Morse matrix elements: An asymptotic expansion treatment

Abstract

An asymptotic expansion method has been used to calculate the Morse matrix elements for the vibration-rotation transition. A general expression has been derived for the quartic matrix elements, which can be reduced to the expressions for the cubic, quadratic, and linear matrix elements. The results agree extremely well with those given by the factorization method outlined by Badawi et al., and are similar to those given by Coquant et al., who used quite complicated and lengthy equations based on the Dunham potential. Earlier works to calculate the electronic transition probability parameters utilizing the above mentioned asymptotic expansion technique have also been extended and modified.

Higher-order phase-space moments for off-diagonal rotating Morse oscillators

“…These moments are important for computing the intensity distribution in the rotation-vibration spectrum of diatomic molecules, as well as for the theoretical investigation of the dipole-moment function of diatomics. Our formula greatly simplifies the evaluation of the different moments, both diagonal (n n J J , 0 = ¢ = ¢ ¹ ) and off-diagonal (n n J J , 0 ¹ ¢ = ¢ ¹ ) matrix elements, as well as for values of J J ¹ ¢ and J J 0 = ¢ = (non-rotating effects), compared to other general expressions deduced by different methods and approaches [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”