Fourth Lecture: Mesons and the Nuclear Force

HC 209H: Discovery of Fundamental Particles and Interactions Fourth Lecture: Mesons and the Nuclear Force

Chris Potter

University of Oregon

HC 209H: Fourth Lecture – p.1/12 Fundamental Particles ca 1935

The following table supersedes the With quantum mechanics, a mathematical Periodic Table of the elements - all theory, the detailed chemical properties of ordinary matter is made of these. elements could be explained based on how electrons arranged themselves around Light Heavy Interaction nuclei. However, problems remained... e−,e+ p γ The electrostatic force of repulsion should ν n keep protons in the nucleus apart. What (stronger) force keeps them bound in the Positron e+ is new twist on ordinary matter. nucleus? Picture of complex atoms: What interaction accounts for nuclear beta decay, n → pe−ν? Is the neutrino a real particle or does it just save energy conservation? The proton p and neutron n are very heavy compared to the electron. Are they fundamental particles (in the sense of Democritus) or composite? The electron e− has an anti-matter version, the positron e+. What about the (Credit: Encyclopedia Brittanica) proton p and neutron n? HC 209H: Fourth Lecture – p.2/12 Complex Atoms

(Credit: Encyclopedia Brittanica)

The nucleus is very small, on the order of 1fm (10−15m), as determined by Rutherford. The atom, including the nucleus and the electrons arranging themselves around it, is much bigger, on the order of 1nm (10−9m)-a million times larger. Most of the mass of the atom is in the nucleus. The nucleus is very dense.

The ratio of the mass of the proton to the mass of the electron is mp/me ≈ 2000. What is keeping the protons and neutrons in the nucleus? Like charge protons repel, and neutral neutrons have no reason to stay in the nucleus. Answer: the nuclear (or strong) interaction.

HC 209H: Fourth Lecture – p.3/12 Yukawa’s Nucleus

Hideki Yukawa (1907-1981), a Japanese physicist, was the ﬁrst theorist to attempt to understand the nuclear interaction as an exchange of particles. The attempt was modeled explicitly on the successful theory of the electromagnetic theory (QED), which posited the photon as a messenger particle. Yukawa’s messenger particle was the pion π.

From the Uncertainty Principle, Yukawa estimated the 2 mass of the π to be mπ ≈ 100 MeV/c , so that me < mπ < mp, the π was a meson or middleweight. Hideki Yukawa (Credit: Wikipedia)

HC 209H: Fourth Lecture – p.4/12 Heisenberg’s Uncertainty Principle

∆ ∆ 1 ~ ∆ Heisenberg’s Uncertainty Principle, E t ≥ 2 , states that an amount of energy E can violate conservation of energy for a little while ∆t. If a virtual pion π mediates the nuclear force, it must live long enough to traverse the length of the nucleus, or about 1fm. Then if the pion π travels near the speed of light, it can travel a distance c∆t ≈1fm. So the energy available is at least

hc ∆E ≈ 4πc∆t 1240 nm eV ≈ 4π fm ≈ 100 MeV

2 2 This energy is stored in the mass of the pion, mπ = E/c ≈100 MeV/c . 2 2 Compare to the mass of the electron: me ≈ 0.5MeV/c and the proton: mp ≈938 MeV/c .

Since the pion mass is between the mass of the electron and proton, me < mπ < mp, it was called a meson, or middle-weight. Another version of the Uncertainty Principle, ∆p∆x ≥ ~/2, is explained here (stop at 7:45).

HC 209H: Fourth Lecture – p.5/12 Ionization Energy Loss

After traveling a short distance dx,a charged particle loses a small amount of energy dE due to ionization of surrounding atoms. p (protons) The rate of energy loss is dE/dx. ? dE/dx depends on the mass m and π± momentum p of the particle, but the µ± form of the curve is the same. The curves at right show how particles with different masses appear in a plot of ± dE/dx vs. momentum p. e (electrons) The positron from Carl Anderson’s cloud chamber had a momentum well below 1 GeV/c (measured by p = qBR), so the proton was ruled out. Another form of energy loss for charged particles is bremstrahlung, German for braking radiation... Credit: Particle Data Group

HC 209H: Fourth Lecture – p.6/12 Bremstrahlung Energy Loss

Bremstrahlung is emitted by charged particles accelerated by electric ﬁelds due to atoms.

Energy loss of electrons in matter vs. energy. For E > 10 MeV bremstrahlung loss dominates. (Credit: Particle Data Group) HC 209H: Fourth Lecture – p.7/12 Discovery of Mesons (1)

Carl Anderson and Seth Neddermeyer published in 1937, ﬁve years after the positron discovery.

HC 209H: Fourth Lecture – p.8/12 Discovery of Mesons (2)

There are two components of cosmic rays: Electrons, which “shower” and lose all of their energy in the plate due to bremstrahlung, and “Penetrating” particles, which do not. They are not protons, which lose all energy to ionization. HC 209H: Fourth Lecture – p.9/12 Mesons: Pion π and Muon µ, and π± → µ±ν

A Bristol, England group exposed photographic plates in the Bolivian Andes. They measured the density of emulsion grains N, proportional to the ionization loss dE/dx. They found two mesons, the pion π and the muon µ, and the pion decay π± → µ±ν. HC 209H: Fourth Lecture – p.10/12 Discovery of Antiprotons p¯ (1955)

Chamberlin, Segre, Wiegand amd Ypsilantis built the experiment: Bevatron protons with E = 6.5 GeV struck target protons in a copper target to produce the reaction p + p → p + p + p +p ¯ .

The challenge was to separate antiprotons p¯ from negatively charged pions π−. A magnet M1 selected for negatively charged particles with p = 1.16 GeV/c. Remember, p = qBR and positively charged particles circled to the left The momenta of pions and antiprotons was the same (p = 1.16 GeV/c), but their velocities were different: mπvπ = mp¯vp¯,

mπ 1 so vp¯ = vπ ≈ vπ . mp¯ 7

Scintillators S1 and S2, separated by distance ∆x gave electric signal when the particles passed by, measuring time ∆t. Then v =∆x/∆t. HC 209H: Fourth Lecture – p.11/12 Worksheet 4 Preparation

Particles known after the discovery of mesons (and their antiparticles, discovered later):

Leptons Mesons Baryons Interaction e−,e+ π+, π− p, p¯ γ ν, ν¯ µ+, µ− n, n¯ π

Heisenberg’s Uncertainty Principle (∆E∆t ≥ ~/2) for virtual interaction messenger particles: a shortrange force (c∆t small) has a messenger particle with m =∆E/c2 large. a longrange force (c∆t large) has a messenger particle with m =∆E/c2 small. Bremstrahlung Energy Loss Bremstrahlung radiation of a photon γ occurs when a charged particle enters an electric ﬁeld and experiences acceleration. For electrons (and positrons), bremstrahlung energy loss is larger than ionization energy loss for energy E ≈ 10 MeV or larger. Energy loss for a particle with mass m, when the acceleration is perpendicular to the velocity, is proportional to 1/m4, or ∆E ∝ 1/m4. To compare the bremstrahlung energy loss of two particles of the same charge, use 4 4 ∆E1/∆E2 = m2/m1.

HC 209H: Fourth Lecture – p.12/12