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Physics Lesson 21.1.4 - Physics of Elementary Particles. The Yukawa Theory
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Welcome to our Physics lesson on Physics of Elementary Particles. The Yukawa Theory, this is the fourth lesson of our suite of physics lessons covering the topic of Elementary Particles, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Physics of Elementary Particles. The Yukawa Theory
As we know, atomic nuclei are made of protons and neutrons. Thus, the hydrogen nucleus contains a proton only, the helium nucleus one proton and one neutron and so on. In previous articles we explained why the structure of nucleus is so stable giving the repelling force existing between like charges (protons). We explained that a new force (we called it "nuclear force" but henceforth we will call it the "strong force" - this is the scientific name of nuclear force as one of the four fundamental forces acting in nature - will appear in order to balance the effect of electric force between protons. This force however is evident only in very small distances (1 - 2 × 10-15 m). It decreases drastically with the increase in distance between particles. This is why the action of strong (or nuclear) force is not observed in macroscopic events.
In classical Physics we have the interaction between charged point objects relying on the concept Coulomb's force. In quantum physics however, this interaction is explain through the exchange (emission or absorption) of photons. When two electrons repel each other, one of them emits a photon and the other electron absorbs it. The following figure shows schematically how this event takes place.
From the above figure, it is evident that in this process electrons change their direction as well. Since there is a time interval during which the collision process occurs, it is clear that the collision of electrons at the point A occurs prior to their separation at the point B. In other words, the collision brings a emission of photon by one of electrons at the point A which is absorbed by the other electron at the point B.
In this way, we can say that the interaction of charged particles takes place through the mediation of photons. The question that arises here is: "Where does the energy needed for the generation of photons come from?" The Heisenberg Uncertainty Principle helps in explaining this point. According to this principle, a short-term state has an uncertainty of energy ΔE given by the relation
where Δt is the time interval during which the process occurs. Based on this principle, the generation of photons having the energy ΔE is possible with the condition that the generation time not exceeds the time interval Δt provided in the Heisenberg formula. Such a photon having a lifespan as much as allowed by Heisenberg uncertainty principle is known as "virtual photon." In analogy with the financial system, we can say that the uncertainty principle relation acts like a "bank" in which we can borrow energy and settle it within a given time. Based on the above relation, it is evident that the more energy is borrowed, the soonest it must be settled.
Now, let's discuss a little more about the carriers of strong interaction, which result in the generation of nuclear force. In 1935, the Japanese scientist Hideki Yukawa introduced the idea that the strong interaction between nucleons is made possible through the exchange of certain particles of mass 200-300 times the mass of electron. The reasoning used by Yukawa to draw this conclusion was more or less as follows:
The distance in which nuclear forces can act, depends on the mass of particle that produces the interaction. The lifespan of this particle must be long enough to allow it move within the range of nuclear forces action. On the other hand, nuclear forces act in distances that are smaller than the nucleus dimensions. Based on this fact (and other information obtained during the experiments) it resulted that the action range of nuclear forces is about r0 = 1.5 × 10-15 m (it is a kind of diameter, not radius). Assuming the speed of the unknown particles comparable to the speed of light (as they are a kind of energy), the lifespan Δt of such particles must be
= 1.5 × 10-15 m/3 × 108 m/s
= 5 × 10-24 s
Thus, based on the uncertainty principle relation
we obtain for the minimum uncertainty of energy ΔE during this process:
= 6.626 × 10-34 J ∙ s/2 ∙ 3.14 ∙ 5 × 10-24 s
= 2.11 × 10-11 J
The equivalent mass of this energy is
= 2.11 × 10-11 J/(3 × 108 m/s)2
= 2.34 × 10-28 kg
This value is about 250 times greater than the mass of electron (9.1 × 10-31 kg). Yukawa proposed the idea of the existence of this particle as a mediator in explaining the operating principle of nuclear forces. This idea was very revolutionary for the time, when no experiment could not confirm yet the existence of this particle.
A few years later (in 1945), after processing the experimental data obtained from the cosmic rays, scientist were able to identify a particle of mass 207 times the mass of electron. Since this value of mass is between the mass of nucleons and electrons (nucleons are more than 1800 times heavier than electrons), the new particle discovered was named "μ-meson" ("meson" means medium value in Greek language) or "muon". It was initially identified with the particle predicted by Yukawa but later on, scientists realized that such particles almost do not interact with atomic nuclei. That means they cannot be the carriers of nuclear interaction. The true carriers of strong interaction were discovered in 1947 by Cecil Frank Powell - an English scientist. These particles were the π-mesons (pi mesons) or simply "pions" predicted by Yukawa.
After accurate measurements, the results show that three types of pions exist, these are π +, π - and π 0 and these have electric charges of +e, -e and 0 respectively. As for their masses, we have:
All nucleons pass some part of their lifespan by experiencing one of the four transformations shown below:
p ⇄ p + π0
n ⇄ p + π-
n ⇄ n + π0
Hence, every nucleon is surrounded by a cloud of π-mesons which form the field of its nuclear force. The exchange of π-mesons between nucleons results in the strong nuclear interaction. For example, one of such interactions can be expressed as
You have reached the end of Physics lesson 21.1.4 Physics of Elementary Particles. The Yukawa Theory. There are 4 lessons in this physics tutorial covering Elementary Particles, you can access all the lessons from this tutorial below.
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