Problem S9.3. The third virial coefficient can be written

where f(q)=(ev

(a) - 1) and V(q) is the interaction potential between particles with relative position, q. The Fourier transform of f(q) is f(k) =feaf (q). The inverse transform is f(q) = (1/2)3 Jeka f(k).

(a) Show that the third virial coefficient can be written B3 = (1/2) jdk f(k) f(k) F(-k).

(b) Compute f(k) for a gas of hard spheres with radius R.

(c) Use part

(b) to compute the third virial coefficient for a hard sphere gas.

B3 912 913 (912) f(913) (913 - 912) dq12