Quantum-Statistical Distribution Functions of a Hard-Sphere System

The singlet and pair distribution functions of a hard-sphere fluid are evaluated. Diagrams in various orders in the hard-sphere diameter $a$ are analyzed. The pseudopotential and the binary-kernel methods are compared. At low temperatures the contribution from chain diagrams is evaluated explicitly in terms of the modified Bessel and Struve functions. These chain diagrams are important at large distances or at low energy. At short distances, first-order diagrams have to be examined, and classical and quantum-mechanical cases are treated.