Subatomic Physics

606 Nuclear and Particle Astrophysics
the Unknown: A Short History of the Universe, Cambridge, New Yrok, 2005. More
serious reviews can be found in Astronomy, Cosmology, and Fundamental Physics,
(M. Caffo et al., eds.) Kluiver, Dordrecht, 1989. A. D. Linde, Particle Physics and
Inflationary Cosmology, Harwood Academic, New York, 1989; F. Lizhi, Creation
of the Universe, World Scientific, Teaneck, NJ, 1989; S. G. Brush, Rev. Mod.
Phys. 62, 43 (1990); E.W. Kolb and M.S. Turner, The Early Universe, Addison-
Wesley, Reading, MA, 1990; The Scientific American Book of the Cosmos, (D.H.
Levy, ed.), St. Martin Press, New York, 2000; The Early Universe and the Cosmic
Microwave Background, (N.G.Sànchez and Y.N. Prijskij, eds.), Dordrecht, Boston,
2003; G. Börner, The Early Universe, Facts and Fiction, Springer, New York, 2003;
The Early Universe and Observational Cosmology, (N. Bretón , J.L. Cervantes-
Cota, and M. Salgado, eds.) Springer, New York, 2004; The Physics of the Early
Universe, (E. Papantonopoulos, ed.) Springer, New York, 2005; G. Veneziano, The
Myth of the Beginning of Time, Sci. Amer. 290, 54, (May 2004); G.D. Starkman
and D.J. Schwarz, Is the Universe Out of Tune?, Sci. Amer. 293, 48, (August
2005).
Problems
19.1. Show that the rate of a low energy reaction between two particles or nuclei
of charges Z1e and Z2e depends exponentially on Z1Z2e 2 /�v, wherev is the
relative velocity of the two objects.
19.2. Discuss some of the difficulties of measuring cross sections relevant to nucleosynthesis
and explain how some of them may be overcome.
19.3. Assume that the density distribution in the Sun (or a star) is given by ρ =
ρc[1 − (r/R) 2 ], where ρc is the central density and R is the radius of the Sun.
(a) Evaluate the variation of the mass with radius by finding dM(r)/dr and
M(r).
(b) Evaluate ρc in terms of the total mass M and radius R of the Sun.
19.4. List some reactions that can be used to test the solar energy cycle and explain
the reason for your choices.
19.5. The total mass of a neutron star is limited by general relativity to be less
than three solar masses or � 6 × 10 33 g. [M. Nauenberg and G. Chapline,
Astrophys. J., 179, 277 (1973)]. Check whether the neutron star illustrated
in Fig. 19.7 satisfies this criterion.
19.6. A star contains ni particles/volume of type i which, at a temperature T ,have
an average velocity vij relative to particles of type j.