Subatomic Physics

218 Additive Conservation Laws
spatial resolution of neutron counters to obtain an estimate on the limit that
could be obtained.
7.5. Assume that nucleons decay with a lifetime of 10 15 y and that all the energy
of the nucleons decaying in the earth is transformed into heat. Compute the
heat flow at the surface of the earth. Compare the energy produced with the
energy that the earth receives from the sun during the same time.
7.6. ∗ Sketch an experimental arrangement for measuring the lifetime of protons
and explain its basic functioning. [See e.g., C. McGrew et al., Phys. Rev. D
59, 052004 (1999) or K. Kobayashi et al., Phys. Rev. D 72, 052007 (2005).]
7.7. The cross section for the absorption of antineutrinos with energies as emitted
by nuclear reactors is about 10 −43 cm 2 .
(a) Compute the thickness of a water absorber needed to reduce the intensity
of an antineutrino beam by a factor of 2.
(b) Consider a liquid scintillator with a volume of 10 3 liters and an antineutrino
beam with an intensity of 10 13 ν/cm 2 sec. How many capture
events [Eq. (7.34)] are expected per day?
(c) How can the antineutrino capture be distinguished from other reactions?
7.8. ∗ How can the reaction of Eq. (7.37) be observed? [See e.g., R. Davis, Jr.
Rev. Mod. Phys. 75, 985(2003).]
7.9. Suppose we assign an additive quantum number to a pion: +1 for π + ,0forπ 0 ,
and −1 forπ − . What are the simplest reactions which allow the production
of pions by photons on protons? What are they for π − on protons? For π +
on protons?
7.10. Can the following reactions occur? If so, do they proceed via strong, electromagnetic,
or weak interactions? Give reasons.
(a) Σ + p → ppπ 0
(b) pp → λ 0 Σ 0
(c) np → Σ − Σ 0
(d) pp → Ξ − p
(e) ep → Σ − pnπ 0 ν
7.11. Can strange particles be produced singly by reactions that involve only nonstrange
particles? If yes, giveapossiblereaction.