Matrix elements for rotating Morse oscillators.

Abstract

In this paper formulas and recursion relations for the expectation values of the operators {1-exp[-a(r-${r}_{e}$${)]\mathrm{}}}^{n}$, (r-${r}_{e}$${)}^{n}$, exp[-a(r-${r}_{e}$${)]}^{n}$, and (r-${r}_{e}$){exp[-a(r-${r}_{e}$${)]\mathrm{}}}^{n}$ are derived for a rotating Morse oscillator. These equations can be used to calculate the diagonal (v=v', J=J') and off-diagonal (v\ensuremath{\ne}v', J\ensuremath{\ne}J') matrix elements. Asymptotic approximations for the diagonal elements of the (r-${r}_{e}$${)}^{n}$ operator, 〈vJ\ensuremath{\Vert}(r-${r}_{e}$)\ensuremath{\Vert}vJ〉 and 〈vJ\ensuremath{\Vert}(r-${r}_{e}$${)}^{2}$\ensuremath{\Vert}vJ〉, are also obtained.