Periodic orbits of the hydrogen molecular ion

Based on our previous work [Yiwu Duan, J.M. Yuan, C.G. Bao, Phys. Rev. A 52 , 3497 (1995)], we study deeply the periodic orbits of the hydrogen molecul ar ion within the Born-Oppenheimer approximation (BOA). The Thiele-Burrau's transformation is introduced to regularize the singularities associated wi th the Coulomb potential terms and to transform the problem into a direct p roduct of a pendulum and an anharmonic oscillator. This facilitates the ana lysis of the bifurcation properties of the periodic orbits. Some more detai ls are also given about the calculation of the semiclassical density-of-sta te distribution using the Berry-Tabor formula.