University:
Massachusetts Institute of Technology
Course:
8.701 | Introduction to Nuclear and Particle Physics
Academic year:

2020
Views:

390

Pages:

3
Author:

Ronald Montoya

Massachusetts Institute of Technology Department of Physics Discussion Problems from recitation on September 17th, 2020 Problem 1: Gell-Mann Nishijima equation Check that the Gell-Mann Nishijima formula works for the quarks u, d, and s. ¯ and s̄? Check you answer What are the appropriate isospin assignments for ū, d, with the Gell-Mann Nishijima formula. • Reminder: the Gell-Mann Nishijima formula goes as follows Q = I3 + 12 (A + S) 1 Figure 1: Answer. 2 Problem 2: The alpha particle The α particle is a bound state of two protons and two neutrons, that is, a 4 He nucleus. There is no isotope of hydrogen with an atomic weight of four (4 H), nor of lithium 4 Li. What do you conclude about the isospin of an α particle? The reaction d + d → απ 0 has never been observed. Explain why. Would you expect 4 Be to exist? How about a bound state of four neutrinos? • Isospin must be zero. The deuterons carry I = 0, so the isospin on the left is zero. The α has I = 0, and π has I = 1, so the isospin on the right is one. This process does not conserve isospin, and hence is not a possible strong interaction. There are ﬁve possible 4-nucleon states: (nnnn), (nnnp) =4 H, (nnpp) =4 He, (nppp) =4 Li, (pppp) =4 Be. In principle they could form an I = 2 multiplet, but since 4 H and 4 Li do not exist, this is out. The answer is no: 4 Be and (nnnn) should not exist. (4 H, 4 He, and 4 Li could make an I = 1 multiplet, but, again, 4 H and 4 Li do not exist, so this too is out. Evidently four nucleons bind only in the I = 0 combination, making 4 He.) 3

8.701 Introduction to Nuclear and Particle Physics, Recitation 5 Solutions

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