Represetation of the Second Virial Coefficient by the Regge Pole

In previous work an attempt was made to represent the second virial coefficient by parameters of Regge poles. A consistent treatment of this problem is given here again. The main improvements are as follows: First, we start with a modified form of the Beth-Uhlenbeck formula, where the effect of the zero energy resonances is correctly treated. Second, the cut in the complex !-plane for the function ln S(l, k) is chosen so as to be consistent with require ment of analyticity and the Levinson theorem. Third, a formula for low-temperature gases is given in a simpler and more convenient form than the previous one. Thus we can attain to a satisfactory theory in which bound states and resonances including the zero energy ones are equally treated. Further, a method leading to the corrected Beth-Uhlenbeck formula is given in the Appendix and it shows also a general method, from which a cluster integral can be represented in terms of the J ost function, and so, which is useful in application to other problems.