.

The potential of force between the neutron and proton should, however, not be of Coulomb type, but decrease more rapidly with distance. It can [be] expressed, for example by ±g² · e^(−λr)/r, where g is a constant with the dimension of electric charge … and λ with the dimension cm.⁻¹

Since this function is a static [solution] with central symmetry of the wave equation (∆ − (1/c²)∂²/∂t² − λ²) U = 0, let this equation be assumed to be the correct equation for U in vacuum. In the presence of the heavy particles, the U–field interacts with them and causes the transition from neutron state to proton state.

Rough estimation shows that the calculated values agree with the experimental results, if we take for λ the value between 10¹² cm⁻¹ and 10¹³ cm⁻¹ and for g a few times of the elementary charge e, although no direct relation between g and e was suggested in the above considerations.

携带这个场的量子

Nature of the Quanta Accompanying the Field

The U–field above considered should be quantized according to the general method of the quantum theory. Since the neutron and the proton both obey Fermi's statistics, the quanta accompanying the U–field should obey Bose's statistics. … The law of conservation of the electric charge demands that the quantum should have charge either +e or −e.

[Writing the free-space wave equation in the form (px² + py² + pz² − W²/c² + mU²c²) U = 0,] the quantum accompanying the field has the proper mass mU = λh/c.

Assuming λ = 5 × 10¹² cm⁻¹., we obtain for mU a value 2 × 10² times as large as the electron mass. As such a quantum with large mass and positive or negative charge has never been found by the experiment, the above theory seems to be on a wrong line. We can show, however, that, in the ordinary nuclear transformation, such a quantum can not be emitted into outer space.

总结，与一个关于宇宙射线的猜测

Summary

The interactions of elementary particles are described by considering a hypothetical quantum which has the elementary charge and the proper mass and which obeys Bose's statistics. The interaction of such a quantum with the heavy particle should be far greater than that with the light particle in order to account for the large interaction of the neutron and the proton as well as the small probability of β-disintegration.

The massive quanta may also have some bearing on the shower produced by cosmic rays.

[ … ]

Department of Physics, Osaka Imperial University · 1935