Formula_21789

\[\begin{gathered}\beta_{1}=V^{-1} \int f_{12} d r_{1} d r_{2} ; \quad \beta_{2}=(1 / 2 ! V) \int f_{12} f_{23} f_{31} d r_{1} d r_{2} d r_{3} ; \\\beta_{3}=(1 / 3 ! V) \int\left(3 f_{12} f_{23} f_{34} f_{41}+6 f_{12} f_{23} f_{34} f_{41} f_{13}+\right. \\\left.+f_{12} f_{23} f_{34} f_{41} f_{13} f_{24}\right) d r_{1} d r_{2} d r_{3} d r_{4} ; \\f_{i j}=\exp \left(-U_{i j} / k T\right)-1 .\end{gathered}\]