A Refined Numerical Result on the First Excitation Energy in the Two-Level Pairing Model

The first excitation energy in the two-level pairing model is investigated in terms of the equilibrium and the small fluctuation around it. The basic idea is an extension of results presented in a previous paper by the present authors. In this investigation, the result obtained in the previous paper plays a central role: At the limit of the weak and the strong interaction strength, the results are in good agreement with the exact one. The former and the latter are calculated in the framework of the $su(2)\otimes su(1,1)$- and the $su(2)\otimes su(2)$-coherent state, respectively. On the basis of the above conclusion, the intermediate region for the interaction strength is described in terms of the idea of the interpolation and it is shown that the agreement of the result with the exact one is quite good.