物理學 1935

論基本粒子的相互作用

湯川秀樹

核力之所以短程，是因為它的傳遞者有質量——一種新粒子，介子。

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把原子核攏在一起的那種力，強到足以壓住質子之間的相互排斥——可只要離開一根頭髮絲那麼遠，它就消失得無影無蹤。湯川用一個大膽的猜想同時解釋了這兩件事：這種力，是由一種全新的粒子來傳遞的，而那粒子，很重。

核心想法

到 1935 年，物理學家已經知道原子核裡擠滿了質子和中子，卻卡在一個悖論上。把它們黏在一起的力必定極其巨大——遠比那本該把原子核炸開的電斥力還強。可這種力，伸不出原子核本身半步；離開一丁點，它就乾脆沒有了。究竟什麼樣的力，近在咫尺時威猛無比、稍遠一步就蕩然無存？

湯川的回答，借用了電磁學裡的一幅圖景。在那裡，兩個電荷之所以能「感覺」到彼此，是因為它們在交換光子——光的粒子。他說，也許，兩個核子之所以能感覺到核力，也是因為它們在交換一種屬於它們自己的新粒子。妙處就在這裡：光子沒有質量，這正是電力與磁力能橫跨整個宇宙的原因。倘若這種新粒子有質量，那麼它所傳遞的力，就會在極短的距離之外迅速消亡。僅憑已知的原子核大小，湯川甚至能預言出這粒子的質量——約為電子的 200 倍。他只是從「一種力能伸多遠」出發，就憑空喚出了一個從未有人見過的粒子。

它是如何誕生的

湯川秀樹，是大阪一位年輕的理論物理學家，身處一個那時才剛剛開始被國際聽見的日本物理學界。歐洲的巨匠們——海森堡、費米——曾試圖讓粒子交換電子和微中子來解釋核的束縛，可算出來的數字實在太弱了。湯川為這道難題度過了許多不眠之夜，而他那驚人的一躍，是不再翻用已知的粒子、而是發明出那個正確的粒子。

他於 1935 年用英文、在一份日本刊物上發表了此文，此後好幾年幾乎無人留意。到 1936 年，宇宙射線中冒出了一種質量大致相符的粒子，人們一陣興奮——可當那粒子被發現幾乎不碰原子核、因而不可能是那團黏合劑時，興奮又變了味。真正的那個粒子——π 介子——直到 1947 年才被捕獲。兩年後，湯川獲得了諾貝爾獎，那是史上第一次有日本科學家獲此殊榮。

它為何重要

湯川改變了「力」這個詞本身的含義。在他之後，自然界中每一種基本力，都被理解為粒子的交換——而一條簡單的規則，把傳遞者的輕重與力的伸展聯繫了起來：傳遞者越重，力程越短。正是這一個洞見，整理了整部現代的「力」之目錄，從那讓光橫跨星系的無質量光子，到那躲在放射性背後的有質量粒子。他還證明了：一位審慎的理論家，僅憑一個悖論和一個波動方程，就能在任何儀器找到它之前，預言出宇宙的一塊新拼圖。

一個可以想像的畫面

想像湖上有兩條船，彼此把一個沉甸甸的藥球拋來拋去。每一次投擲，都把投的人往後一推、把接的人往前一送——這一來一回的交換，本身就像兩條船之間的一種力。再注意一點：因為球很重，你只能把它拋出很短一段，它就「撲通」落了水。兩條船必須靠得很近，這遊戲才玩得起來。換成一個輕飄飄的沙灘球，你就能把它一拋拋過整個湖面——那便是一種長程的力。湯川的核力，是那場重球遊戲；電磁力，則是那個沙灘球。所拋之物的輕重，定下了力能伸多遠。

它的位置

湯川站在一場漫長接力賽的中途。馬克士威把電磁作用鑄成了一個場；量子論又把那個場的量子定為光子；湯川則把這一步推廣到一種需要有質量量子的力上，由此開啟了「粒子交換」的時代。從他的想法，有一條直線通向弱力的 W 與 Z 粒子、通向夸克與膠子，也通向希格斯玻色子——而正是它的「湯川耦合」（這個以他命名的詞，從此固定下來），讓其他粒子獲得了質量。他當年追尋的那團核黏合劑，如今被看作更深層力的殘餘；但他所開創的那種思考方式，至今仍是整個粒子物理共用的語言。

The original document

Original source text

導言——核力的難題

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.

描述相互作用的場

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.

攜帶這個場的量子

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.

總結，與一個關於宇宙射線的猜測

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