Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Question
Chapter 4.4, Problem 4.38P
(a)
To determine
The possible spins for baryons.
(b)
To determine
The possible spins for mesons.
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Identify the particles corresponding to the quark states (a) suu, (b) ūd, (c)s- d, and (d) ssd.
The range of the nuclear strong force is believed to be about 1.2 x 10-15 m. An early theory of nuclear physics proposed that the particle that “mediates” the strong force (similar to the photon mediating the electromagnetic force) is the pion. Assume that the pion moves at the speed of light in the nucleus, and calculate the time ∆t it takes to travel between nucleons. Assume that the distance between nucleons is also about 1.2 x 10-15 m. Use this time ∆t to calculate the energy ∆E for which energy conservation is violated during the time ∆t. This ∆E has been used to estimate the mass of the pion. What value do you determine for the mass? Compare this value with the measured value of 135 MeV/c2 for the neutral pion.
You have entered a graduate program in particle physics and are learning about the use of symmetry. You begin by repeating the analysis that led to the prediction of the Ω- particle. Nine of the spin- 3/2 baryons are four ∆ particles, each with mass 1232 MeV/c2 , strangeness 0, and charges +2e, +e, 0, and -e; three Σ* particles, each with mass 1385 Me/c2 , strangeness -1, and charges +e, 0, and -e; and two Ξ* particles, each with mass 1530 MeV/c2 , strangeness -2, and charges 0 and -e. (a) Place these particles on a plot of S versus Q. Deduce the Q and S values of the tenth spin- 3/2 baryon, the Ω- particle, and place it on your diagram. Also label the particles with their masses. The mass of the Ω- is 1672 MeV/c2 ; is this value consistent with your diagram? (b) Deduce the three-quark combinations (of u, d, and s) that make up each of these ten particles. Redraw the plot of S versus Q from part (a) with each particle labeled by its quark content. What regularities do you see?
Chapter 4 Solutions
Introduction To Quantum Mechanics
Ch. 4.1 - Prob. 4.1PCh. 4.1 - Prob. 4.3PCh. 4.1 - Prob. 4.4PCh. 4.1 - Prob. 4.5PCh. 4.1 - Prob. 4.6PCh. 4.1 - Prob. 4.7PCh. 4.1 - Prob. 4.8PCh. 4.1 - Prob. 4.9PCh. 4.1 - Prob. 4.10PCh. 4.1 - Prob. 4.11P
Ch. 4.2 - Prob. 4.12PCh. 4.2 - Prob. 4.13PCh. 4.2 - Prob. 4.14PCh. 4.2 - Prob. 4.15PCh. 4.2 - Prob. 4.16PCh. 4.2 - Prob. 4.17PCh. 4.2 - Prob. 4.18PCh. 4.2 - Prob. 4.19PCh. 4.2 - Prob. 4.20PCh. 4.3 - Prob. 4.21PCh. 4.3 - Prob. 4.22PCh. 4.3 - Prob. 4.23PCh. 4.3 - Prob. 4.24PCh. 4.3 - Prob. 4.25PCh. 4.3 - Prob. 4.26PCh. 4.3 - Prob. 4.27PCh. 4.4 - Prob. 4.28PCh. 4.4 - Prob. 4.29PCh. 4.4 - Prob. 4.30PCh. 4.4 - Prob. 4.31PCh. 4.4 - Prob. 4.32PCh. 4.4 - Prob. 4.33PCh. 4.4 - Prob. 4.34PCh. 4.4 - Prob. 4.35PCh. 4.4 - Prob. 4.36PCh. 4.4 - Prob. 4.37PCh. 4.4 - Prob. 4.38PCh. 4.4 - Prob. 4.39PCh. 4.4 - Prob. 4.40PCh. 4.4 - Prob. 4.41PCh. 4.5 - Prob. 4.42PCh. 4.5 - Prob. 4.43PCh. 4.5 - Prob. 4.44PCh. 4.5 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - Prob. 4.48PCh. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Prob. 4.52PCh. 4 - Prob. 4.53PCh. 4 - Prob. 4.54PCh. 4 - Prob. 4.55PCh. 4 - Prob. 4.56PCh. 4 - Prob. 4.57PCh. 4 - Prob. 4.58PCh. 4 - Prob. 4.59PCh. 4 - Prob. 4.61PCh. 4 - Prob. 4.62PCh. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Prob. 4.65PCh. 4 - Prob. 4.66PCh. 4 - Prob. 4.70PCh. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Prob. 4.75PCh. 4 - Prob. 4.76P
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- A particle, which is a composite state of three quarks u,d and s, has electric charge, spin and strangeness respectively, equal to 1 1 (a) 1, 2 (b) 0,0,–1 0, 2 (d) –1, +1arrow_forwardin 1975 it was estimated that the so-called constituent quark masses are: m_u = m_d = 336 MeV/c^2, m_s = 540 MeV/c^2, and m_c = 1500 MeV/c^2 (the bottom quark is about 4500 MeV/c^2). If this is right the average binding energy of the baryon octet is -62MeV. If they all had exactly this binding energy, what would their masses be? Compare the actual values and give the percent error. (Excluding supermultiplets)arrow_forwardThe reaction π+ + p → Δ++ (described in the preceding problem) takes place via the strong force. (a) What is the baryon number of the Δ++ particle?(b) Draw a Feynman diagram of the reaction showing theindividual quarks involved.arrow_forward
- The quark compositions of the proton and neutron are, respectively, uud and udd, where u is an up quark (charge + 2/3 e) and d is a down quark (charge - 1/3 e). There are also antiup u (charge - 2/3 e) and antidown d (charge + 1/3 e) quarks. The combination of a quark and an antiquark is called a meson. The mesons known as pions have the composition π+ = ud- and π- = u-d. Suppose a proton collides with an antineutron. During such collisions, the various quarks and antiquarks annihilate whenever possible. When the remaining quarks combine to form a single particle, it is aA. Proton B. Neutron C. π+ D. π-arrow_forwardthe baryon number p + p → 2y. Determine (b) the baryon number and (c) the electron-lepton number of the reaction N → A° + K¯. Determine of the reactionarrow_forwardWhat do the quark compositions and other quantum numbers imply about the relationships between the ∆+ and the proton? The ∆0 and the neutron?arrow_forward
- More than 60 years ago, future Nobel laureate Sheldon Glashow predicted that if an antineutrino — the antimatter answer to the nearly massless neutrino — collided with an electron, it could produce a cascade of other particles. The Glashow resonance phenomenon is hard to detect, in large part because the antineutrino needs about 1,000 times more energy than what's produced in the most powerful colliders on Earth. Let's compare this event to an ordinary baseball with a mass of 146 g. Please use three significant figures in your calculations. 1.What is the threshold antineutrino energy for the Glashow resonance in peta electronvolts (PeV)? 2.What is this threshold energy in units of joules? 3.Now consider a baseball with the same kinetic energy as that of the Glashow resonance. What speed in m/s would correspond to this energy? 4.What is this rate in units of inches/second? please help!!arrow_forward30 SSM www Using the up, down, and strange quarks only. construct, if possible, a baryon (a) with q = +1 and strangeness S = -2 and (b) with q = +2 and strangeness S = 0.arrow_forwardIn a classical model, a scalar (spin-0) meson consists of a quark and an antiquark bound by a potential V(r)= ar +- where a = 200 MeV fm and b = 100 MeV fm If the masses of the quark and antiquark are negligible, the mass of the meson can be estimated as approximately (a) 141 MeV/c? (b) 283 MeV/c? (c) 353 MeV/c² (d) 425 MeV/c²arrow_forward
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