Analytical and algebraic solutions of the rotating Morse oscillators: Matrix elements of arbitrary powers of (r-re)lexp[-ma(r-re)]

Abstract

Analytical expressions for the matrix elements 〈v’J‖(r-$r_e$ ${)}^l$exp[-ma(r-${\mathrm{r}}_{\mathrm{e}}$) ]‖vJ〉 of a rotating Morse oscillator are obtained, where l is a non-negative integer and m is any number. These matrix elements are also obtained by a recursive method that obviates the need for using explicit eigenfunctions. This procedure is based on the hypervirial theorem together with the second-quantization formalism. The results permit the diagonal (v=v’,J=J’) and off-diagonal (v≠v’,J=J’) matrix elements of the operator (r-$r_e$ ${)}^l$ to be calculated.