By Saul A. Teukolsky, Stuart L. Shapiro
This self-contained textbook brings jointly many various branches of physics--e.g. nuclear physics, sturdy nation physics, particle physics, hydrodynamics, relativity--to research compact gadgets. the newest astronomical info is classified. Over 250 workouts.
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Extra info for Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects
Example text
25 Calculate the nuclear surface energy in the Fernu gas model as follows: The number density in phase space, excluding spin effccts. dp h’ - for the number of states between p and p + dp. One can also obtain this expression by solving the free-particle Schriidinger equation inside a cubical box. In this solution, however, one should not count states for w h c h the components p , o r p , or p2 are zero, as these correspond to a vanishing wave function. Show that this refinement leads to the expression where S is the area of the box.
Nonrelativisticelectrons, po << lo6 g ~ m - x~<< , 1, + ( X I -+ x5/15r2, 2. Extremely relativisticelectrons, p >> lo6 g ~ m -x ~>>, 1, +(x) + x4/12n2, The above results may be scaled trivially with particle mass mi and statistical weight g, to determine the equation of state of an arbitrary species i of ideal fermions. For example, for pure neutrons, Eqs. 26) Cold Equation of State Below Neutron Drip 28 where the two limiting regimes are: 1. Nonrelativistic neutrons, po << 6 r = 5- K= 3’ 2. 3802 x 109cgs.
In the next section, we discuss improvements in the regime from lo7 g cm-3 to neutron drip. 2. 7 The Baym-Pethick-Sutherland Equation of State The HW equation of state has the advantag;e that M ( A , 2 ) is represented by a fairly simple function. However, real nuclei have discrete values of A and 2, and shell effects play an important role in determining the binding energy of a given nucleus. 4 x 10" g cm-3 (onset of neutron drip) taking these effects into account. Baym, Pethick, and Sutherland (1971b) (hxeafter BPS) improved on Salpeter's ' ~ also by noting that treatment by using a better semiempirical miiss f o r m ~ l aand the lattice energy, Eq.